From rrosebru@mta.ca Sat Apr 1 19:19:08 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 01 Apr 2006 19:19:08 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FPpHu-0001gl-NX for categories-list@mta.ca; Sat, 01 Apr 2006 19:13:46 -0400 Date: Sat, 1 Apr 2006 08:01:53 -0500 (EST) From: Michael Barr To: categories Subject: categories: re: fundamental theorem of algebra MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 1 Let me reiterate this: There can in principle be no purely algebraic proof of the FToA because the reals have no purely algebraic definition. (Unless you define them as a real closed field of transcendence degree c, but that leaves the FToA as a trivial consequence and cannot be what is wanted.) The proof I outlined, which someone showed me 45 years ago, uses only the fact that R is a complete ordered field. Given that that is the analytic definition of R, it is impossible to avoid. That fact is, of course, at the heart of the fact that the circle is not contractible in a punctured plane. Incidentally, even constructivists (well even Errett Bishop, anyway) agree that odd order real polynomials have a real root and that positive numbers have square roots, since there are obvious constructions for these things. Their real line is not complete (it is countable, but the missing numbers are not constructible), but these roots are there anyway. The argument I outlined is elementary, even if not especially easy. First you have to construct the reals, the least elementary part of the argument. Then comes the theorem on symmetric functions. It is not a deep result; it needs a careful proof, but a student can follow it without knowing anything sophisticated. The construction of a splitting field (without getting into UFDs) is a bit tricky. To adjoin a root to an irreducible polynomial p of degree n, you start with a vector space whose basis is called 1, u, u^2,..., u^{n-1} and define a multiplication, by having p(u) = 0. This is analogous to how you get from R to C. Of course, you use the division algorithm to show you get a field. Michael From rrosebru@mta.ca Sat Apr 1 19:19:08 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 01 Apr 2006 19:19:08 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FPpKb-0001oA-L9 for categories-list@mta.ca; Sat, 01 Apr 2006 19:16:33 -0400 Date: Sat, 01 Apr 2006 09:59:36 -0500 From: jim stasheff User-Agent: Thunderbird 1.5 (Windows/20051201) MIME-Version: 1.0 To: categories Subject: categories: Re: fundamental theorem of algebra Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 2 Yet the one that is hard to see is easy to prove, while the one that is easy to see is hard to prove. Ain't that the truth or as Rene Thom once remarked about one of his assertions Very easy to see, very had to prove jim Vaughan Pratt wrote: [...] > > These questions are probably more appropriate for a philosophy of > mathematics list than this one. What makes FTAlg such an interesting > case study for those with something at stake in such questions is that > the tensions here are so extreme. The final result (FTAlg) is not at > all obvious, whereas the lemma it rests on, whether it be that |P(z)| > attains its minimum, or that circles around a hole don't retract, or the > intermediate value theorem, or the existence of a root for a real > polynomial of odd degree, seems self-evident. Yet the one that is hard > to see is easy to prove, while the one that is easy to see is hard to > prove. > > If seeing is believing, what is proof? In the real world, when > something is easy to see it is up to the opposition to demonstrate that > it is nonetheless false. How did mathematics evolve to play by a > different rule book? > > Vaughan Pratt > From rrosebru@mta.ca Sat Apr 1 19:19:08 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 01 Apr 2006 19:19:08 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FPpFN-0001cM-Q4 for categories-list@mta.ca; Sat, 01 Apr 2006 19:11:09 -0400 Date: Sat, 1 Apr 2006 10:44:05 +0100 (BST) From: "Prof. Peter Johnstone" To: categories Subject: categories: Re: fundamental theorem of algebra MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 3 On Thu, 30 Mar 2006, Vaughan Pratt wrote: > Regarding 3, the authors of the Britannica article seemed not to think > so, but perhaps this just reflects Garrett Birkhoff's attitude that "I > don't consider this algebra, but this doesn't mean that algebraists > can't use it" cited by Michael Artin when proving FTAlg in his 1991 book > "Algebra". Who on this list considers the fundamental theorem of > algebra "not algebra"? > The theorem is algebra, but its proof isn't: any proof has to involve some topological input (though that can be reduced to the Intermediate Value Theorem). Vaughan seems to have a problem with the phrase "elementary algebraic proof": of course, not all elementary proofs are algebraic (and not all algebraic proofs are elementary), and it is the word "algebraic" that matters here. Incidentally, I used that Birkhoff quote in the Introduction to "Stone Spaces" (1982). Did Mike Artin get it from me, or did he discover it independently? Even more incidentally, the first published proof of the Fundamental Theorem is not by Gauss. It appears in the only mathematical paper (in Phil. Trans. Roy. Soc. volume 88, 1798) of the Reverend James Wood, who was then a Fellow (and subsequently Master) of St John's College, Cambridge. (His other publications were all theological -- he was a Doctor of Divinity.) Wood's argument is essentially the same as Gauss's second proof (1816); by modern standards, what he writes in the paper doesn't constitute a rigorous proof, but (to quote the late Frank Smithies) "anyone reading Wood's paper must end up with the conviction that there is a proof somewhere there". Peter Johnstone From rrosebru@mta.ca Sat Apr 1 19:20:15 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 01 Apr 2006 19:20:15 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FPpMw-0001tF-1j for categories-list@mta.ca; Sat, 01 Apr 2006 19:18:58 -0400 Date: Sat, 01 Apr 2006 10:01:48 -0500 From: jim stasheff User-Agent: Thunderbird 1.5 (Windows/20051201) MIME-Version: 1.0 To: categories@mta.ca Subject: categories: re: WHY ...CONCERNED? III Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 4 Who is so preoccupied? Folks I know usually use category theory without worrying about size jim F W Lawvere wrote: > WHY ARE WE CONCERNED? III > > The second main misconception about category theory > > Part of the perception that category theory is "foundations" (in the > pejorative sense of being remote from applications and development) is due > to a preoccupation with huge size. Since such perceptions hold back the > learning of category theory, and hence facilitate its misuse as a > mystifying shield, they are among our concerns. We need to deal with the > size preoccupation head on. > [...quotation omitted by moderator...] From rrosebru@mta.ca Sat Apr 1 19:23:49 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 01 Apr 2006 19:23:49 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FPpQ6-00023n-WE for categories-list@mta.ca; Sat, 01 Apr 2006 19:22:15 -0400 Date: Sat, 01 Apr 2006 10:11:33 -0500 From: jim stasheff User-Agent: Thunderbird 1.5 (Windows/20051201) MIME-Version: 1.0 To: categories@mta.ca Subject: categories: Re: cracks and pots and Mac Lane Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 5 Eduardo quotes Mac Lane as saying (paraphrased) If it hasn't been proved, it isn't mathematics Much as I admire Mac Lane and owe much to him, that's rather at odds with what most of us do even those who insist on getting a proof ultimately. case in point: http://www.oxfordtoday.ox.ac.uk/2005-06/v18n2/04.shtml if that isn't math, what is it? (perjorative adjective of your choice) mathematics? Was Newton doing *only* physics? jim From rrosebru@mta.ca Sun Apr 2 20:44:38 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 02 Apr 2006 20:44:38 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FQC9k-0003YY-7Q for categories-list@mta.ca; Sun, 02 Apr 2006 20:38:52 -0300 Date: Sat, 01 Apr 2006 16:59:43 -0800 From: Vaughan Pratt MIME-Version: 1.0 To: categories Subject: categories: Re: fundamental theorem of algebra Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 6 Even in my original posting starting this thread I acknowledged that contractibility of the circle was not elementary: > Except, that is, for the theorem that a loop wound d times around the > hole in the punctured plane cannot be continuously retracted to a point, > which was tacitly smuggled in there. But that statement is less > intimidating than anything based on holomorphic functions. I haven't at any time claimed that it was not necessary to prove this, nor that the proof was easy. What I have been claiming is that the result has a certain self-evident quality to it that, it seemed to me, qualified the argument as at least sufficiently "morally elementary" as to qualify it for inclusion in the Britannic article on algebra. How could the definitive encyclopedia article on algebra not give at least a hint as to why that subject's fundamental theorem was true? However I've been reflecting on just what is behind the very uniform insistence on the distinction between an algebraic proof and an analytic one. Since algebra is descended from analysis, it seems unkind for algebra to deny its parentage in this way. But I see now that this denial is logically necessary. For consider the algebraic plane, the least algebraically closed subfield of the complex plane, consisting of the algebraic numbers. The FTAlg is by definition true there, so it ought to be provable there. One can carry out the same proof, and it all goes through in the same way (using circles of growing algebraic radius, all of which are dense in their complex completion to a connected circle) right up to the last step when we claim that the wildly growing loop that is the image of the tamely growing circle must eventually collide with the origin, d times in fact for a degree d polynomial. And indeed it does, all d times, exactly as with the complex numbers, and with the same roots (the coefficients of the polynomial necessarily being algebraic in this domain). But now analysis has nothing to do with it, since these circles and their image loops while dense are totally disconnected. For all we know the origin could have missed the loop by going through any of its uncountably many gaps. Indeed the loop has measure zero, so the chances of the origin colliding with it even once are less than Buckley's. But with aim that would be the envy of any sniper the origin hit the loop with every one of its d shots. And how do we know this? Using analysis. The consensus would seem to be that there is no other way. Logic alone cannot help. If that's the case, then without analysis there is no algebraic plane. Without the huge continuum to support it, that tiny countable set would not exist! It is ironic that a theorem of algebra about an algebraic domain that itself has no element of analysis to it, being just the algebraic closure of the rationals, a small and totally disconnected space, should require analysis, the parent of algebra, for its proof. The fundamental theorem of algebra is like a student calling home for more money. It takes a continuum to raise an algebraic number. Vaughan Pratt From rrosebru@mta.ca Sun Apr 2 20:44:38 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 02 Apr 2006 20:44:38 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FQC5Z-0003LS-If for categories-list@mta.ca; Sun, 02 Apr 2006 20:34:33 -0300 Date: Sat, 01 Apr 2006 18:40:28 -0500 From: wlawvere@buffalo.edu To: categories@mta.ca Subject: categories: Re: WHY ...CONCERNED? III MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii; format=flowed Content-Transfer-Encoding: 7bit Content-Disposition: inline Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 7 Jim, Perhaps complacency is another form of preoccupation. Very often topologists or geometers who want a functor category say things like "this may not exist". Of course that is slightly better than use of quotients or limits in analysis without asking whether they exist, but in the 21st century such waffling is unbecoming to mathematics, especially when, as I suggest, it can be replaced by crisp algebra. Bill --On Saturday, April 1, 2006 10:01 AM -0500 jim stasheff wrote: > Who is so preoccupied? > Folks I know usually use category theory without worring about size > jim > > F W Lawvere wrote: >> WHY ARE WE CONCERNED? III >> >> The second main misconception about category theory >> >> Part of the perception that category theory is "foundations" (in the >> pejorative sense of being remote from applications and development) is >> due to a preoccupation with huge size. Since such perceptions hold back >> the learning of category theory, and hence facilitate its misuse as a >> mystifying shield, they are among our concerns. We need to deal with the >> size preoccupation head on. [balance of quotation omitted...] From rrosebru@mta.ca Sun Apr 2 20:44:38 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 02 Apr 2006 20:44:38 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FQCBM-0003fX-SM for categories-list@mta.ca; Sun, 02 Apr 2006 20:40:32 -0300 From: Colin McLarty To: categories@mta.ca Date: Sat, 01 Apr 2006 20:42:32 -0500 MIME-Version: 1.0 Content-Language: en Subject: categories: Re: cracks and pots and Mac Lane X-Accept-Language: en Content-Type: text/plain; charset=us-ascii Content-Disposition: inline Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 8 I am not sure I understand this. Jim, do you mean to say that these people are using some mathematical statments that are not proved? The article seems to me to say the opposite: They are using numerical calculations, which I suppose can be routinely verified as such, but with novel applications in biology. Colin ----- Original Message ----- From: jim stasheff > Eduardo quotes Mac Lane as saying > (paraphrased) If it hasn't been proved, it isn't mathematics > > Much as I admire Mac Lane and owe much to him, > that's rather at odds with what most of us do > even those who insist on getting a proof ultimately. > > case in point: > > http://www.oxfordtoday.ox.ac.uk/2005-06/v18n2/04.shtml From rrosebru@mta.ca Sun Apr 2 20:44:38 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 02 Apr 2006 20:44:38 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FQCCW-0003kV-Tp for categories-list@mta.ca; Sun, 02 Apr 2006 20:41:44 -0300 From: "Mamuka Jibladze" To: Subject: categories: Re: cracks and pots and Mac Lane Date: Sun, 2 Apr 2006 12:36:16 +0500 MIME-Version: 1.0 Content-Type: text/plain;format=flowed; charset="iso-8859-1";reply-type=response Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 9 > Eduardo quotes Mac Lane as saying > (paraphrased) If it hasn't been proved, it isn't mathematics > > Much as I admire Mac Lane and owe much to him, > that's rather at odds with what most of us do > even those who insist on getting a proof ultimately. > > case in point: > > http://www.oxfordtoday.ox.ac.uk/2005-06/v18n2/04.shtml > > if that isn't math, what is it? > (perjorative adjective of your choice) mathematics? > > Was Newton doing *only* physics? > > jim In fact standards of proof and rigor have undergone quite some transformation in time, so why could they not change drastically in future? Again lacking proper knowledge I want to ask those who know more history to confirm or reject something I've been told. Namely, seemingly in times of Euler and Bernoullis, to be able to prove one's statements was just a matter of honour, but nobody was obliged to accompany announcement of a theorem with a proof - you could keep the latter to yourself and should only present it if somebody would challenge you by expressing doubt; which probably did not happen that often. So how do we know that what we consider a rigorous proof today will not be viewed as something insufficient or even irrelevant in a couple of centuries? For example, if mathematics would develop my way, I would give a fact the status of being established only after seeing its validity does not require any serious effort or expertise from an average mathematician (maybe even a student). This would not necessarily mean waiting much more time - in case mathematicians would continue to learn *seeing* more and more. I mean, if you have to explain to a person in the street how to reach some place, the amount and kind of explanation you need depends critically on whether the person is blind or not. Mamuka From rrosebru@mta.ca Sun Apr 2 20:44:55 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 02 Apr 2006 20:44:55 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FQCEw-0003so-R8 for categories-list@mta.ca; Sun, 02 Apr 2006 20:44:14 -0300 Date: Sun, 02 Apr 2006 14:43:09 -0400 From: "Fred E.J. Linton" MIME-Version: 1.0 To: categories Subject: categories: Re: fundamental theorem of algebra Content-Type: text/plain; charset=us-ascii; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 10 For the bookworms among the readers of this FToA thread, let me offer four older references to undergraduate-accessible expositions of proofs along the lines already mentioned: First, in Birkhoff & Mac Lane (my own undergraduate algebra text), Section 3 of Chapter V of the 1953 ("revised") edition offers a proof along winding number lines on pp. 107-109. Next, in the 1975 MIR English edition of Kurosh's Higher Algebra (described as the "second printing"), section 23 of Chapter 5 offers a proof relying on the D'Alembert Lemma (on pp. 142-151). In the same Kurosh volume, moreover, section 55 of Chapter 11 offers a proof along symmetric function lines on pp. 337-340. Finally, one may find the Artinian proof in the real-closed fields section of van der Waerden's pre-WWII classic, Modern[e] Algebra. I refrain from citing other textbooks, and I remark that numberings (of pages, sections, chapters) may differ in other editions. Cheers, -- Fred Prof. Peter Johnstone wrote: > On Thu, 30 Mar 2006, Vaughan Pratt wrote: > > >>Regarding 3, the authors of the Britannica article seemed not to think >>so, but perhaps this just reflects Garrett Birkhoff's attitude that "I >>don't consider this algebra, but this doesn't mean that algebraists >>can't use it" cited by Michael Artin when proving FTAlg in his 1991 book >>"Algebra". Who on this list considers the fundamental theorem of >>algebra "not algebra"? >> > > The theorem is algebra, but its proof isn't: any proof has to involve > some topological input (though that can be reduced to the Intermediate > Value Theorem). Vaughan seems to have a problem with the phrase > "elementary algebraic proof": of course, not all elementary proofs > are algebraic (and not all algebraic proofs are elementary), and it is > the word "algebraic" that matters here. > > Incidentally, I used that Birkhoff quote in the Introduction to > "Stone Spaces" (1982). Did Mike Artin get it from me, or did he > discover it independently? > > Even more incidentally, the first published proof of the Fundamental > Theorem is not by Gauss. It appears in the only mathematical paper > (in Phil. Trans. Roy. Soc. volume 88, 1798) of the Reverend James > Wood, who was then a Fellow (and subsequently Master) of St John's > College, Cambridge. (His other publications were all theological > -- he was a Doctor of Divinity.) Wood's argument is essentially the > same as Gauss's second proof (1816); by modern standards, what he > writes in the paper doesn't constitute a rigorous proof, but (to > quote the late Frank Smithies) "anyone reading Wood's paper must > end up with the conviction that there is a proof somewhere there". > > Peter Johnstone > > > From rrosebru@mta.ca Sun Apr 2 20:49:22 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 02 Apr 2006 20:49:22 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FQCJ3-0004Aw-5B for categories-list@mta.ca; Sun, 02 Apr 2006 20:48:29 -0300 From: "Marta Bunge" To: categories@mta.ca Subject: categories: RE: cracks and pots 93 Date: Sun, 02 Apr 2006 10:03:51 -0400 Mime-Version: 1.0 Content-Type: text/plain; format=flowed Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 11 Dear Eduardo, I promised to comment on your posting partly since you praise me in having started this discussion but also since you touch on something very relevant to the questions that I have been asking. > >In recent years J.Baez and his followers have been occupying more and more >space in the categorical community (this fact is at the starting point of >the present debate). You refer to the list of meetings where John Baez has played a prominent role as speaker in recent years -- and I forgot to mention Coimbra 1999 (School on Category Theory and Applications). I do not recall of anybody, with the exception perhaps also of Steve Awodey, to have been given so much attention in recent years. I was perhaps misled by "theological considerations", namely the Templeton Foundation and its efforts in trying to mix up science and religion. This is unfortunately true enough, but it has nothing to do with our present discussion. This is the conclusion that I have reached, and it is my obligation to say so publicly. You offer some interesting explanation for the state of affairs in category theory meetings. > >I think this is so because they have some interesting category theory to >show, but they are occupying more space than their mathematics deserves >because they bring a refreshing air to a community until now dominated by >an old guard that has not shown signs of necessary evolution, and that has >not being able to attract very good and talented young mathematicians to >the community. There is now not other exiting body of developments within >the community. The old guard is being pushed out (prone or supine ?), but, >alas, not by better mathematicians. A general comment is that, whereas some of it may be true, there is much that should be justified, or questioned. For instance, that "they have sone interesting category theory to show", that "they bring a refreshing air", that ours is "a community until now dominated by an old guard that has shown no signs of necessary evolution", that our community "has not been able to attract very good and talented mathematicians", at present there is "no other exiting body of developments within the community". Would you care to be more explicit? At the request of others, and to the risk of attracting a lot of criticism, I have done so and have been grossly misunderstood. If I did not request it, others will do so. That way, it would be easier to respond to the above. Let us assume for the moment that the is a rift in our category theory community -- the "old guard" versus the "new guard". We could even put names to represent each one -- it may seem obvious to many that, whereas Marta Bunge "must have been influenced by Bill Lawvere (and others)", Eduardo Dubuc "must be influenced by Andre Joyal (and others)". I am still speculating. This imaginary discussion I want to refute, and I am sure that you would want to do the same, or maybe not. But, is there such a rift and, if so, why take one side against the other? I believe that *all* progressive forces within category theory (no matter where they come from) should join efforts rather than split over issues that very few people understand or care about. I am a great admirer of both Bill Lawvere and Andre Joyal (and of many others, eg Peter Freyd, Ross Street, Ieke Moerdijk, to name a few -- of course, beginning with Grothendieck) because, even if they may have different philosophies of mathematics (in particular of category theory), they all bring in novel ideas derived from great experience and insight. >The old guard is being pushed out (prone or supine ?), but, >alas, not by better mathematicians. This too, is cryptic, and too sweep a generalization. I believe that there is poor mathematics no matter which area of category theory, but there is also good mathematics both sides of the imaginary (?) rift. Instead of making divisions of the sort "the young against the old", which can be used to justify almost anything, let us make no divisions and try to preserve excellence and promise in whatever is being done, whether applied or not, whether fashionable or not, and filter out (as editors of journals, organizers of conferences) the sort of mathematics that is sure to discredit us. Who will then be the judges? Obviously good mathematicians, not biased, completely accountable for their choices, not short-sighted, independent, very well informed, anxious to preserve high standards. Is there anybody left after so many requirements? Well, Peter Johnstone is one such person, but there are several others, of course and it is not for me to make such a list. Once identified by general consensus (here is the hard part!), let them consistently make all the decisions (for a certain period of time, at least). That way, it will be unlikely that the same people be invited over and over again, and also unlikely that bad papers will be accepted to be presented at meetings or published in our journals. Sammy Eilenberg and Saunders MacLane may have represented different tendencies within category theory, and most of us feel having been influenced by one rather than by the other (some by both). Yet, there was never any open rift between them, which was wonderful. I decided to work on category theory after a brilliant lecture by Eilenberg at Haverford College in (I think) 1963. I thought -- this is what I want to do! And there (at Penn, where I was a grad student) was Peter Freyd giving a course in Algebraic Topology, and later one in Abelian Categories.The sheer beauty and depth of these new ideas (new then) was overwhelming, and I decided to ask Peter to let me become his student. As I said publicly at a recent celebration of Peter's 65th Birthday in Philadephia, this was to determine the rest of my (I think, most interesting) life. I met Bil Lawvere later, at a congress in Jerusalem in 1964. His new ideas were in a different direction, but equally fascinating, and I learnt a lot from him the following year at the Forschunsinstitut fur Matematik at the E.T.H. in Zurich, where I also met Anders Kock, Jim Lambek, and Fritz Ulmer, among others. I met "the others" (Myles Tierney, Jon Beck, Jean Benabou, Saunders MacLane, and others) at the first (1966) Oberwolfach meeting, where I was allowed to present the results of my thesis at the very end of it. I count as my advisors both Freyd and Lawvere (made official in the Genealogy Project). It was the confluence of ideas and people working in harmony that was so wonderful in those days. Why should they be gone forever? Let us work together to bring them back, if possible. Something good has to come out of this discussion, or else it may have been something worse than just a waste of time. What do you say, Eduardo? Best wishes, Marta From rrosebru@mta.ca Sun Apr 2 23:47:22 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 02 Apr 2006 23:47:22 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FQF27-0005qk-VN for categories-list@mta.ca; Sun, 02 Apr 2006 23:43:12 -0300 Date: Sun, 2 Apr 2006 19:17:36 -0500 From: Peter May Message-Id: <200604030017.k330HaLo026957@math.uchicago.edu> To: categories@mta.ca Subject: categories: Reminder: Mac Lane Memorial Conference Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 12 The conference is April 7 -- 11. There have been a few minor changes of schedule. That and other updated details may be found at: http://www.math.uchicago.edu/~may/MACLANE/index.html http://www.math.uchicago.edu/~eugenia/maclane/ Since it has not yet been posted, here is a list (still slightly tentative) of titles for the talks. Steven Awodey Topology and Modality John Baez (Namboodiri Lectures) Higher category theory, higher gauge theory Julie Bergner Model categories, dg categories, and derived Hall algebras Eugenia Cheng The periodic table of n-categories Alissa Crans Lie 2-groups, Lie 2-algebras, and Loop groups Zig Fiedorowicz n-Fold categories and n-fold loop spaces Tom Fiore Double categories and pseudo algebras Peter Freyd New structures on old categories Nick Gurski >From bicategories to tricategories Peter Johnstone Potential invertibility and presheaf toposes Andre Joyal The theory of quasi-categories William Lawvere Smooth and Simplicial Toposes Ieke Moerdijk Quasi-categories and quasi-operads Peter May Duality in bicategories and topological applications Michael Shulman Anchored bicategories Danny Stevenson Lie 2-algebras and the geometry of gerbes As noted in the schedule, John Baez will be giving the 2006 Namboodiri Lectures at the University of Chicago in conjunction with the conference. This fact has also been noted in the (interminable) crack/pot thread of postings. Unni Namboodiri was a student of mine who was killed in a car crash. The lecture series was generously endowed by his parents. The choice of Baez as the speaker was entirely mine, and it has nothing whatsoever to do with the subjects of those postings. In particular, it has nothing to do with the role of category theory in physics, the mathematical or sociological relationship between physics and mathematics, or the relationship between category theory and foundations. Rather, I like John's mathematics, as mathematics, and I know him to be a superb speaker. I myself don't share his interest in physics, but I won't hold it against him. The conference is in honor of Saunders Mac Lane, who was my colleague and friend for over thirty-five years. It has been organized by Eugenia Cheng (now at the University of Chicago) and myself. As Saunders would have liked, there is all of a sudden a real categorical community at Chicago. We are eager to share our enthusiasm and describe our interests to others. One of the things that John, Eugenia, and many of the other speakers have in common is that they are especially good at making category theory interesting and appealing, at sharing their joy in the mathematics. That is the intended spirit of the conference. I urge people who have not yet decided to come to make their way to Chicago next week. There we shall all try to make joyful mathematics, some category theory and some not, in celebration of the memory of Saunders Mac Lane. Peter May From rrosebru@mta.ca Mon Apr 3 21:29:38 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 03 Apr 2006 21:29:38 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FQZGy-00008p-TY for categories-list@mta.ca; Mon, 03 Apr 2006 21:19:53 -0300 Date: Mon, 03 Apr 2006 11:02:02 -0400 From: jim stasheff To: categories@mta.ca Subject: categories: Re: cracks and pots and Mac Lane Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 13 No, guess I was too telegraphic I meant to ask if They are using numerical > calculations, which I suppose can be routinely verified as such, but > with novel applications in biology. but they themselves are not *proving* anything then they are not doing mathematics??? jim Colin McLarty wrote: > I am not sure I understand this. Jim, do you mean to say that these > people are using some mathematical statments that are not proved? The > article seems to me to say the opposite: They are using numerical > calculations, which I suppose can be routinely verified as such, but > with novel applications in biology. > > Colin > From rrosebru@mta.ca Mon Apr 3 21:29:38 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 03 Apr 2006 21:29:38 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FQZDt-0007Y2-Pm for categories-list@mta.ca; Mon, 03 Apr 2006 21:16:42 -0300 Date: Sun, 02 Apr 2006 21:18:54 -0700 From: Vaughan Pratt MIME-Version: 1.0 To: categories Subject: categories: Re: fundamental theorem of algebra Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 14 Fred E.J. Linton wrote: > First, in Birkhoff & Mac Lane (my own undergraduate algebra text), > Section 3 of Chapter V of the 1953 ("revised") edition offers a > proof along winding number lines on pp. 107-109. Thanks, Fred, I wish I'd noticed that before. I have the sixth printing (1948) of the 1941 edition, which says, "Many proofs...are known; ...we have selected one whose non-algebraic part is *especially plausible intuitively*." (My emphasis.) Then they give the proof "I like". To administer one more lash to this dead horse, the wording in the Britannica article implies that the absence of an elementary algebraic argument was the reason for omission of a proof of FTAlg. Whence the change of heart about arguments that are "especially plausible intuitively?" If they're good enough for an algebra text they should be even more acceptable for an encyclopaedia article. Vaughan Pratt From rrosebru@mta.ca Mon Apr 3 21:29:38 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 03 Apr 2006 21:29:38 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FQZFL-0007kR-0z for categories-list@mta.ca; Mon, 03 Apr 2006 21:18:11 -0300 Date: Mon, 03 Apr 2006 09:36:40 -0400 From: jim stasheff User-Agent: Thunderbird 1.5 (Windows/20051201) MIME-Version: 1.0 To: categories@mta.ca Subject: categories: RE: cracks and pots 93 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 15 Marta Bunge wrote (inter alia): It was the confluence of ideas and people working in harmony that was so wonderful in those days. Why should they be gone forever? Let us work together to bring them back, if possible. A consummation devoutly to be wished. In algebraic topology, throughout my career, there has been most of the time such harmony and a willingness to acknowledge each ohters work. Only briefly have there been periods of `turf claiming' and antagonism between individuals if not `camps'. (Of course funding was plentiful in my early days.) Should it not be sufficient to acknowledge good work who ever produces it? jim > > Dear Eduardo, > > I promised to comment on your posting partly since you praise me in having > started this discussion but also since you touch on something very relevant > to the questions that I have been asking. >> >> In recent years J.Baez and his followers have been occupying more and >> more >> space in the categorical community (this fact is at the starting point of >> the present debate). > > You refer to the list of meetings where John Baez has played a prominent > role as speaker in recent years -- and I forgot to mention Coimbra 1999 > (School on Category Theory and Applications). I do not recall of anybody, > with the exception perhaps also of Steve Awodey, to have been given so much > attention in recent years. > > I was perhaps misled by "theological considerations", namely the Templeton > Foundation and its efforts in trying to mix up science and religion. > This is > unfortunately true enough, but it has nothing to do with our present > discussion. This is the conclusion that I have reached, and it is my > obligation to say so publicly. > > You offer some interesting explanation for the state of affairs in category > theory meetings. >> >> I think this is so because they have some interesting category theory to >> show, but they are occupying more space than their mathematics deserves >> because they bring a refreshing air to a community until now dominated by >> an old guard that has not shown signs of necessary evolution, and that >> has >> not being able to attract very good and talented young mathematicians to >> the community. There is now not other exiting body of developments within >> the community. The old guard is being pushed out (prone or supine ?), >> but, >> alas, not by better mathematicians. > > > A general comment is that, whereas some of it may be true, there is much > that should be justified, or questioned. For instance, that "they have sone > interesting category theory to show", that "they bring a refreshing air", > that ours is "a community until now dominated by an old guard that has > shown > no signs of necessary evolution", that our community "has not been able to > attract very good and talented mathematicians", at present there is "no > other exiting body of developments within the community". > > Would you care to be more explicit? At the request of others, and to the > risk of attracting a lot of criticism, I have done so and have been grossly > misunderstood. If I did not request it, others will do so. That way, it > would be easier to respond to the above. > > Let us assume for the moment that the is a rift in our category theory > community -- the "old guard" versus the "new guard". We could even put > names > to represent each one -- it may seem obvious to many that, whereas Marta > Bunge "must have been influenced by Bill Lawvere (and others)", Eduardo > Dubuc "must be influenced by Andre Joyal (and others)". I am still > speculating. This imaginary discussion I want to refute, and I am sure that > you would want to do the same, or maybe not. But, is there such a rift and, > if so, why take one side against the other? > > I believe that *all* progressive forces within category theory (no matter > where they come from) should join efforts rather than split over issues > that > very few people understand or care about. I am a great admirer of both Bill > Lawvere and Andre Joyal (and of many others, eg Peter Freyd, Ross Street, > Ieke Moerdijk, to name a few -- of course, beginning with Grothendieck) > because, even if they may have different philosophies of mathematics (in > particular of category theory), they all bring in novel ideas derived from > great experience and insight. > > >> The old guard is being pushed out (prone or supine ?), but, >> alas, not by better mathematicians. > > This too, is cryptic, and too sweep a generalization. I believe that there > is poor mathematics no matter which area of category theory, but there is > also good mathematics both sides of the imaginary (?) rift. Instead of > making divisions of the sort "the young against the old", which can be used > to justify almost anything, let us make no divisions and try to preserve > excellence and promise in whatever is being done, whether applied or not, > whether fashionable or not, and filter out (as editors of journals, > organizers of conferences) the sort of mathematics that is sure to > discredit > us. Who will then be the judges? Obviously good mathematicians, not biased, > completely accountable for their choices, not short-sighted, independent, > very well informed, anxious to preserve high standards. Is there anybody > left after so many requirements? Well, Peter Johnstone is one such person, > but there are several others, of course and it is not for me to make such a > list. Once identified by general consensus (here is the hard part!), let > them consistently make all the decisions (for a certain period of time, at > least). That way, it will be unlikely that the same people be invited over > and over again, and also unlikely that bad papers will be accepted to be > presented at meetings or published in our journals. > > Sammy Eilenberg and Saunders MacLane may have represented different > tendencies within category theory, and most of us feel having been > influenced by one rather than by the other (some by both). Yet, there was > never any open rift between them, which was wonderful. > > I decided to work on category theory after a brilliant lecture by Eilenberg > at Haverford College in (I think) 1963. I thought -- this is what I want to > do! And there (at Penn, where I was a grad student) was Peter Freyd > giving a > course in Algebraic Topology, and later one in Abelian Categories.The sheer > beauty and depth of these new ideas (new then) was overwhelming, and I > decided to ask Peter to let me become his student. As I said publicly at a > recent celebration of Peter's 65th Birthday in Philadephia, this was to > determine the rest of my (I think, most interesting) life. I met Bil > Lawvere > later, at a congress in Jerusalem in 1964. His new ideas were in a > different > direction, but equally fascinating, and I learnt a lot from him the > following year at the Forschunsinstitut fur Matematik at the E.T.H. in > Zurich, where I also met Anders Kock, Jim Lambek, and Fritz Ulmer, among > others. I met "the others" (Myles Tierney, Jon Beck, Jean Benabou, > Saunders > MacLane, and others) at the first (1966) Oberwolfach meeting, where I was > allowed to present the results of my thesis at the very end of it. I count > as my advisors both Freyd and Lawvere (made official in the Genealogy > Project). It was the confluence of ideas and people working in harmony that > was so wonderful in those days. Why should they be gone forever? Let us > work together to bring them back, if possible. > > Something good has to come out of this discussion, or else it may have been > something worse than just a waste of time. What do you say, Eduardo? > > Best wishes, > Marta > > > From rrosebru@mta.ca Mon Apr 3 21:37:25 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 03 Apr 2006 21:37:25 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FQZWY-0001F2-9h for categories-list@mta.ca; Mon, 03 Apr 2006 21:35:58 -0300 Subject: categories: Re: fundamental theorem of algebra To: categories@mta.ca (categories) Date: Mon, 3 Apr 2006 16:41:24 -0700 (PDT) From: "John Baez" MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 16 Vaughan writes: > However I've been reflecting on just what is behind the very uniform > insistence on the distinction between an algebraic proof and an analytic > one. Since algebra is descended from analysis, it seems unkind for > algebra to deny its parentage in this way. I thought people knew how to add before they knew how to take limits. :-) > But I see now that this denial is logically necessary. For consider the > algebraic plane, the least algebraically closed subfield of the complex > plane, consisting of the algebraic numbers. The FTAlg is by definition > true there, so it ought to be provable there. Hmm. How do you propose to show there *exists* an algebraically closed subfield of the complex numbers? I would do it using the fundamental theorem of algebra - the usual one, for the complex numbers. Unless you have some other way, I don't understand how you hope to circumvent the use of analysis by introducing such an entity. Indeed, the usual proof that the real numbers contains a square root of 2 uses the completeness of the real numbers, which also counts as "analysis". > It is ironic that a theorem of algebra about an algebraic domain that > itself has no element of analysis to it, being just the algebraic > closure of the rationals, a small and totally disconnected space, should > require analysis, the parent of algebra, for its proof. That the rational numbers has an algebraic closure is a purely algebraic result, with no mention of topology in either the statement or proof. That the complex numbers is algebraically closed is not an algebraic result: it has topology built into the statement, and also the proof(s). That the algebraic closure of the rationals embeds in the complex numbers has topology in the statement - and I bet also in every proof. Best, jb From rrosebru@mta.ca Mon Apr 3 21:38:09 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 03 Apr 2006 21:38:09 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FQZXy-0001Mf-Lm for categories-list@mta.ca; Mon, 03 Apr 2006 21:37:26 -0300 Subject: categories: Higher categories, higher gauge theory To: categories@mta.ca (categories) Date: Mon, 3 Apr 2006 17:01:03 -0700 (PDT) From: "John Baez" X-Mailer: ELM [version 2.5 PL6] MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 17 Hi - Some of you may enjoy these lecture notes, especially given how people have been drumming up interest in my talks. Best, jb ......................................................................... Higher Gauge Theory, Higher Categories http://math.ucr.edu/home/baez/namboodiri/ Abstract: The work of Eilenberg and Mac Lane marks the beginning of a trend in which mathematics based on sets is generalized to mathematics based on categories and then higher categories. We illustrate this trend towards "categorification" by a detailed introduction to "higher gauge theory". Gauge theory describes the parallel transport of point particles using the formalism of connections on bundles. In both string theory and loop quantum gravity, point particles are replaced by 1-dimensional extended objects: paths or loops in space. This suggests that we seek some kind of "higher gauge theory" that describes the parallel transport as we move a path through space, tracing out a surface. Surprisingly, this requires that we "categorify" concepts from differential geometry, replacing smooth manifolds by smooth categories, Lie groups by Lie 2-groups, Lie algebras by Lie 2-algebras, bundles by 2-bundles, sheaves by stacks or gerbes, and so on. The basic tool used here is Ehresmann's notion of "internalization". To explain how higher gauge theory fits into mathematics as a whole, we begin with a lecture reviewing the basic principle of Galois theory and its relation to Klein's Erlangen program, covering spaces and the fundamental group, Eilenberg-Mac Lane spaces, and Grothendieck's ideas on fibrations. The second lecture treats connections on trivial bundles and 2-connections on trivial 2-bundles, explaining how they can be described either in terms of their holonomies or in terms of Lie-algebra-valued differential forms. For a clean treatment of these concepts, we recall Chen's theory of "smooth spaces", which generalize smooth finite-dimensional manifolds. The third lecture explains connections on general bundles and 2-connections on general 2-bundles, explaining how they can be described either in terms of holonomies or local data involving differential forms. We also explain how 2-bundles are classified using nonabelian Cech 2-cocycles, and how the theory of 2-connections relates to Breen and Messing's theory of "connections on nonabelian gerbes". From rrosebru@mta.ca Mon Apr 3 21:39:32 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 03 Apr 2006 21:39:32 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FQZZL-0001WG-Hr for categories-list@mta.ca; Mon, 03 Apr 2006 21:38:51 -0300 Date: Mon, 03 Apr 2006 08:09:23 -0700 From: Vaughan Pratt MIME-Version: 1.0 To: categories@mta.ca Subject: categories: Demystifying the categorial approach Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 18 Reinhard Boerger wrote: Of course, category > theoty usrather abstract and can hardly be explained to non-mathematians. Would this not be both true and false of any mathematical subject worth its salt? Such a subject will include deep results and/or abstract concepts that are inaccessible even to many mathematicians, let alone nonmathematicians. At the same time it should be possible to trace the chains of reasoning motivating those results and concepts back to origins that should be easy to motivate for the nonspecialist and/or nonmathematician. As a case in point, category theory can be motivated by presenting it as an approach to axiomatizing sets and functions (and more generally algebraic structures and homomorphisms as their structure-respecting functions, but one need not start there). In that approach, instead of defining a function to be a binary relation of a certain form, one postulates functions as primitives in their own right, axiomatized by the laws of composition and the existence of identities. One should not feel obliged to axiomatize in full the morphisms of Set, certainly not at the outset, and moreover not if one plans to apply the same ideas to the morphisms of other categories at some point. This central tenet of category theory should be one of the factors guiding the order of development, with associative composition foremost. Along similar lines one can point up the parallels with how the very words with which we speak combine associatively to form phrases and sentences, and how addition and multiplication of both integers and reals also obey those laws but differ in furthermore being commutative. It should be possible to make such an account of the category-theoretic axiomatization of functions very accessible both to non-mathematicians and to eighth-graders with some interest in mathematics. One should also avoid the common jargon of the category theory literature. Everyday language about everyday concepts is to be preferred to new notions that need to be defined before they can be understood. One could also dwell on the politics of the status quo, were it as easy to explain ZF. Indeed, when one compares the compositional approach with how functions are introduced into mathematics founded on ZF, one has to wonder how the latter came to be preferred over a framework that axiomatizes functions as primitives. To any save those that have long since come to live and breathe the ZF-based definition, it is unnatural, unmotivated, and hard to explain to nonmathematicians by comparison with associatively composing functions. One hypothesis for why set theory is the preferred basis today for the concept of function is that the primitive-function approach is just too simple to take seriously. But that can't be true, as we saw at the Universal Algebra and Category Theory conference at MSRI 17 years ago, where every algebraist there understood the motivation for defining formal languages and relation algebras abstractly as monoids, a really simple abstraction with a rich literature of implications. Few of them however seemed to fully appreciate the power of applying the same abstraction, subject to essentially the same laws, to the definition of function, being content with the ZF picture of functions. Or am I grossly misinterpreting what we all witnessed at that meeting? Walt Taylor, of McKenzie, McNulty, and Taylor, "Algebras, Lattices, Varieties: Volume I", spoke on his highly developed theory of varieties back to back with Fred Linton's talk on monads. It was like ships passing in the night. I pointed this out to George McNulty at lunch after Fred's talk, but though we both struggled mightily and without rancour to communicate, we just could not get to square one, in the time available before the first afternoon talk, with the concepts of monad, adjunction, or their relevance to what Walt had just spoken about. And it's not as though George and I can't communicate at all, as can be inferred from my profuse acknowledgements of his considerable help at both the start and end of http://boole.stanford.edu/pub/iowatr.pdf, followed up by http://boole.stanford.edu/pub/jelia.pdf (work done entirely in the universal algebra tradition with no mention of categories, since that was the audience for those papers). Except for his being the master and I the student, George and I are very much on the same wavelength in algebraic matters, it was only category theory that was a closed channel between us then. Ralph McKenzie seemed to be more keen than Walt or George for algebraists to embrace category theory, but even for the prime mover of tame congruence theory it seemed to be something of an uphill battle. It's not just monads and adjunctions that noncategorist mathematicians have a hard time with. In his welcoming remarks at the start of the meeting, MSRI director and formidable geometer Bill Thurston expressed his discomfort with Set^op, and the incredulity of half the audience was palpable for a second. Even today category theory labors under the dual impressions that it is too abstract to explain to the non-specialist, yet too trivial to take seriously. This screwy situation is not unlike the days when oxygen was perceived only as the absence of phlogiston, oxygen being harder to "see" than phlogiston despite our constant immersion in it, just as we are constantly immersed in associatively composing functions. The chemists of the pre-oxygen era, who believed that burning wood gave up phlogiston to the air, would have found quite mystical the idea that the absence of phlogiston constitutes 20% of air. Category innocents are in much the same boat. Complicating matters is that this works both ways. It is hard to understand someone who finds it hard to understand the "obvious," whether true or not. How should a categorist understand a talented mathematician unable to process the concept of the opposite of a concrete category? (Useful trick: define a function to be a binary relation and consider its converse. Why didn't Thurston think of that? Why didn't someone suggest it to him?) Marta should look forward to a time when functions are taught as associatively composing entities as routinely as nitrogen and oxygen are taught today as the principal constituents of air. High school math teachers will look back at the 21st century and marvel at how confused people were about the nature of functions in those days. It might of course never happen, with the concept of graph of a function forever taken as prior to the function concept itself. One big obstacle is that the concept of binary relation is sufficiently well motivated in its own right as to justify being introduced first (but in that case try to at least get *that* defined via relation algebra, Tarski's program, which so far has not taken hold). Another is that there does not seem to be any knockdown argument making composition prior to application, and the mathematical world is currently strongly wedded to the opposite. But the biggest obstacle is that such a sea change can't happen via an independently written book focused on the need for that change. Rather the viewpoint needs to be integrated into the existing literature, either by adapting existing texts or providing superior alternatives whose primary purpose is to meet the extant curriculum requirements and which accepts that getting the definitions right is only a matter of good hygiene and not a subject in its own right to be added to an already crowded curriculum. It has to be an inside job. Vaughan Pratt From rrosebru@mta.ca Mon Apr 3 21:40:35 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 03 Apr 2006 21:40:35 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FQZaN-0001cg-HT for categories-list@mta.ca; Mon, 03 Apr 2006 21:39:55 -0300 Date: Mon, 03 Apr 2006 20:07:21 -0400 From: jim stasheff MIME-Version: 1.0 To: Categories List Subject: categories: language Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 19 query: functor is to multiplicative morphism as __________ is to strongly homotopy multiplicative morphism (aka A_\infty morphism) That's thr trouble with affixes like quasi- or pseudo- though lax might do From rrosebru@mta.ca Mon Apr 3 21:43:21 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 03 Apr 2006 21:43:21 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FQZcs-0001qx-AT for categories-list@mta.ca; Mon, 03 Apr 2006 21:42:30 -0300 From: "Reinhard Boerger" To: Vaughan Pratt Date: Mon, 03 Apr 2006 10:21:19 +0200 MIME-Version: 1.0 Subject: categories: Re: fundamental theorem of algebra To: categories@mta.ca Content-type: text/plain; charset=US-ASCII Content-transfer-encoding: 7BIT Content-description: Mail message body Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 20 Hello, Vaughan Pratt wrote: > 3. It is certainly not necessary to prove A before B merely because B > depends on A; indeed one common-sense practice when proving a > two-lemma proof is to get the easier lemma out of the way first, even > if it depends on the harder one. Is it kosher to truncate such a > proof after the first lemma (or in this case the final result), call > it an exposition, and point to the literature for the second lemma? Indeed, should we expect non-mathematicians "believe in" results like the Jordan curve theorem, which is very easy to see and very hard to prove? Maybe they do not appreciate a proof of something that looks completely obvious. Or, another veryeasy thing: If somebody walks from A to B and somebody walks fron B to A at the same time on the same route, they will me meet somewhere, even if they don't walk with constant speed or if they stop somewhwere. Rigorously, this is essentiaally equivalent to the intermediate value theorem, which is not too hard to prove, but nevertheless not trivial. I think there are better subjects to illustrate what mathematics is about. Some months about I was asked to contribute to a calender, in which people working in different scientific subjects give an insight in their work and their subjects. I contributed the party theorem that a (simple) finite graph with at n>1 vertices has two vertices of the same dergree. The proof just uses the pidgeon-hole principle and the observation that a vertex of degree zero and a vetex of degree n-1 cannot both exist. If course, I avoided mathematical terminology not known to the general public and spoke of guests of a party, where some shake hands with each other and some don't. I think this example may give a flavour of what a proof is, but does not bother them with formalisms which are not necessay here (but somewhere else). Of course, category theoty usrather abstract and can hardly be explained to non-mathematians. One remark ti the fundamental theory of algebra. From Harald Holman I learned a proof based on a simple ideas, which can be made rigorous quite easily: Since a non- constant complex polynomial is large outside a sufficiently large circle, its modulus must have a (local am global) minimum inside the circle (by compactness); we can shift it into zero (by translation) and assume the minimum is attained in zero. Since the polynomial is not constant, it is of the form a_0+a_m*z^m+higher terms, a_m different from 0. If a_0=0, the polynomial has a zero in 0, and we are done, so assume that a_0 is not 0. Then there exists a complex number w with w^m=- a_m/a_0; this follows from the polar coordinate representation, which is taught in calculus courses. Then for sufficienly every positive real h<1, the modulus of a_0+a_m*(hw)^m is smaller than the modulus of a_0; if we choose h small enough, the modulus of value of the polynomial at hw is also smaller than a_0, because the higher terms can be neglected. This contradicts our assumption that the modulus attains a minimum in 0. Greetings Reinhard From rrosebru@mta.ca Tue Apr 4 02:27:50 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 04 Apr 2006 02:27:50 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FQe14-0000Er-V2 for categories-list@mta.ca; Tue, 04 Apr 2006 02:23:47 -0300 Date: Mon, 3 Apr 2006 21:08:03 -0400 (EDT) From: Michael Barr To: categories Subject: categories: Re: fundamental theorem of algebra MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 21 Perhaps the moral is not to bother with the Britannica. Wikipedia has several proofs including the winding number argument and the one I outlined using the symmetric function argument. Then a couple of analytic ones. Of course, Wiki has no size limitations. Perhaps we have flogged this particular horse enough. On Sun, 2 Apr 2006, Vaughan Pratt wrote: > Fred E.J. Linton wrote: > > First, in Birkhoff & Mac Lane (my own undergraduate algebra text), > > Section 3 of Chapter V of the 1953 ("revised") edition offers a > > proof along winding number lines on pp. 107-109. > > Thanks, Fred, I wish I'd noticed that before. I have the sixth printing > (1948) of the 1941 edition, which says, "Many proofs...are known; ...we > have selected one whose non-algebraic part is *especially plausible > intuitively*." (My emphasis.) Then they give the proof "I like". > > To administer one more lash to this dead horse, the wording in the > Britannica article implies that the absence of an elementary algebraic > argument was the reason for omission of a proof of FTAlg. Whence the > change of heart about arguments that are "especially plausible > intuitively?" If they're good enough for an algebra text they should be > even more acceptable for an encyclopaedia article. > > Vaughan Pratt > > From rrosebru@mta.ca Tue Apr 4 02:27:50 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 04 Apr 2006 02:27:50 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FQe2v-0000HK-Vg for categories-list@mta.ca; Tue, 04 Apr 2006 02:25:42 -0300 Subject: categories: RE: cracks and pots 93 Date: Mon, 03 Apr 2006 22:07:10 -0400 From: wlawvere@buffalo.edu To: categories@mta.ca MIME-Version: 1.0 Content-Type: text/plain Content-Transfer-Encoding: 8bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 22 Dear Jim Your question "Should it not be sufficient to acknowledge good work whoever does it ? " would I think receive the obvious answer YES from all participants in the list. Yet it lies it the heart of most of the 200 messages, public and private, that I have received since Marta opened the discussion. For as I concluded in III, the problem is, How can we know ? We cannot acknowledge good work unless we have knowledge of it. This was not a problem for 40 years, or rather if there was temporary problem, it was usually due to the need to acquire prerequisites, which could be done. But in the past few years, a "new" barrier to finding out has been added to the mathematical culture (it was common in other parts of the culture already); disdain for communicating, starting with disdain for revealing definitions. That this trend is not due to a few individual culprits within our community is illustrated by the attempts to justify it "theoretically" by show business or business practice or by pop Oxbridge philosophy. Whether in exposition, in popularization, or in professional lectures, of course the practice of noncommunication typically begins with "'I am going to be your special communicator about this", etc. These additional barriers we are presented with make "How can we know" ( whether a work is good) much more difficult, and an accumulation of such difficulties has led to a lot of concern. Best regards Bill Quoting jim stasheff : > > > Marta Bunge wrote (inter alia): > > It was the confluence of ideas and people working in harmony that > was so wonderful in those days. Why should they be gone forever? Let > us > work together to bring them back, if possible. > > A consummation devoutly to be wished. In algebraic topology, > throughout > my career, there has been most of the time such harmony and a > willingness to acknowledge each ohters work. Only briefly have > there > been periods of `turf claiming' and antagonism between individuals > if > not `camps'. (Of course funding was plentiful in my early days.) > > Should it not be sufficient to acknowledge good work who ever > produces it? > > jim > [ balance of quotation omitted... ] From rrosebru@mta.ca Tue Apr 4 02:27:50 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 04 Apr 2006 02:27:50 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FQe0D-0000DS-8p for categories-list@mta.ca; Tue, 04 Apr 2006 02:22:53 -0300 Mime-Version: 1.0 (Apple Message framework v746.3) Content-Type: text/plain; charset=US-ASCII; delsp=yes; format=flowed Message-Id: <5C0C5FD8-E724-473B-A268-16FB12A580D6@linus.math.tulane.edu> Content-Transfer-Encoding: 7bit From: Michael Mislove Subject: categories: MFPS 22 Call for Participation Date: Mon, 3 Apr 2006 19:54:27 -0500 To: categories@mta.ca Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 23 Dear Colleagues, Registration for MFPS 22 is now open. The Twenty Second Conference on the Mathematical Foundations of Programming Semantics will take place on the campus of the University of Genoa, Italy from May 23 through May 27, 2006. In addition to six plenary addresses, there will be three special sessions, on security, quantum computing and timed systems, each featuring talks by invited speakers in these areas. The remainder of the program will be composed of papers selected by the Program Committee from those that were selected from the submissions to the Call for Papers. Finally, there will also be a Tutorial Day devoted by lectures on Separation Logic on May 22, preceding the meeting. All of the details, including the list of accepted papers, can be found at the MFPS 22 home page, http://www.math.tulane.edu/~mfps/mfps22.htm There is a link there to the Registration Page where you can also register online for the meeting. Of particular importance is the short time window to reserve a hotel room for the meeting. Blocks of rooms are being held at a number of hotel in Genoa, but these will not be withheld from general availability after April 20. Because of this, it is important that you make your reservations for a hotel room as soon as possible. (I apologize for the tardy delay in notifying you about this, but we didn't want to announce the opening of registration until the program was finalized.) As usual, if you have any questions or problems, please send email to mfps@math.tulane.edu and we will respond. Best regards, Mike Mislove, Co-Organizer MFPS Conference Series From rrosebru@mta.ca Tue Apr 4 02:29:27 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 04 Apr 2006 02:29:27 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FQe5M-0000N1-Qx for categories-list@mta.ca; Tue, 04 Apr 2006 02:28:12 -0300 Subject: categories: cracks and pots 106 From: Eduardo Dubuc To: categories@mta.ca Date: Mon, 3 Apr 2006 19:47:29 -0300 (ART) X-Mailer: ELM [version 2.5 PL2] MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Message-Id: Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 24 In his April 2 posting (Reminder: Mac Lane Memorial Conference) P. May refers to the "crack/pot thread" , and we can see his feeling about it. In particular, he is fed-up. Many people probably share these feelings (more or less), so I will use him as a generic symbol in this posting. The cracks and pots debate is "(interminable)" for him. Probably it is disturbing, and when a disturbing thing refuses to go away, May may get angry. He says he choose Baez as an speaker because he likes his mathematics: What is the point ?. Besides Motl's original reservations about Baez mathematics applied to Physics, nobody said that "do not like Baez mathematics". Simply it was said that it occupied much too room for what it was worth. And I said that this was so because to-day (for a category theory meeting) there is no other enthusiastic body of work to take predominant place. So, what is his point ? I myself, having to-day to organize a meeting in category theory, will certainly invite Baez. Related to, but not the same thing, he goes on saying: "I myself don't share his interest in physics, but I won't hold it against him." What does he mean by "but I won't hold it against him." ?. Had anybody hold the interest in physics against anyone ? In cracks_and_pots nobody is holding or had ever hold against Baez his interest in Physics !! In cracks and pots it was only objected that > The category theory community seems happy to accept uncritically, and > give centre-stage to, any interest shown by an external field. It is known that ~(p ==> q) does not mean p ==> ~q , as he seems to believe (where p = he has interest in physics, q = he is good, and "~" stands for negation). Concerning the meeting proper: "I urge people who have not yet decided to come to make their way to Chicago next week. There we shall all try to make joyful mathematics, some category theory and some not, in celebration of the memory of Saunders Mac Lane." why "try" ? I warn, "joyful" is not enough. But, after this warning, do not take me wrong. The joyful side of mathematics is certainly in the spirit of Saunders, and besides, judging by the list of speakers, it will certainly be worth while to attend. I hope Baez will electronically publish an account of the talks, as he had done in the past with other meetings. Everybody interested in categories profit with Baez online. I toast for a good meeting, the memory of Saunders Mac Lane deserves it. Eduardo Dubuc From rrosebru@mta.ca Thu Apr 6 10:04:47 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 06 Apr 2006 10:04:47 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FRU5O-00023y-MD for categories-list@mta.ca; Thu, 06 Apr 2006 09:59:42 -0300 Subject: categories: RE: cracks and pots 93 To: categories@mta.ca (Categories List) Date: Tue, 4 Apr 2006 13:15:23 -0300 (ADT) MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit From: selinger@mathstat.dal.ca (Peter Selinger) Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 25 wlawvere@buffalo.edu wrote: > > Dear Jim > > Your question "Should it not be sufficient to acknowledge good work > whoever does it ? " would I think receive the obvious answer YES > from all participants in the list. > > Yet it lies it the heart of most of the 200 messages, public and > private, that I have received since Marta opened the discussion. For > as I concluded in III, the problem is, How can we know ? I have been raised to believe that the answer to this is peer-review, not public-trial-by-mailing-list. One problem with the latter method is that, since nobody wants to discuss particular cases, the discussion tends to center on generalities, innuendo and "I have heard it repeated many times"-type arguments, and not on evidence or actual facts that could be verified. Such evidence and facts, on the other hand, are available to editors and referees, who are also largely independent of public opinion. As I see it, this is exactly as it should be. -- Peter From rrosebru@mta.ca Thu Apr 6 10:04:48 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 06 Apr 2006 10:04:48 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FRU3U-0001vZ-0r for categories-list@mta.ca; Thu, 06 Apr 2006 09:57:44 -0300 From: "Reinhard Boerger" Date: Tue, 04 Apr 2006 10:29:57 +0200 MIME-Version: 1.0 Subject: categories: Re: Demystifying the categorial approach To: categories@mta.ca Content-type: text/plain; charset=US-ASCII Content-transfer-encoding: 7BIT Content-description: Mail message body Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 26 Hello, Vaughan Pratt wrote: > Reinhard Boerger wrote: > Of course, category > > theoty usrather abstract and can hardly be explained to > > non-mathematians. Sorry for the misprints. > Would this not be both true and false of any mathematical subject > worth its salt? Such a subject will include deep results and/or > abstract concepts that are inaccessible even to many mathematicians, > let alone nonmathematicians. At the same time it should be possible > to trace the chains of reasoning motivating those results and concepts > back to origins that should be easy to motivate for the nonspecialist > and/or nonmathematician. I agree but that is not my point. I did not want to judge what is "good" or "deep" mathematics. Of course, deep results are difficult to uderstand even for specialists, and the existence of infinitely many primes or the party theorem are definitively not deep. But their proofs require some amount of mathemtical thinking, which is on the other hand still comprehensible for non mathematicians. So they can learn how mathematics works. Then we can tell them about Fermat's Last Theorem or applications in computerized tomography, certainly without proofs. > As a case in point, category theory can be motivated by presenting it > as an approach to axiomatizing sets and functions (and more generally > algebraic structures and homomorphisms as their structure-respecting > functions, but one need not start there). In that approach, instead > of defining a function to be a binary relation of a certain form, one > postulates functions as primitives in their own right, axiomatized by > the laws of composition and the existence of identities. One point is selling mathematics to nonmathematicians, the other is selling categories to other mathematicians (not necessarily to physicists). In general, nonmathematicians don't even know what sets and functions are and why they are needed in mathematics. I think that category theory makes several things clearer (and also easier) and reveals connections and similarities between different branches of mathematics. It is quite nice if it can also be used as a foundation, but for me this is not the most important aspect. Greetings Reinhard From rrosebru@mta.ca Thu Apr 6 10:04:48 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 06 Apr 2006 10:04:48 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FRU2J-0001qt-Uu for categories-list@mta.ca; Thu, 06 Apr 2006 09:56:32 -0300 Date: Tue, 4 Apr 2006 00:50:51 -0700 From: Toby Bartels To: categories@mta.ca Subject: categories: Specific examples? (Was: cracks and pots) Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Disposition: inline In-Reply-To: User-Agent: Mutt/1.4i Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 27 Vincent Schmitt wrote in part: >Now that theoretical physics, computer >science, phylo., a mix of those, or whatever? , >is used to justify poor "categorical" work is, >in my view, an existing problem. More or less >everyone is conscious of it (come on!...) but so far >that has not been publically debated. I am happy >that it happens now. Actually, I've had great difficulty with this thread [*] because I am ~not~ conscious of this (justification of poor work). It seems all too obvious to many of the posters here; you are probably more familiar than I with the bulk of the literature. But unless I've missed it, nobody has given an example of this. (The closest is that John Baez's work has too much prominence, but nobody wants to claim that his work is poor, quite the opposite. And there was a work by a philosopher that was cited, but that did not pretend to be mathematics.) I would understand your concerns much better if I knew a few examples, hopefully from various fields, of poor work that has been unjustifiably accepted. I know that it may be hard to give specific examples without running the risk of insulting colleagues, and I'm sorry about that; but without them, I really don't have any idea what you're all complaining about. (Not just Vincent, but Marta and all of the others supporting her are included in this request, please!) [*] Incidentally, "thread" is an old Internet term for a discussion resulting from a single "original post" ("OP"); the thread consists of the OP, every post written in reply to the OP, everything written in reply to those posts, and so on (recursively). So Marta's first email on this topic is the OP, and the 100 or so public emails since constitute the thread. -- Toby From rrosebru@mta.ca Thu Apr 6 10:04:48 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 06 Apr 2006 10:04:48 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FRU4f-00020x-SF for categories-list@mta.ca; Thu, 06 Apr 2006 09:58:58 -0300 Date: Tue, 04 Apr 2006 09:45:56 -0400 From: jim stasheff MIME-Version: 1.0 To: categories@mta.ca Subject: categories: RE: cracks and pots 93 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 28 My experience has ben quite the opposite within math (politics is another matter) by receiving daily list of titles and abstracts from the arXiv I can then followup with the detials of anything that looks intersting or suspicious to me doesn't `everyone' use the arXiv at least those computer connected enough to be on this list? jim wlawvere@buffalo.edu wrote: > Dear Jim > Your question > "Should it not be sufficient to acknowledge good work whoever does it ? " > would I think receive the obvious answer YES from all participants in the list. > > Yet it lies it the heart of most of the 200 messages, public and private, that > I have received since Marta opened the discussion. For as I concluded in III, > the problem is, How can we know ? We cannot acknowledge good work > unless we have knowledge of it. This was not a problem for 40 years, or > rather if there was temporary problem, it was usually due to the need to > acquire prerequisites, which could be done. > > But in the past few years, a "new" barrier to finding out has been added > to the mathematical culture (it was common in other parts of the > culture already); disdain for communicating, starting with disdain for > revealing definitions. That this trend is not due to a few individual culprits > within our community is illustrated by the attempts to justify it > "theoretically" by show business or business practice or by pop Oxbridge > philosophy. Whether in exposition, in popularization, or in professional > lectures, of course the practice of noncommunication typically begins > with "'I am going to be your special communicator about this", etc. > > These additional barriers we are presented with make "How can we know" > ( whether a work is good) much more difficult, and an accumulation of > such difficulties has led to a lot of concern. > > Best regards > Bill > From rrosebru@mta.ca Thu Apr 6 10:05:07 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 06 Apr 2006 10:05:07 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FRU9x-0002YZ-DW for categories-list@mta.ca; Thu, 06 Apr 2006 10:04:25 -0300 X-ME-UUID: 20060404215036751.124E81C0008B@mwinf3007.me.freeserve.com Message-ID: <021e01c65831$d1a79360$0201a8c0@RONNIENEW> From: "Ronnie Brown" To: Subject: categories: Re: Demystifying the categorial approach Date: Tue, 4 Apr 2006 22:49:53 +0100 MIME-Version: 1.0 Content-Type: text/plain;format=flowed; charset="iso-8859-1";reply-type=response Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 29 I have not been able to keep up with all this correspondence, but would like to take up Vaughan Pratt's counter to Reinhard Boerger's point saying: `it can't be done' which would be better as a question: `How should one do it?' The many books and films on maths show there is some kind of hunger to know what this subject is about, but the books and films often avoid the subject itself in order to emphasise the weirdness of their chief characters. The Bangor approach has for years been `advanced mathematics from an elementary viewpoint', and we have been trying this out on 13 year olds, and the general public, for the last 22 years. We have gained a lot from the exercise, and have used the experience in talks to mathematicians, science festivals and other scientists. Here are some references. 136. (with T. Porter), `Category theory and higher dimensional algebra: potential descriptive tools in neuroscience', Proceedings of the International Conference on Theoretical Neurobiology, Delhi, February 2003, edited by Nandini Singh, National Brain Research Centre, Conference Proceedings 1 (2003) 80-92. 137. (with R.Paton and T. Porter), `Categorical language and hierarchical models for cell systems', in Computation in Cells and Tissues - Perspectives and Tools of Thought, Paton, R.; Bolouri, H.; Holcombe, M.; Parish, J.H.; Tateson, R. (Eds.) Natural Computing Series, Springer Verlag. (2004) 289-303. I presented the talk for 136. and it went well. One aim was to explain the concept of colimit, as a way of putting structures together. A scientist from the Salk Inst said he kept on thinking about the ideas that night and could not go to sleep! This is a better reaction than I get generally from algebraic topologists (pace Marta's comments)! Here is another article: 146. (with T. Porter) `Category Theory: an abstract setting for analogy and comparison', Advanced Studies in Mathematics and Logic (to appear) UWB Math Preprint 05.10 . http://www.informatics.bangor.ac.uk/public/mathematics/research/preprints/05/cathom05.html#05.10 If you examine our pages on www.popmath.org.uk, you will find discussion of many topics, such as AIMS. My whole approach to higher dimensional algebra since 1965 or so has been to give expression to intuitions such as expressing a big object as a composition of small objects, i.e. the algebraic inverse to subdivision, and also explaining the notion of commutative cube. There are deep ideas (e.g. knots) that can be explained to children, and so to a general audience, and others for which this is much more difficult. There is a hunger among scientists and the general public to get some idea of what is going on in mathematics, apart from solving some famous but weird problems. The idea of `structure' is a good way to start, perhaps. I have used Bill Lawvere's tag: The mathematical notion of space is for the representation of motion, i.e. of change of data. How can space be structured? How can we calculate and control ideas in that context? How strange is space? In 1987 or so, I gave a lecture on knots to an audience from schools, and a teacher came up to me afterwards and said: `That is the first time in my mathematical career that anyone has used the word `analogy' in relation to mathematics.' Think on it! So I have made something of a song and dance on the theme of `analogy' in the new edition of my book: and the notion of universal property as a way of making analogies, to obtain understanding and calculation. Finally, to see an argument about physics and maths, see an article S. Novikov `The Second Half of the 20th Century and its Conclusion: Crisis in the Physics and Mathematics Community in Russia and in the West', published in American Math Society Translations, (2) vol 212, 2004 which might rise some ire among some of us. There are also important points. It is certainly an aspect of the debate, e.g. `7. Second half of the 20th century: excessive formalization of mathematics.' I was sent a pdf file of this. But I do not have a url for this English translation. Ronnie Brown www.bangor.ac.uk/r.brown ----- Original Message ----- From: "Vaughan Pratt" To: Sent: Monday, April 03, 2006 4:09 PM Subject: categories: Demystifying the categorial approach > Reinhard Boerger wrote: > Of course, category >> theoty usrather abstract and can hardly be explained to non-mathematians. > > Would this not be both true and false of any mathematical subject worth > its salt? Such a subject will include deep results and/or abstract > concepts that are inaccessible even to many mathematicians, let alone > nonmathematicians. At the same time it should be possible to trace the > chains of reasoning motivating those results and concepts back to > origins that should be easy to motivate for the nonspecialist and/or > nonmathematician. > > As a case in point, category theory can be motivated by presenting it as > an approach to axiomatizing sets and functions (and more generally > algebraic structures and homomorphisms as their structure-respecting > functions, but one need not start there). In that approach, instead of > defining a function to be a binary relation of a certain form, one > postulates functions as primitives in their own right, axiomatized by > the laws of composition and the existence of identities. > [balance of quotation omitted...] From rrosebru@mta.ca Thu Apr 6 10:06:36 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 06 Apr 2006 10:06:36 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FRUBN-0002i1-Bc for categories-list@mta.ca; Thu, 06 Apr 2006 10:05:53 -0300 Date: Tue, 4 Apr 2006 21:02:11 -0700 Message-Id: <200604050402.k3542Bga004787@gateway.knighten.org> From: Robert Knighten To: categories@mta.ca Subject: categories: Category theory question from Solovay Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 30 Bob Solovay posted the following question to the Foundations of Mathematics mailing list. I can't answer it, but it looked likely that members of this list would have useful comments, so with his permission I am posting it here. [There were two postings but I have just combined them.] -- Bob -- Robert L. Knighten Robert@Knighten.org Date: Mon, 3 Apr 2006 09:18:33 -0700 (PDT) From: solovay@Math.Berkeley.EDU Subject: [FOM] Fraenkel-Mostowski-Specker method and category theory To: "Foundations of Mathematics" I have come across a curious question related to the FMS method and category theory. Before stating the problem I need to recall some definitions. Let G be a group. A normal filter of subgroups of G, Gamma, is a non-empty collection of subgroups of G which has the following properties: 1) If H_1 and H_2 are members of Gamma then so is their intersection H_1 \cap H_2; 2) If H is in Gamma and K is a subgroup of G which is a supergroup of H, then K is in Gamma; 3) If H is in Gamma and x is an element of G then the conjugate subgroup xHx^{-1} is in Gamma. Now let G be a group and Gamma a normal filter of subgroups of G. To this data we associate a category C(G,Gamma) as follows: The objects of our category consist of sets X equipped with an action of H on X [ for some H in the filter Gamma] such that for every x in X the isotropy subgroup H_x [consisting of those elements of H which fix the element x] lies in Gamma. Now let X_1 and X_2 be objects of our category carrying actions of H_1 and H_2 respectively. The morphisms of our category from X_1 to X_2 are those maps from X_1 to X_2 [in the category of sets] which (for some subgroup K of H_1 \cap H_2) lying in Gamma are K-equivariant. The basic question is: when are C(G_1, Gamma_1) and C(G_2,Gamma_2) equivalent categories: Here are some obvious sufficient conditions: (a) If there is an isomorphism of G_1 with G_2 that carries Gamma_1 onto Gamma_2 then the two categories are equivalent. (b) Let G be a group and Gamma a normal filter of subgroups of G. Let H be a subgroup of G lying in Gamma, and let Gamma' be the collection of all subgroups of H lying in Gamma. Then C(G, Gamma) and C(H, Gamma') are equivalent. My question is this: Are (a) and (b) the only reasons that two such categories are equivalent. That is, if C(G_1, Gamma_1) and C(G_2, Gamma_2) are equivalent then are there subgroups H_1 of G_1 and H_2 of G_2 [lying in the respective filters] such that letting Gamma_1' and Gamma_2' be the evident restricted filters we have C(H_1, Gamma_1') equivalent to C(H_2, Gamma_2'). I suspect that the answer is no. Also welcome [for the undisclosed application I have in view] would be additional sufficient criteria other than (a) and (b). --Bob Solovay >> My question is this: Are (a) and (b) the only reasons that two >> such >> categories are equivalent. That is, if C(G_1, Gamma_1) and C(G_2, >> Gamma_2) are equivalent then are there subgroups H_1 of G_1 and H_2 >> of G_2 [lying in the respective filters] such that letting Gamma_1' >> and Gamma_2' be the evident restricted filters we have C(H_1, >> Gamma_1') equivalent to C(H_2, Gamma_2'). > > I must be missing something about this question. Isn't the answer > automatically yes once we put H_1 = G_1 and H_2 = G_2 ? I feel > tempted to replace the conclusion by (H_1, Gamma_1') isomorphic to > (H_2, Gamma_2'). > > > regards, > Volodya Shavrukov You are right. I stated my question wrongly and what I intended is your proposed repair. --Bob From rrosebru@mta.ca Thu Apr 6 15:38:29 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 06 Apr 2006 15:38:29 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FRZJW-00058G-VV for categories-list@mta.ca; Thu, 06 Apr 2006 15:34:39 -0300 Date: Thu, 6 Apr 2006 16:49:08 +0100 (BST) From: John Stell To: categories@mta.ca Subject: categories: Re: Demystifying the categorial approach MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 31 When Venet's commutative diagrams as art appeared in the AMS Notices (vol 49 no6 2002, pp663-668) this was mystification of the categorical approach by the artist. Good art but nothing to do with mathematics. Since many attempts to demystify mathematics have a visual aspect, the role of art here is interesting, as well as how artists see this kind of activity. One aspect of the continuing discussion seems to concern disciplinary boundaries -- complaints that some computer scientists, physicists, philosophers etc 'misuse' category theory or deride it. It's interesting that efforts to explain mathematics to the general public can fall foul of exactly similar complaints from an opposite quarter. Often public participation projects involve art in some way and these are indeed often funded under 'art-science' programmes. Most such projects are valuable for engaging the public and succeed in getting people interested, however the art is usually of no interest to artists concerned with current issues in contemporary art. This is not to say they are poor projects, but labelling them as "art-science" creates the false impression there is an engagement with art in a meaningful way. On the other hand there is art which references mathematics, but which has absolutely no mathematical content. For example Venet's work and others who lift elaborate equations to great visual effect. Yet other work (e.g. Conrad Shawcross) involves references to physics in a quite different, but still non-expository, way. It seems to be an open question how art might be used to promote or facilitate a genuine understanding of mathematics (which must involve the reasoning processes and apreciation of abstract structure). Perhaps Sol LeWitt (despite his writings and some critics (e.g. Rosalind Krauss)) indicates a possible way forward. Some of his work (just like Venet's) has nothing to do with mathematics despite the superficial apperance; other parts are worth thinking about. John Stell From rrosebru@mta.ca Thu Apr 6 15:38:29 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 06 Apr 2006 15:38:29 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FRZJz-0005C6-KQ for categories-list@mta.ca; Thu, 06 Apr 2006 15:35:07 -0300 Subject: categories: Glasgow PSSL From: Tom Leinster To: categories@mta.ca Content-Type: text/plain Date: Thu, 06 Apr 2006 16:54:02 +0100 Message-Id: <1144338842.20059.36.camel@tl-linux.maths.gla.ac.uk> Mime-Version: 1.0 Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 32 Dear All, This is a reminder that the 83rd PSSL will take place in Glasgow one month from now, Sat 6th and Sun 7th May. Special attractions: * Jon Woolf will give an introduction to derived categories. In the last decade or so, derived categories have become very important in certain parts of geometry; they now seem to be a standard part of a modern algebraic geometer's toolkit. Jon's introduction will be tailored to category theorists, and won't assume any specialist knowledge. * (an attraction for most): thanks to a brand new law, all of Scotland's pubs, cafes, restaurants, bars, etc are now smoke-free. For information, including the current list of participants and talks, see http://www.maths.gla.ac.uk/~tl/pssl There's no pressing need to register, unless (a) you want to give a talk, or (b) you want to be in the same hotel as other participants. Best wishes, Tom Leinster Richard Steiner From rrosebru@mta.ca Sat Apr 8 11:01:24 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 08 Apr 2006 11:01:24 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FSDuf-0001UH-Pb for categories-list@mta.ca; Sat, 08 Apr 2006 10:55:41 -0300 Mime-Version: 1.0 (Apple Message framework v749.3) Content-Type: text/plain; charset=US-ASCII; delsp=yes; format=flowed Content-Transfer-Encoding: 7bit From: Steve Stevenson Subject: categories: A challenge (Re: Demystifying the categorial approach) Date: Fri, 7 Apr 2006 13:28:17 -0400 To: Categories List Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: RO X-Status: X-Keywords: X-UID: 33 As an outsider, let me say something about outsiders in this. In a word, "Where's the rosetta stone?" Here's what I mean. I'm a numerical analyst/computer scientist. I'm ancient (much older than 50), so I was brought up in the Dark Ages pre-computer, set- theoretic world. So I pick up Walters book, "Categories and computer science" and read it. At the end, I say: OK, how do I work this into my undergraduate classes? graduate classes? They've had discrete math in the Math department and got no introduction to category theory. What does it tell students about designing their current homework program? What does this mechanism tell an undergrad about writing data structures? What does it tell them about performance in networks? I see the point about denotational semantics etc; I know none of our grad students could read Walters. But if you can't retrain undergrads to switch from what they know to a new world, it is not accepted because as grad students they're not going to accept it either. Now you can take a purist view and go your own way and I can go mine. That's kinda silly. Hence, I'd settle for a rosetta stone. Who will help me write an undergraduate text book on classic computability concepts but from a categorical point of view? Pick your favorite text. I suspect it would not be any help to anyone's tenure case because it's all so obvious --- except to outsiders --- but it would be a interesting and perhaps useful pedagogical device. Would such a text be thinner or thicker than the original? What new insights would we receive? best regards, steve -------- D. E. Stevenson, Department of Computer Science Director, Institute for Modeling and Simulation Applications Clemson University, Clemson, SC 29634-0974 864.656.5880 http://www.cs.clemson.edu/~steve On Apr 4, 2006, at 5:49 PM, Ronnie Brown wrote: > I have not been able to keep up with all this correspondence, but > would > like to take up Vaughan Pratt's counter to Reinhard Boerger's point > saying: > `it can't be done' which would be better as a question: `How > should one do > it?' > [balance of quotation omitted...] From rrosebru@mta.ca Sat Apr 8 11:01:24 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 08 Apr 2006 11:01:24 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FSDr7-0001Ld-O7 for categories-list@mta.ca; Sat, 08 Apr 2006 10:52:01 -0300 From: "Oege de Moor" To: Subject: categories: AOSD 2007 Date: Fri, 7 Apr 2006 16:56:00 +0100 Organization: University of Oxford MIME-Version: 1.0 Content-Type: text/plain;charset="us-ascii" Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 34 *** apologies for multiple copies *** AOSD 2007 CALL FOR RESEARCH PAPERS 6th International Conference on Aspect-Oriented Software Development http://www.aosd.net/2007/cfc/research.php AOSD is the premier conference on software modularity that crosscuts traditional abstraction boundaries. It welcomes papers on this topic from all relevant communities, including software engineering, programming languages, type systems, formal methods, as well as applications and experience reports. From rrosebru@mta.ca Mon Apr 10 09:54:27 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 10 Apr 2006 09:54:27 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FSvmf-0002j6-Le for categories-list@mta.ca; Mon, 10 Apr 2006 09:46:21 -0300 Date: Mon, 10 Apr 2006 12:31:25 +0100 From: Georgios Lajios MIME-Version: 1.0 To: categories@mta.ca Subject: categories: SegraVis Advanced School on Visual Modelling Techniques Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: quoted-printable Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 35 [please forward this call to your students and colleagues] The SegraVis Research Training Network invites doctoral students and post-doctoral researchers from both within and outside the network to join the Advanced School on Visual Modelling Techniques Friday Afternoon 08/09/2006 - Monday 11/09/2006 at University of Leicester, United Kingdom http://www.cs.le.ac.uk/events/segravis OBJECTIVES =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D Model-driven approaches to software development require precise definitions for modelling languages, their syntax and semantics, their notions of consistency and refinement, as well as their mappings into implementations. Modelling languages and processes, however, are subject to continuous evolution, and different constellations and dialects are required in different application domains, organisations, and even individual projects. So in order to support model driven development in a variety of contexts, we must find efficient ways of designing languages and processes, accepting that definitions are subject to change and extension and that tools need to be delivered in a timely fashion. Thus, rather than ad-hoc solutions, a discipline of language engineering is required to support the definition and implementation visual modelling languages with respect to their * abstract syntax and well-formedness rules * operational and denotational semantics * consistency and refinement relations * model transformations With this motivation, the objectives of this school are to provide tutorial-like introductions to fundamental techniques supporting the above tasks, to present examples of applications to specific languages and problem domains, and to offer the opportunity for practical experience in applying techniques and tools in sample projects. LECTURE PROGRAM =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D The School marks the closing of the SegraVis network on Syntactic and Semantic Integration of Visual Modelling Techniques. Results of four years of work by its members and close correspondents will be presented through: * introductory lectures * tutorials on fundamental aspects * advanced lectures * application-oriented talks School Speakers and Topics =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D KEYNOTE Stuart Kent: Domain Specific Development: Present & Future LECTURES * Hartmut Ehrig: Algebraic Approach * Gregor Engels: Graph Transformation for Service Specification * Jos=E9 Fiadeiro: A Coordination Language for SOA * Jan Hendrik Hausmann: Semantics of Visual Modelling Techniques * Reiko Heckel: Graph Transformation in a Nutshell * Hans-J=F6rg Kreowski: Advanced Transformation Concepts * Tom Mens: Model-based Software Evolution * Mark Minas: Syntax of Visual Modelling Techniques * Ugo Montanari: Synchronized Hyperedge Replacement: Synchronization Styles for Global Computing * Arend Rensink: Analysis of Graph Transformation-based Models * Grzegorz Rozenberg: DNA Computing * Andy Sch=FCrr: Model Transformations * Gabriele Taentzer: Graph Transformation-based Tools VENUE =3D=3D=3D=3D=3D The School will be held at Beaumont Hall, University of Leicester, United Kingdom. Beaumont Hall is delightfully located within the University Botanic Gardens, providing * Lecture halls, seminar rooms, computer facilities with Internet access for every participant * Optimal working atmosphere and en-suite accommodation More information is available at http://www.le.ac.uk/conferences. APPLICATIONS, NOTIFICATIONS, FEES, ETC. =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D Candidates should fill out the application form provided at http://www.cs.le.ac.uk/events/segravis/applicationform.txt and send it via email to Georgios Lajios (gl51@mcs.le.ac.uk) before May 31, 2006. Notifications of acceptance will be sent out during June. The participation fee, including full board and accomodation for 3 nights= , will be 225 British Pounds (about 325 Euro), approximately. Information on how to register, travel information, etc. shall be given with the notification of acceptance. More information on the objectives, lecture program, applications, etc. can be found at http://www.cs.le.ac.uk/events/segravis/. The Organizers Reiko Heckel and Karsten Ehrig and Georgios Lajios From rrosebru@mta.ca Tue Apr 11 09:05:03 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 11 Apr 2006 09:05:03 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FTHai-0003x8-Am for categories-list@mta.ca; Tue, 11 Apr 2006 09:03:28 -0300 Message-ID: <443A94DD.3090303@cs.stanford.edu> Date: Mon, 10 Apr 2006 10:24:45 -0700 From: Vaughan Pratt MIME-Version: 1.0 To: categories list Subject: categories: Logicians as peaceniks: the early days Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 36 This occurred to me this morning as I was contemplating the differences between the formalist, algebraic, and categorial schools of mathematical reasoning for an encyclopaedia article. Whereas Boolean logic is certainly the logic of sets, Aristotelian logic, especially the syllogisms Barbara and Celarent, would seem to be more that of *-autonomous categories. LOGICIANS AS PEACENIKS: The Early Days Alexander lived a hearty life of dames and kings, While his tutor Aristotle nattered on of names and things. But while Alexander's military followed him to wars, Aristotle's syllogisms followed from his laws. Darius and Alexander fought a mighty war. The likes of such an argument had not been seen before. But by Barbara and Celarent did Aristotle swear As the mistresses of argument that never hurt a hair. Vaughan Pratt, 4/10/06 From rrosebru@mta.ca Tue Apr 11 09:05:03 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 11 Apr 2006 09:05:03 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FTHWT-0003jU-MR for categories-list@mta.ca; Tue, 11 Apr 2006 08:59:05 -0300 Date: Mon, 10 Apr 2006 16:30:22 +0100 From: Bob Coecke To: categories@mta.ca Subject: categories: Cats, Kets and Cloisters, Oxford University, July 17-23 (2006) Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Disposition: inline Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 37 This summer several workshops will take place July 17-23 (2006) at Oxford University: * NEW MODELS OF QUANTUM INFORMATICS * AXIOMATICS FOR QUANTUM MECHANICS * TENSORS KNOTS AND BRAIDS IN LOGIC AND PHYSICS * QUANTUM PROGRAMING LANGUAGES (QPL IV) The whole event will take place under the name ``CATS, KETS and CLOISTERS'': * http://se10.comlab.ox.ac.uk:8080/FOCS/CKCinOXFORD_en.html [SURVEYS/TUTORIALS:] Each workshop will include tutorial and/or survey talks. Preliminary informal contacts concerning have confirmed several people willing to provide these survey/tutorial lectures, including Samson Abramsky (Oxford), Richard Jozsa (Bristol) and Sam Lomonaco Jr (UMBC), among others. Topics under consideration include: measurement-based quantum computation, topological quantum computation, simulations of quantum computations, knots and braids in logic, quantum geometry and topology, categorical algebra for quantum mechanics, and semantics for quantum computing. [CALL FOR CONTRIBUTIONS:] The call for QPL IV is available at: * http://www.mathstat.dal.ca/~selinger/qpl2006/ We invite you to propose contributions for the three other workshops, either by submitting a short description, short abstract, extended abstract or full paper. These contributions will then be considered by the Program Committee: Jens Eisert (Imperial College, UK) Richard Jozsa (University of Bristol, UK) Samuel Lomonaco Jr. (UMBC, Maryland, US) Prakash Panangaden (McGill University, CA) Phil Scott (University of Ottawa, CA) Samson Abramsky (University of Oxford, UK) Bob Coecke (University of Oxford, UK) Relevant proposals for surveys/tutorials are also still welcome. Preference will be given to talks which are accessible beyond the boundaries of the distinct workshops. The three workshops should indeed be conceived as ``themes'' within a bigger event. Slots will be allocated to speakers to some extend on a first-come-first-serve base, subject to a quality check and ``sufficiently broad relevance'' check by the PC. Please send your contributions to: * bob.coecke@comlab.ox.ac.uk [POSTER SESSION:] Students and other young researchers in particular are encouraged to propose posters, which will be displayed in the workshop area throughout the whole event, and to which a session will be dedicated. [PRACTICALITIES:] The local organizing committee consists of: Samson Abramsky (Computing) Dan Browne (Physics) Bob Coecke (Computing) Hilary Priestley (Mathematics) Oxford is a pleasant place to visit during the summer, with many things to see (including London, only an hour by train), and a wealth of tourist attractions and beautiful country-side conveniently accessible. * http://www.oxfordcity.co.uk/ Oxford has a wide variety of places to stay, including both junior and senior College Accomodation, Hotels, Hostels, and Bed and Breakfasts (B&Bs) and Guest Houses. We would in particular recommend the B&Bs and Guest Houses since they tend to be much cheaper than hotels, and the British breakfast keeps you going for the whole day. For detailed information concerning accommodation in Oxford please consult: * http://se10.comlab.ox.ac.uk:8080/FOCS/Where_to_stay_en.html For traveling to Oxford please consult: * http://se10.comlab.ox.ac.uk:8080/FOCS/Where_to_go_en.html From rrosebru@mta.ca Tue Apr 11 09:05:03 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 11 Apr 2006 09:05:03 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FTHYX-0003ql-Mj for categories-list@mta.ca; Tue, 11 Apr 2006 09:01:13 -0300 Subject: categories: CT2006 List of Talks and Call for Participation To: categories@mta.ca (Categories List) Date: Mon, 10 Apr 2006 18:44:23 -0300 (ADT) MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit From: selinger@mathstat.dal.ca (Peter Selinger) Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 38 New in this announcement: - list of accepted talks - accommodations deadline reminder: April 20 LIST OF SPEAKERS AND CALL FOR PARTICIPATION International Category Theory Conference CT 2006 including a special commemorative session on the works of Mac Lane and Eilenberg June 25 - July 1, 2006 White Point, Nova Scotia http://www.mathstat.dal.ca/~selinger/ct2006/ * * * The International Category Theory Conference (CT) covers all areas of pure and applied category theory. CT 2006 will be held at White Point Beach Resort (http://www.whitepoint.com/), a seaside resort in Nova Scotia (Canada), about 100 minutes' drive from Halifax. All those interested in category theory and its applications are welcome to attend the conference. Participants should register by April 20. The current list of speakers appears below. A preliminary program is posted on the conference website. Please book your accommodations by *** APRIL 20 ***. INVITED SPEAKERS: Kathryn Hess (EPF Lausanne) Steve Lack (University of Western Sydney) Tom Leinster (University of Glasgow) Steve Schanuel (SUNY Buffalo) Peter Selinger (Dalhousie University) SPECIAL SESSION ON THE WORKS OF MAC LANE AND EILENBERG: Peter Freyd, "New structures on old categories" Bill Lawvere, "TBA" Walter Tholen, "Mac Lane and Factorizations" CONTRIBUTED TALKS: Jiri Adamek, "Iterative Algebras and Iterative Monads" Richard Blute, "Deep Inference and Probabilistic Coherence Spaces" Dominique Bourn, "Homological properties of the categories of Hausdorff groups and Hausdorff semi-abelian algebras" Ronnie Brown, "Applications of crossed complexes" Eugenia Cheng, "Towards an n-category of cobordisms" Jeff Egger, "The Frobenius relations meet linear distributivity" Josep Elgueta, "2-categories of representations of a 2-group" Thomas M. Fiore, "Double Categories and Pseudo Algebras" Stefan Forcey, "A categorification of the associahedra: combinatorics, realizations and weak enrichment" Emmanuel Galatoulas, "Towards an interpretation of Quantum Mechanics from a bicategorical point of view" Marino Gran, "Torsion theories and Galois coverings of topological groups" Marco Grandis, "Fundamental lax 2-categories in Directed Algebraic Topology" Nick Gurski, "Algebraifying tricategories" Michael J. Healy, "Applying Category Theory to Improve the Performance of a Neural Architecture" Michel Hebert, "A Completeness Theorem for Injectivity Logic" Dirk Hofmann, "Lax algebraic theories and closed objects" Pieter Hofstra, "The category of realizability toposes" John Iskra, "Smoothness in Zariski Categories" Mike Johnson, "Constant complements, reversibility and universal view updates" Toby Kenney, "Injective Power Objects and the Axiom Of Choice" Robert E. Kent, "The information flow framework: New architecture" Juergen Koslowski, "Simulations as a genuinely categorical concept" Bill Lawvere, "Axiomatic theory of cohesive space" Gabor Lukacs, "Non-commutative k-spaces" Michael Makkai, "Higher dimensional diagrams via computads" J. Martinez-Moreno, "The actor of a categorical crossed module" Matias Menni, "Combinatorial functional and differential equations applied to differential posets" Stefan Milius, "Recursive coalgebras" Jeffrey Morton, "Higher Dimensional Algebra and Quantum Mechanics" Susan Niefield, "Biexponentiability in Homotopy Slices of Top" Matt Noonan, "Differential Geometry on Categories" Thorsten Palm, "Categories with slicing" Elango Panchadcharam, "Mackey functors and Green functors" Simona Paoli, "Semistrict models of connected 3-types and Tamsamani's weak 3-groupoids" Robert Pare, "Spans for 2-categories" Claudio Pisani, "On the reflection and the coreflection of categories over a base in discrete fibrations" Dorette Pronk, "The Path-ology of Double Categories" Jiri Rosicky, "Homotopy varieties" Luigi Santocanale, "Properties of Free Sigma-Pi Categories" Robert Seely, "Differential Categories" Lurdes Sousa, "A complete orthogonality logic" Richard Steiner, "Omega-categories and chain homotopies" Isar Stubbe, "Q-modules are Q-suplattices" Paul Taylor, "On the Reaxiomatisation of General Topology" Myles Tierney, "Quasi-categories can model homotopy theories" Christine Vespa, "The functor category F_quad associated to quadratic spaces over F_2" Enrico Vitale, "Derivations of internal groupoids" Mark Weber, "2-toposes and higher dimensional algebra" Derek Wise, "Chain field theory" Richard Wood, "Cartesian Bicategories II" Joao J. Xarez, "Galois theories of internal groupoids via congruence relations for Maltsev varieties" Noson S. Yanofski, "Towards a Definition of an Algorithm" Marek Zawadowski, "Combinatorial description of positive multitopes" REGISTRATION The registration fees for CT 2006 are as follows: $150 - regular $100 - reduced (students, postdocs, and researchers without grant) The early registration rates ($120/$75 for those who registered before March 1) have now expired. Please register by April 20 at: https://sigma.mathstat.dal.ca/~selinger/ct2006/registration.php ARRIVAL AND DEPARTURE: Arrival date: Sunday, June 25 Departure date: Saturday, July 1 Opening reception: Sunday, June 25, 6:30-10:30pm. The normal check-in time is 2pm and check-out time is 11am. If you need to make special arrangements for early arrival or late departure, please make them by contacting White Point directly. Subject to availability, White Point Beach Resort has agreed to extend the conference rates to the weeks before and after the conference in case any guests wish to stay longer. If you would like to arrange this, please contact White Point directly. AIRPORT TRANSPORTATION: We will arrange for shared transportation between Halifax International Airport and White Point Beach Resort on the days of arrival and departure (June 25 and July 1), at no extra charge to conference participants and their guests. To take advantage of this, please let us know, at ct06@mathstat.dal.ca, your arrival and departure times, airline, and flight numbers, as soon as you have this information. Please note that White Point Beach Resort is 150km from the airport, and there is no convenient alternative transportation available except for renting a car. ACCOMMODATIONS (deadline: April 20): The conference venue offers a choice of accommodation, both in comfortable finished cabins and in "hotel-style" rooms. All meals are included in the price of the rooms. For reservations, please contact White Point Beach Resort: Tel: 1-800-565-5068 (U.S. and Canada) Tel: +1-902-354-2711 (international) Fax: +1-902-354-7278 Email reservations: greatday@whitepoint.com Rooms must be booked by *** APRIL 20 *** to be guaranteed availability. IMPORTANT DATES: Apr 20, 2006: room booking deadline Apr 20, 2006: cancellation of registrations Jun 25, 2006: arrival date, opening reception 6:30pm Jun 26, 2006: conference starts at 9am Jul 1, 2006: departure date, conference ends at 1pm SCIENTIFIC COMMITTEE: Jiri Adamek John Baez Michael Barr Eugenia Cheng Maria Manuel Clementino Marcelo Fiore Peter Freyd Jonathon Funk Peter Johnstone Steve Lack Susan Niefield Phil Scott Ross Street Walter Tholen (chair) Enrico Vitale ORGANIZERS: Robert Dawson (rdawson@cs.stmarys.ca) Dorette Pronk (pronk@mathstat.dal.ca) Peter Selinger (selinger@mathstat.dal.ca) CONFERENCE EMAIL AND WEBSITE: ct06@mathstat.dal.ca http://www.mathstat.dal.ca/~selinger/ct2006/ From rrosebru@mta.ca Tue Apr 11 09:21:08 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 11 Apr 2006 09:21:08 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FTHqj-00054j-EG for categories-list@mta.ca; Tue, 11 Apr 2006 09:20:01 -0300 MIME-Version: 1.0 Content-Type: text/plain;charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Subject: categories: Re: A challenge (Re: Demystifying the categorical approach) Date: Tue, 11 Apr 2006 08:02:38 -0400 From: "Wojtowicz, Ralph" To: categories@mta.ca Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: RO X-Status: X-Keywords: X-UID: 39 > Steve Stevenson wrote: >As an outsider, let me say something about outsiders in this. >In a word, "Where's the rosetta stone?" >From my experience, "Conceptual Mathematics" by Lawvere and Schanuel can serve as a Rosetta stone for undergraduate students interested in dynamic systems. I had the opportunity to use "Conceptual Mathematics" as a reference in an upper-level applied math class at the University of Dallas. Sample course materials are available at: http://www.adjoint-functors.net/teaching/notes1.pdf http://www.adjoint-functors.net/teaching/exam1.pdf http://www.adjoint-functors.net/teaching/quiz3.pdf http://www.adjoint-functors.net/teaching/lifeS.pdf Lawvere's definitions of symbolic dynamics and chaos were of particular interest to the students and to me. I found that categorical ideas also provided useful exercises and organization into an analysis course I taught using Rudin's "Principles of Mathematical Analysis". The following notes provide examples: page 8 of http://www.adjoint-functors.net/teaching/rudin1.pdf pages 1--7 and 11 of http://www.adjoint-functors.net/teaching/rudin2.pdf pages 2--6, 8, 10--12, and 16 of http://www.adjoint-functors.net/teaching/rudin4.pdf There are many other opportunities to introduce categorical notions throughout the course perhaps using material from "Sets for Mathematics" by Lawvere and Rosebrugh. As a graduate student, I found that "Conceptual Mathematics" clarified concepts from dynamic systems theory and provided insights into Lawvere's categorical dynamics program and into the core literature on dynamic systems. See http://www.adjoint-functors.net/aipcasys2.pdf and the references cited. For applications to computer science, recent papers by Katis, Rosebrugh, and Walters have applications to concurrency; provide categorical definitions of transition systems, bisimulation, and related concepts; and clarify the treatment of those topics in the books by Arnold and by Clarke, et al. Although not in textbook form, some of these articles are accessible to undergraduates. Model-checking and automatic software verification researches get considerable financial support=20 from U.S. government sponsors (see http://www.sba.gov/SBIR). Another Rosetta stone for students interested in computer science is the literature on sketch-based data models. Papers by Johnson, Piessens, Rosebrugh, Steegmans, and others are accessible to advanced undergraduates with faculty guidance. Interoperability of information systems is also a focus area of the sponsors mentioned above. In a previous e-mail, Peter Selinger suggested that "[categorical research with applications to physics] is supported because it is original, timely, and interesting". Since taking a non-academic position, I have found that the novelty of category-based proposals does get the attention of sponsors looking for new ideas (although I have not submitted any proposals for physics research). In seeking applications of categories to new areas, we are fortunate to already have a theory of such great depth. How would thermodynamics be taught now if Truesdell had been born 100 years earlier? I will be eager to purchase an undergraduate text on computability concepts from a categorical perspective. A few years ago I spent time trying to learn this material from Soare's text without much success. Sincerely, Ralph Wojtowicz Metron, Inc. 11911 Freedom Drive, Suite 800 Reston, VA=A0 20190-5602 wojtowicz@metsci.com From rrosebru@mta.ca Tue Apr 11 16:03:08 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 11 Apr 2006 16:03:08 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FTO4u-00061D-Ge for categories-list@mta.ca; Tue, 11 Apr 2006 15:59:04 -0300 Date: Tue, 11 Apr 2006 15:36:46 +0200 From: vigano@inf.ethz.ch To: categories@mta.ca Subject: categories: 2nd CFP: FCS-ARSPA'06 (Workshop on Foundations of Computer Security and Automated Reasoning for Security Protocol Analysis) Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Disposition: inline Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 40 apologies for multiple copies ****************************************** *** NEW: post-workshop Special Issue *** *** of Information and Computatation *** ****************************************** ************************ **** **** **** FCS-ARSPA'06 **** **** **** ************************ A LICS'06 (and FLoC'06) Affiliated Workshop on FOUNDATIONS OF COMPUTER SECURITY and AUTOMATED REASONING FOR SECURITY PROTOCOL ANALYSIS Seattle, Washington, August 15-16, 2006 http://www.inf.ethz.ch/~vigano/fcs-arspa06 *********************** *** CALL FOR PAPERS *** *********************** Submission deadline: May 10, 2006 BACKGROUND, AIM AND SCOPE ========================= Computer security is an established field of computer science of both theoretical and practical significance. In recent years, there has been increasing interest in logic-based foundations for various methods in computer security, including the formal specification, analysis and design of security protocols and their applications, the formal definition of various aspects of security such as access control mechanisms, mobile code security and denial-of-service attacks, and the modeling of information flow and its application to confidentiality policies, system composition, and covert channel analysis. The workshop FCS-ARSPA'06 is the fusion of two workshops. The workshop FCS continues a tradition, initiated with the Workshops on Formal Methods and Security Protocols (FMSP) in 1998 and 1999, then with the Workshop on Formal Methods and Computer Security (FMCS) in 2000, and finally with the LICS satellite Workshop on Foundations of Computer Security (FCS) in 2002 through 2005, of bringing together formal methods and the security community. The ARSPA workshop is the third in a series of workshops on Automated Reasoning for Security Protocol Analysis, bringing together researchers and practitioners from both the security and the formal methods communities, from academia and industry, who are working on developing and applying automated reasoning techniques and tools for the formal specification and analysis of security protocols. The first two ARSPA workshops were held as satellite events of IJCAR'04 and of ICALP'05, respectively. The aim of the joint workshop FCS-ARSPA'06 is to provide a forum for continued activity in these areas, to bring computer security researchers in closer contact with the LICS community, and to give LICS attendees an opportunity to talk to experts in computer security. We thus solicit submissions of papers both on mature work and on work in progress. We are interested both in new results in theories of computer security and also in more exploratory presentations that examine open questions and raise fundamental concerns about existing theories, as well as in new results on developing and applying automated reasoning techniques and tools for the formal specification and analysis of security protocols. Possible topics include, but are not limited to: Automated reasoning techniques Access control and resource usage control Composition issues Authentication Formal specification Availability and denial of service Foundations of verification Covert channels Information flow analysis Confidentiality Language-based security Integrity and privacy Logic-based design for Intrusion detection Program transformation Malicious code Security models Mobile code Static analysis Mutual distrust Statistical methods Privacy Tools Security policies Trust management Security protocols All submissions will be peer-reviewed. Authors of accepted papers must guarantee that their paper will be presented at the workshop. SUBMISSION ========== Submissions should be at most 15 pages (a4paper, 11pt), including references, in the Springer LNCS style available at the URL http://www.springer.de/comp/lncs/authors.html The cover page should include title, names of authors, co-ordinates of the corresponding author, an abstract, and a list of keywords. It is recommended that submissions adhere to the specified format and length. Submissions that are clearly too long may be rejected immediately. Additional material intended for the referees but not for publication in the final version - for example details of proofs - may be placed in a clearly marked appendix that is not included in the page limit. Simultaneous submissions to a journal or another conference are accepted. Authors are invited to submit their papers electronically, as portable document format (pdf) or postscript (ps); please, do not send files formatted for work processing packages (e.g., Microsoft Word or Wordperfect files). The only mechanism for paper submissions is via the electronic submission web-site (which will soon be available). IMPORTANT DATES =============== Papers due: May 10, 2006 Notification of acceptance: June 16, 2006 Final paper versions due: July 14, 2006 Workshop: August 15-16, 2006 PUBLICATION =========== Informal proceedings will be made available in electronic format and they will be distributed to all participants of the workshop. Moreover, workshop participants will be invited to submit full versions of their papers to a special issue of Information and Computation, which will be open also to non-participants, in all cases with fresh reviewing. INVITED TALKS ============= To be announced PROGRAM COMMITTEE ================= * Alessandro Armando (Universita` di Genova, Italy) * Jorge R. Cuellar (SIEMENS AG, Munich, Germany) * Anupam Datta (Stanford University, USA) * Pierpaolo Degano (Universita` di Pisa, Italy; co-chair) * Pablo Giambiagi (Swedish Institute of Computer Science, Sweden) * Virgil Gligor (University of Maryland, USA) * Roberto Gorrieri (Universita` di Bologna, Italy) * Carl A. Gunter (University of Illinois at Urbana-Champaign, USA) * Joshua Guttman (Mitre, USA) * Ralf Kuesters (Christian-Albrechts-Universitaet zu Kiel, Germany; co-chair) * Ninghui Li (Purdue University, USA) * Sjouke Mauw (University of Eindhoven, The Netherlands) * Peter Ryan (University of Newcastle, UK) * Luca Vigano` (ETH Zurich, Switzerland; co-chair) * Laurent Vigneron (INRIA-LORRAINE, Nancy, France) * Bogdan Warinschi (INRIA-LORRAINE, Nancy, France) * Steve Zdancewic (University of Pennsylvania, USA; co-chair) FCS Steering Committee: * Martin Abadi (University of California at Santa Cruz, USA) * Joshua Guttman (MITRE, USA) * John Mitchell (Stanford University, USA) * Andrei Sabelfeld (Chalmers, Sweden; chair) * Andre Scedrov (University of Pennsylvania, USA) ADDITIONAL INFORMATION ====================== Information about registration, travel, and venue can be found at the LICS'06 and FLoC'06 web-sites. For further information send an email to the workshop co-chairs at fcs-arspa06 -at- lists.inf.ethz.ch From rrosebru@mta.ca Tue Apr 11 16:03:08 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 11 Apr 2006 16:03:08 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FTO6z-0006Fm-7G for categories-list@mta.ca; Tue, 11 Apr 2006 16:01:13 -0300 Date: Tue, 11 Apr 2006 09:51:57 -0400 From: jim stasheff User-Agent: Thunderbird 1.5 (Windows/20051201) MIME-Version: 1.0 To: categories@mta.ca Subject: categories: Re: A challenge (Re: Demystifying the categorical approach) Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 41 F. Scott Williams has similar praise for "Conceptual Mathematics" by Lawvere and Schanuel in the latest NAM newsletter and for an even broader range of students. jim Wojtowicz, Ralph wrote: >> Steve Stevenson wrote: >> As an outsider, let me say something about outsiders in this. >> In a word, "Where's the rosetta stone?" > >>From my experience, "Conceptual Mathematics" by Lawvere and Schanuel > can serve as a Rosetta stone for undergraduate students interested > in dynamic systems. I had the opportunity to use "Conceptual > Mathematics" as a reference in an upper-level applied math class > at the University of Dallas. Sample course materials are available at: > http://www.adjoint-functors.net/teaching/notes1.pdf > http://www.adjoint-functors.net/teaching/exam1.pdf > http://www.adjoint-functors.net/teaching/quiz3.pdf > http://www.adjoint-functors.net/teaching/lifeS.pdf > Lawvere's definitions of symbolic dynamics and chaos were of > particular interest to the students and to me. [balance of quotation omitted...] From rrosebru@mta.ca Tue Apr 11 16:03:08 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 11 Apr 2006 16:03:08 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FTO7y-0006MQ-9Q for categories-list@mta.ca; Tue, 11 Apr 2006 16:02:14 -0300 Date: Tue, 11 Apr 2006 17:59:09 +0100 From: Conor McBride User-Agent: Mozilla Thunderbird 1.0.2 (Macintosh/20050317) X-Accept-Language: en-us, en MIME-Version: 1.0 To: categories@mta.ca Subject: categories: Deadline Extension: Mathematically Structured Functional Programming Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 42 Deadline Extension: Mathematically Structured Functional Programming +*->+*->+*->+*->+*->+*->+*->+*->+*->+*->+*->+*->+*->+*->+*->+*->+*->+*->+*-> DEADLINE-EXTENSION-DEADLINE-EXTENSION-DEADLINE-EXTENSION-DEADLINE-EXTENSION Workshop on Mathematically Structured Functional Programming http://cs.ioc.ee/mpc-amast06/msfp/ New deadlines: 17 April (abstracts); 21 April (papers) DEADLINE-EXTENSION-DEADLINE-EXTENSION-DEADLINE-EXTENSION-DEADLINE-EXTENSION +*->+*->+*->+*->+*->+*->+*->+*->+*->+*->+*->+*->+*->+*->+*->+*->+*->+*->+*-> We're delighted to be able to extend the deadline for MSFP 2006. The Workshop on Mathematically Structured Functional Programming will be held in Kuressaare, Estonia, on 2 July 2006, with invited speakers Andrzej Filinski and John Power. MSFP 2006 is a satellite workshop of MPC 2006 and a "small workshop" of the TYPES project. MSFP is about organizing functional programs more effectively with the aid of mathematical structures from semantics and elsewhere. The proceedings of MSFP 2006 will be published in the Electronic Workshops in Computing (eWiC) series of the British Computer Society. After the workshop, the authors of the best papers will be invited to submit revised and expanded versions to a special issue of the Journal of Functional Programming from Cambridge University Press. We look forward to hearing from you Conor McBride Tarmo Uustalu From rrosebru@mta.ca Thu Apr 13 21:31:10 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 13 Apr 2006 21:31:10 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FUC1n-00021I-UX for categories-list@mta.ca; Thu, 13 Apr 2006 21:19:11 -0300 To: categories@mta.ca Subject: categories: MPC/AMAST 2006 Call for Participation Mime-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable Date: Thu, 13 Apr 2006 13:20:16 +0300 From: Tarmo Uustalu Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: RO X-Status: X-Keywords: X-UID: 43 NEWS: = - Registration is now open. - Early registration is until 15 May 2006. Accommodation in the conference hotels is only guaranteed until this = date. CALL FOR PARTICIPATION 8th International Conference on = Mathematics of Program Construction MPC '06 11th International Conference on = Algebraic Methodology and Software Technology AMAST '06 Kuressaare, Estonia, 2-8 July 2006 http://cs.ioc.ee/mpc-amast06/ Following on from the successful joint conference AMAST/MPC 2004 at Stirling, UK, 2004, the two biennial conferences on mathematical methods in software technology are colocating also in 2006. The joint event will take place in Kuressaare, Estonia, in early July. A perfect place and time to enjoy the Nordic white nights - at 58=B0 N in the midsummer season. MPC will be held 3-5 July, followed by AMAST 5-8 July. = Two satellite workshops of MPC, the 5th International Workshop on Contructive Methods for Parallel Programming, CMPP 2006, and Workshop on Mathematically Structured Functional Programming, MSFP 2006 = will take place 2 July. Important dates = Early registration: 15 May 2006 Late registration: 5 June 2006 MPC invited speakers Robin Cockett, University of Calgary Olivier Danvy, Aarhus Universitet Oege de Moor, University of Oxford AMAST invited speakers Ralph-Johan Back, =C5bo Akademi University Lawrence S. Moss, Indiana University Till Mossakowski, Universit=E4t Bremen MPC and AMAST accepted paper lists appear on the conference website. PC lists appear on the conference website. Important dates = * Early registration: 15 May 2006 * Late registration: 5 June 2006 Registration Registration is now open. Registration, accommodation and travel information are available on the conference website. To register, please fill out the online registration form. = Booking of accommodation at Kuressaare is handled by the local organization. Accommodation in one of the conference hotels is = only guaranteed until the early registration deadline of 15 May. = After this date, we will do what we can, but Kuressaare is a small = town and July is in the peak season. Venue Kuressaare (pop. 16000) is the main town on Saaremaa (=D6sel), the second-largest island of the Baltic Sea. Kuressaare is a charming seaside resort on the shores of the Gulf of Riga highly popular with Estonians as well as visitors to Estonia. The scientific sessions of MPC/AMAST 2006 will take place at Saaremaa Spa Hotel Meri, one among the several new spa hotels in the town. The social events will involve a number of sites, including the 14th-century episcopal castle and the impact craters of Kaali. Accommodation will be at Saaremaa Spa Hotels Meri and R=FC=FCtli. To get to Kuressaare, one normally passes through Tallinn (pop. 402000), Estonia's capital city. Tallinn is famous for its picturesque medieval Old Town, inscribed on UNESCO's World Heritage List. =46rom Tallinn, Kuressaare is easily reached by scheduled coach (incl. a ferry ride). We may arrange chartered coaches from Tallinn to Kuressaare and back both for MPC and AMAST, but this depends on the demand. There are also twice-daily flights to Kuressaare from Tallinn and twice-weekly direct flights from Helsinki and Stockholm. Local organizers MPC/AMAST 2006 is organized by Institute of Cybernetics, a research institute of Tallinn University of Technology. Contact email address: mpc06(at)cs.ioc.ee. From rrosebru@mta.ca Fri Apr 14 11:16:28 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 14 Apr 2006 11:16:28 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FUP1L-0000Zm-N8 for categories-list@mta.ca; Fri, 14 Apr 2006 11:11:35 -0300 Date: Fri, 14 Apr 2006 10:17:46 +0200 From: Computer Science Logic '06 Conference MIME-Version: 1.0 To: categories@mta.ca Subject: categories: CSL'06 CALL FOR PAPERS [final version] Content-Type: text/plain; charset=ISO-8859-2; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 45 ********************************************************************** * CSL'06 * * Annual Conference of the European Association for * * Computer Science Logic * * September 25 -- 29, 2006, Szeged, Hungary * * http://www.inf.u-szeged.hu/~csl06/ * * CALL FOR PAPERS * ********************************************************************** Computer Science Logic (CSL) is the annual conference of the European Association for Computer Science Logic (EACSL). The conference is intended for computer scientists whose research activities involve logic, as well as for logicians working on issues significant for computer science. CSL'06, the 15th annual EACSL conference will be organized by the Institute of Informatics, University of Szeged. Suggested topics of interest include: automated deduction and interactive theorem proving, constructive mathematics and type theory, equational logic and term rewriting, automata and formal logics, modal and temporal logic, model checking, logical aspects of computational complexity, finite model theory, computational proof theory, logic programming and constraints, lambda calculus and combinatory logic, categorical logic and topological semantics, domain theory, database theory, specification, extraction and transformation of programs, logical foundations of programming paradigms, verification of security protocols, linear logic, higher-order logic, nonmonotonic reasoning, logics and type systems for biology. Programme Committee: Invited speakers: Krzysztof Apt(Amsterdam/Singapore) Martin Escardo (Birmingham) Matthias Baaz (Vienna) Paul-Andre Mellies (Paris) Michael Benedikt (Chicago) Luke Ong (Oxford) Pierre-Louis Curien (Paris) Luc Segoufin (Orsay) Rocco De Nicola (Florence) Miroslaw Truszczynski(Lexington,KY) Zoltan Esik (Szeged, chair) Dov Gabbay (London) Fabio Gadducci (Pisa) Organizing Committee: Neil Immerman (Amherst) Michael Kaminski (Haifa) Zoltan Esik (Szeged, co-chair) Bakhadyr Khoussainov (Auckland) Zsolt Gazdag (Szeged) Ulrich Kohlenbach (Darmstadt) Eva Gombas (Szeged, co-chair) Marius Minea (Timisoara) Szabolcs Ivan (Szeged) Damian Niwinski (Warsaw) Zsolt Kakuk (Szeged) R. Ramanujam (Chennai) Lorand Muzamel (Szeged) Philip Scott (Ottawa) Zoltan L. Nemeth (Szeged) Philippe Schnoebelen (Cachan) Sandor Vagvolgyi Alex Simpson (Edinburgh) (Szeged, workshop-chair) Proceedings will be published in the LNCS series. Each paper accepted by the Programme Committee must be presented at the conference by one of the authors, and final copy prepared according to Springer's guidelines. Submitted papers must be in Springer's LNCS style and of no more than 15 pages, presenting work not previously published. They must not be submitted concurrently to another conference with refereed proceedings. The PC chair should be informed of closely related work submitted to a conference or journal by 1 April, 2006. Papers authored or coauthored by members of the Programme Committee are not allowed. Submitted papers must be in English and provide sufficient detail to allow the Programme Committee to assess the merits of the paper. Full proofs may appear in a technical appendix which will be read at the reviewer's discretion. The title page must contain: title and author(s), physical and e-mail addresses, identification of the corresponding author, an abstract of no more than 200 words, and a list of keywords. The submission deadline is in two stages. Titles and abstracts must be submitted by 24 April, 2006 and full papers by 1 May, 2006. Notifications of acceptance will be sent by 12 June, 2006, and final versions are due 3 July, 2006. A submission server will be available from 15 March, 2006. The Ackermann Award for 2006 will be presented to the recipients at CSL'06. Important Dates: Submission - title & abstract: 24 April, 2006 - full paper: 1 May, 2006 Notification: 12 June, 2006 Final papers: 3 July, 2006 Conference address: CSL'06 c/o Prof. Zoltan Esik Institute of Informatics, University of Szeged H-6701, Szeged, P.O.B. 652, Hungary web site: http://www.inf.u-szeged.hu/~csl06/ e-mail: csl06@inf.u-szeged.hu phone: +36-62-544-289 or +36-62-544-205 fax: +36-62-544-895 or +36-62-546-397 ********************************************************************** ********************************************************************** From rrosebru@mta.ca Fri Apr 14 11:16:28 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 14 Apr 2006 11:16:28 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FUP1u-0000bj-Rj for categories-list@mta.ca; Fri, 14 Apr 2006 11:12:10 -0300 To: LiCS 2006 List From: Kreutzer + Schweikardt Subject: categories: LICS 2006 Call for Short Presentations Date: Fri, 14 Apr 2006 14:30:39 +0200 (CEST) Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: RO X-Status: X-Keywords: X-UID: 46 CALL FOR SHORT PRESENTATIONS Twenty-First Annual IEEE Symposium on LOGIC IN COMPUTER SCIENCE (LICS 2006) August 12th - 15th, 2006, Seattle, Washington http://www.informatik.hu-berlin.de/lics/lics06/ The LICS Symposium is an annual international forum on theoretical and practical topics in computer science that relate to logic broadly construed. LICS 2006 will be organized as part of the Fourth Federated Logic Conference (FLoC 2006) to be held in Seattle from August 10 to August 22, 2006. Visit http://research.microsoft.com/floc06/ for information regarding FLoC 2006 and the participating meetings. As in the previous LICS meetings, LICS 2006 will have a session of short (5-10 minutes) presentations. This session is intended for descriptions of work in progress, student projects, and relevant research being published elsewhere; other brief communications may be acceptable. Submissions for these presentations, in the form of short abstracts (1 or 2 pages long in IEEE 2-column style file), should be entered at the LICS 2006 submission site by 21st April 2006 (see the LICS 2006 homepage for submission instructions). Authors will be notified of acceptance or rejection by 28th April 2006. From rrosebru@mta.ca Sun Apr 16 16:31:21 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 16 Apr 2006 16:31:21 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FVCpH-0000S9-S2 for categories-list@mta.ca; Sun, 16 Apr 2006 16:22:27 -0300 Date: Sun, 16 Apr 2006 13:23:44 -0400 From: jim stasheff MIME-Version: 1.0 To: Categories List Subject: categories: [Fwd: du Sautoy] Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 47 with or without proofs? a worthwhile activity -------- Original Message -------- Subject: du Sautoy Date: Sat, 15 Apr 2006 14:49:02 -0400 (EDT) From: Peter Freyd To: MathPeople@saul.cis.upenn.edu Most people's idea of what I do as a research mathematician is long division to lots of decimal places. But fundamentally, mathematics isn't about numbers - it's about finding structure and logic and connections that help us negotiate the complex world we live in. Copyright 2006 TSL Education Limited The Times Higher Education Supplement April 14, 2006 SECTION: OPINION; No.1738; Pg.14 LENGTH: 831 words HEADLINE: Scales Fall Short Of Grand Symphonies In Maths BYLINE: Marcus du Sautoy BODY: Pique children's interest in maths with elegant epics, enigmatic mysteries and cold hard cash, says Marcus du Sautoy. World pi Day was marked at 1:59 on March 14 - 3.14159 being the beginning of the decimal expansion of pi. Although I am appreciative of any publicity mathematics can get, I found that most people were interested in how many decimal places I knew of this important number. They were disappointed that five was my limit. To me, that response revealed the deep misconception people have of what mathematics is really about. Most people's idea of what I do as a research mathematician is long division to lots of decimal places. But fundamentally, mathematics isn't about numbers - it's about finding structure and logic and connections that help us negotiate the complex world we live in. The belief that mathematics is no more than long division is fuelled by the way most pupils are taught the subject at school. Imagine a student learning a musical instrument by playing only scales and arpeggios and never even hearing a symphony. No one would judge them for giving up. Yet all too often in pupils' mathematical education, this is all they are exposed to. Pupils I talk to are surprised to learn that there are complex mathematical equations controlling the evolution of their PlayStation games or that the sine waves that they learn about in trigonometry are the building blocks used by their MP3 players to recreate the sound of the Arctic Monkeys in their headphones. Practical applications are a powerful way to awaken people to the importance of the subject. But beauty and elegance can also attract many to the subject. It is the great stories of mathematics, many of them unfinished, that I believe have the potential to capture pupils' imaginations when they doubt the value of mathematics. Therefore, it is the responsibility of those who create these stories, the research mathematicians, to bring the subject alive. There is no escaping the hard graft of doing your arithmetic scales and arpeggios. But if these are set in the context of the big mathematical symphonies they help write, students may feel more inclined to apply themselves. The story of the primes is one of the sagas that I have found can pull young people on to the mathematical bandwagon. They are the building blocks of all numbers. And as you play with them, they very soon draw you into one of our biggest mathematical mystery stories. The great challenge is to understand how nature chose these enigmatic numbers. The search for a pattern behind the primes goes to the heart of what it means for me to be a mathematician. Yet intriguingly, our subject seems to be built out of numbers with no patterns to them at all. The biggest prime we know has more than 9 million digits - a number that would take more than a month and a half to read aloud. But bigger primes will always be discovered - there is a prize of $100,000 (Pounds 57,000) waiting for the first person to break the 10 million digit mark. The records to date are not held by boffins with big computers but amateurs with desktops. Money is a great incentive for getting kids' eyes to light up. And one can use it to introduce the deeper meaning behind the headline. Once they have won $100,000, then they can move on to the million-dollar prize of finding the underlying structure that makes these numbers tick, which involves solving the Riemann hypothesis. The National Centre for Excellence in Teaching Mathematics, to be launched in May, has the potential to communicate some of the big stories of mathematics to teachers who can, in turn, spread the word in our schools and colleges. But it is important for those at universities to play their part in keeping alive the narrative tradition. In our conferences and journals, we are all engaged in telling the tales of our mathematical adventures. If we want more young explorers to join us on the hard treks across the mathematical mountains, then research mathematicians have a part to play in telling those outside the ivory towers our best stories. Scientific research consists of two important components: discovery and communication. Without one, the other will die. Oswald Veblen, in his opening address to the International Congress of Mathematicians in 1952, expressed well this need to perform our theorems: "Mathematics is terribly individual. Any mathematical act, whether of creation or apprehension, takes place in the deepest recesses of the individual mind. Mathematical thoughts must nevertheless be communicated to other individuals and assimilated into the body of general knowledge. Otherwise they can hardly be said to exist." Marcus du Sautoy is professor of mathematics at Oxford University and author of The Music of the Primes, published by Harper Perennial, Pounds 8.99. This article is based on his inaugural Drapers lecture on teaching and learning at Queen Mary, University of London. From rrosebru@mta.ca Mon Apr 17 09:39:38 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 17 Apr 2006 09:39:38 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FVSvq-0002nb-H7 for categories-list@mta.ca; Mon, 17 Apr 2006 09:34:18 -0300 Content-Transfer-Encoding: quoted-printable Content-Type: text/plain; charset=ISO-8859-1; delsp=yes; format=flowed To: categories@mta.ca From: Dan Ghica Subject: categories: Games for logic an programming languages workshop : CFP Date: Mon, 17 Apr 2006 11:35:42 +0100 Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 48 GAMES FOR LOGIC AND PROGRAMMING LANGUAGES 2006 GALOP II -- A FLOC 2006 WORKSHOP http://www.cs.bham.ac.uk/galop Seattle, Washington, USA, August 10 - 22, 2006 CALL FOR PAPERS TOPIC Game semantics has emerged as a successful paradigm in the field of =20 semantics of logics and programming languages. Game-semantic =20 techniques led to the development of the first syntax-independent =20 fully-abstract models for a variety of programming languages, ranging =20= from the purely functional to languages with imperative features such =20= as control, references or concurrency. There are also connections =20 between game semantics and other semantic theories, including the the =20= pi-calculus and domain theory. In addition to semantic analysis, an =20 algorithmic approach to game semantics has recently been developed, =20 with a view to applications in computer assisted verification and =20 program analysis. SUBMISSIONS * Submission: May 19 * Notification: June 9 This is intended to be an informal workshop. Participants are =20 encouraged to present work in progress, overviews of more extensive =20 work, and programmatic/position papers, as well as completed =20 projects. We therefore ask for submission both of short abstracts =20 outlining what will be presented at the workshop and of longer papers =20= describing completed work, either published or unpublished, in the =20 following areas: * Game theory and interaction models in semantics * Games-based design and verification * Logics for games and games for logics * Algorithmic aspects of games To submit please follow the EasyChair link http://www.easychair.org/=20 GALOP2/. A special journal issue associated with the workshop is being =20 considered; this will be discussed at the workshop. INVITED SPEAKERS Luke Ong, Oxford Madhusudan Parthasarathy, UIUC PROGRAM COMMITTEE Samson Abramsky, Oxford Pierre-Louis Curien, Paris VII Claudia Faggian, Padova Dan Ghica, Birmingham Radha Jagadeesan, DePaul (Chair) Paul-Andr=E9 Melli=E8s, Paris VII Guy McCusker, Sussex Olivier Laurent, Paris VII Andrea Schalk, Manchester --- Dr. Dan Ghica, Lecturer School of Computer Science University of Birmingham Birmingham B15 2TT tel: +44 121 414 8819 mailto:D.R.Ghica@cs.bham.ac.uk http://www.cs.bham.ac.uk/~drg From rrosebru@mta.ca Mon Apr 17 09:39:38 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 17 Apr 2006 09:39:38 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FVSuJ-0002hg-Sp for categories-list@mta.ca; Mon, 17 Apr 2006 09:32:43 -0300 Date: Sun, 16 Apr 2006 15:53:27 -0700 From: Vaughan Pratt To: Categories List Subject: categories: Re: [Fwd: du Sautoy] Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 49 > The story of the primes is one of the sagas that I have found can pull > young people on to the mathematical bandwagon. They are the building > blocks of all numbers. And as you play with them, they very soon draw you > into one of our biggest mathematical mystery stories. > Marcus du Sautoy is professor of mathematics at Oxford University and > author of The Music of the Primes Challenge would appear to be a key ingredient here. To continue the recent thread on bringing categories to the masses, is there a short list of such sagas whose challenges big and small might pull young people on to the category theory bandwagon? Abelian categories? Toposes? Monads? Synthetic differential geometry? n-categories? All would seem to be fairly easily accessed from very accessible parts of respectively topology (coffee cups, Betti numbers), constructive logic (Brouwer vs. Hilbert, proofs as programs), number systems (Galois and unsolvability by radicals), analysis (infinitesimals according to Cauchy, Weierstrass, Robinson, Kock), and cosmology (the organization of strings). What other challenges, big and small, met and unmet, might young people find a compelling lead-in to categorical thinking? In all these areas, bringing the novice to the mathematics is surely a less promising strategy than bringing the mathematics to the novice. If home delivery can radicalize the pizza business, why can't it do the same for category theory? Vaughan Pratt From rrosebru@mta.ca Mon Apr 17 16:55:13 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 17 Apr 2006 16:55:13 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1FVZgI-0002Q7-Ao for categories-list@mta.ca; Mon, 17 Apr 2006 16:46:42 -0300 Subject: categories: longdivision From: Eduardo Dubuc To: categories@mta.ca Date: Mon, 17 Apr 2006 15:23:21 -0300 (ART) MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 50 "Most people's idea of what I do as a research mathematician is long division to lots of decimal places. But fundamentally, mathematics isn't about numbers - it's about finding structure and logic and connections." Yes, but do not despise long division !! Certainly, mathematics is about "finding structure and logic and connections", but it is also about numbers and particulary about "long division to lots of decimal places". I belive that those who did not found any pleasure in developing the ability to perform long division to a lot of decimal places when they were kids, will never find and/or develop mathematically meaningful "structure and logic and connections". I belive that good mathematicians are able to perform complicated calculations, and find pleasure on it, even if it is not what they currently do. "Numbers, algorithms and calculations" as well as "structure, connections and logic", are at the core of mathematics. Ah !, and do not forget "proofs". e.d. From rrosebru@mta.ca Mon Apr 17 16:55:13 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 17 Apr 2006 16:55:13 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1FVZfq-0002O5-TQ for categories-list@mta.ca; Mon, 17 Apr 2006 16:46:14 -0300 From: "Marta Bunge" To: categories@mta.ca Subject: categories: Re: [Fwd: du Sautoy] Date: Mon, 17 Apr 2006 10:19:22 -0400 Content-Type: text/plain; format=flowed Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 51 >Challenge would appear to be a key ingredient here. To continue the >recent thread on bringing categories to the masses, is there a short >list of such sagas whose challenges big and small might pull young >people on to the category theory bandwagon? Abelian categories? >Toposes? Monads? Synthetic differential geometry? n-categories? > I have given introductory courses in Category Theory (including Monads), Toposes, Locales, Synthetic Differential Geometry in Mexico (UNAM), Spain (University of the Balearic Islands, Spain), and Egypt (Cairo University). The background material can be incorporated intro the lectures as needed. Bdest wishes, Marta From rrosebru@mta.ca Mon Apr 17 16:55:13 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 17 Apr 2006 16:55:13 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1FVZgo-0002SG-AP for categories-list@mta.ca; Mon, 17 Apr 2006 16:47:14 -0300 Mime-Version: 1.0 (Apple Message framework v749.3) Content-Type: text/plain; charset=US-ASCII; delsp=yes; format=flowed Content-Transfer-Encoding: 7bit From: Michael Mislove Subject: categories: MFPS 22 Call for Participation Date: Mon, 17 Apr 2006 13:55:37 -0500 To: categories@mta.ca Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: RO X-Status: X-Keywords: X-UID: 52 Dear Colleagues, This is a reminder that the deadline for making hotel reservations for MFPS 22 at the conference rate is this Thursday, April 20. The meeting will take place from Wednesday, May 24 through midday Saturday, May 27 at the University of Genoa, Italy, with a Tutorial Day on Separation Logic preceding it on May 23. Information about the invited speakers, the special session speakers and the accepted papers is available at the MFPS 22 web site, http:// www.math.tulane.edu/~mfps/mfps22.htm where there is a link to the Registration Page and information about hotel reservations. There is also a link to the University of Genoa page for MFPS 22 which includes some information about the local scene. The URL for that page is http://mfpsxxii.disi.unige.it/ One further note: we are only able to accept credit card payments for the registration fee for the meeting, so participants will have to register online, and then call us with their credit card information. This will be possible even after this week, but if you are planning on attending, it is helpful if you register now, since that aids in our planning for the meeting. Best regards, Mike Mislove MPFS 22 Co-Organizer =============================================== Professor Michael Mislove Phone: +1 504 862-3441 Department of Mathematics FAX: +1 504 865-5063 Tulane University URL: http://www.math.tulane.edu/~mwm New Orleans, LA 70118 USA =============================================== From rrosebru@mta.ca Tue Apr 18 21:23:36 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 18 Apr 2006 21:23:36 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1FW0L2-0001Hh-VH for categories-list@mta.ca; Tue, 18 Apr 2006 21:14:33 -0300 Date: Tue, 18 Apr 2006 10:12:59 -0700 From: Vaughan Pratt MIME-Version: 1.0 To: categories@mta.ca Subject: categories: Re: [Fwd: du Sautoy] Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 53 Dear Marta, I couldn't agree more. Usually I find myself disagreeing with some picky point or other but somehow your message managed to completely avoid my (too many) hot buttons! Your two points (broad publicity for the general benefits of the subject but only taking the best students to actually work in it) are of course applicable to any subject. Executing well on both brings a new subject up to the stature of the established subjects. CT has done very well on the latter but might be judged as having fallen short on the former so far, though perhaps not for want of trying but rather the manner of presentation. When in Rome speak Italian (and don't mention home delivery pizza). On the concern you raised a while back about perceptions of crankiness, physics runs the gamut from well-publicized spectacular advances to more cranks than just about any other scientific discipline; in that respect it nicely brackets both CT and chemistry on both sides. Whether CT has accumulated more cranks than chemists is an interesting question, which brings to mind the category theory professors from the Mahareshi Yogi's TM university in Fairfield buttonholing Bill Lawvere at an AMAST meeting in Iowa a while back. Wish I could have video'd that. Best, Vaughan Marta Bunge wrote: > Dear Vaughan, > > I meant to write a more substantial reply to your question, but I was > interrupted by an important telephone call and accidentally I sent a > partial reply. > > I meant to say that there are many attractive results in classical > mathematics than can be shown to advantage using category theory, and > that I found that emphasizing those in my courses (which of course I > have given also repeatedly here at McGill, not just in Spain, Mexico and > Egypt) is the key to interest students whlo do not even intend to work > in categories. After all, we want to educate future analysts, > topologists, algebraists, computer scientists, logicians to feel that > knowing a bit of categories can help in their fields. To me, this is the > goal in teaching categories. I only take (or have taken so far) students > with a broad mathematical culture and who can get motivated to do > categories with a view to better understand and relate different > mathematical fields. This is how Gorthendieck pursued mathematics and of > course, as it must happen, often going off tangent to develop a theory > suggested by obstructions in ordinary work. I feel happier when that > happens and do not necessarily think that one ought to aim at forming > (often poor) students in category theory. Only the very best, if they > can be lured to do so, should work in category theory. Of course, I > would mysef have been eliminated at the onset had my "rules" been > applied in those days. But in the 60's it was different and I now see > that catgegory theory must come after the "matrhematica;l experience", > not before. > > I can take the time some time this summer to make a list of such > atractive results in the fields I know within category theory. I am too > busy now. > > Best wishes, > Marta > > From rrosebru@mta.ca Tue Apr 18 21:23:36 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 18 Apr 2006 21:23:36 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1FW0Is-0001Ar-Go for categories-list@mta.ca; Tue, 18 Apr 2006 21:12:18 -0300 From: "Marta Bunge" To: categories@mta.ca Subject: categories: Re: [Fwd: du Sautoy] Date: Tue, 18 Apr 2006 09:59:56 -0400 Mime-Version: 1.0 Content-Type: text/plain; format=flowed Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 54 Dear Vaughan, I meant to write a more substantial reply to your question, but I was interrupted by an important telephone call and accidentally I sent a partial reply. I meant to say that there are many attractive results in classical mathematics than can be shown to advantage using category theory, and that I found that emphasizing those in my courses (which of course I have given also repeatedly here at McGill, not just in Spain, Mexico and Egypt) is the key to interest students who do not even intend to work in categories. After all, we want to educate future analysts, topologists, algebraists, computer scientists, logicians to feel that knowing a bit of categories can help in their fields. To me, this is the goal in teaching categories. I only take (or have taken so far) students with a broad mathematical culture and who can get motivated to do categories with a view to better understand and relate different mathematical fields. This is how Gorthendieck pursued mathematics and of course, as it must happen, often going off tangent to develop a theory suggested by obstructions in ordinary work. I feel happier when that happens and do not necessarily think that one ought to aim at forming (often poor) students in category theory. Only the very best, if they can be lured to do so, should work in category theory. Of course, I would myself have been eliminated at the onset had my "rules" been applied in those days. But in the 60's it was different and I now see that catgegory theory must come after the "mathematical experience", not before. I can take the time some time this summer to make a list of such attractive results in the fields I know within category theory. I am too busy now. Best wishes, Marta From rrosebru@mta.ca Wed Apr 19 15:07:59 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 19 Apr 2006 15:07:59 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1FWH3x-000027-6d for categories-list@mta.ca; Wed, 19 Apr 2006 15:06:01 -0300 From: "Marta Bunge" To: categories@mta.ca Subject: categories: Re: [Fwd: du Sautoy] Date: Wed, 19 Apr 2006 07:35:27 -0400 Mime-Version: 1.0 Content-Type: text/plain; format=flowed Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 55 Dear Steve, >I think this is exactly the key to the success of Mac Lane's book. >Throughout, he shows how working mathematicians are applying category >theory already without realizing it. One of the basic expositional >problems for teaching CT in computer science is that our students do not >have the body of mathematical experience that Mac Lane presumed. > Of course, by "mathematical experience" one need not assume that it should be the same for everybody. MacLane was thinking of the pure mathematicians only, because that was what motivated him all along. I think that "Conceptual Mathematics" by Lawvere and Schanuel, though seemingly too elementary, is a great introduction to categorical thinking that can be widely appreciated, since the examples chosen therein to illustrate new concepts are simple. I say this in more detail in a review (in Spanish) that can be found in my home page (http://www.math.mcgill.ca/bunge/LS.pdf (.ps)). Even so, you must agree that computer scientists ought to have learnt a certain amount of pure mathematics, or else how are they going to appreciate the more sophisticated developments in their field, or even less contribute to it? I used "Categories and Computer Science" by Bob Walters twice when teaching "Computability and Linguistics" at McGill. Although I have heard some negative comments about it (sorry to mention it, Bob), I liked it a lot. The exercises are often quite demanding, and the exposition clear. I do not know what you think about it. Of course, with a book like that, as with any other, it is up to the instructor to use it to his advantage, and to complement it as needed by the particular audience he has to face. Nice hearing from you, Marta From rrosebru@mta.ca Wed Apr 19 15:07:59 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 19 Apr 2006 15:07:59 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1FWH21-0007gc-44 for categories-list@mta.ca; Wed, 19 Apr 2006 15:04:01 -0300 Content-Type: text/plain; charset=US-ASCII; delsp=yes; format=flowed To: categories@mta.ca From: Steve Vickers Subject: categories: Re: [Fwd: du Sautoy] Date: Wed, 19 Apr 2006 08:14:52 +0100 Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 56 On 18 Apr 2006, at 14:59, Marta Bunge wrote: > ... I now see that catgegory theory must come after the > "mathematical experience", not before. ... Dear Marta, I think this is exactly the key to the success of Mac Lane's book. Throughout, he shows how working mathematicians are applying category theory already without realizing it. One of the basic expositional problems for teaching CT in computer science is that our students do not have the body of mathematical experience that Mac Lane presumed. Regards, Steve. From rrosebru@mta.ca Wed Apr 19 15:08:20 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 19 Apr 2006 15:08:20 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1FWH5Y-00008p-6I for categories-list@mta.ca; Wed, 19 Apr 2006 15:07:40 -0300 From: "Marta Bunge" To: categories@mta.ca Subject: categories: Re: [Fwd: du Sautoy] Date: Wed, 19 Apr 2006 08:03:55 -0400 Mime-Version: 1.0 Content-Type: text/plain; format=flowed Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 57 Dear Vaughan, >On the concern you raised a while back about perceptions of crankiness, >physics runs the gamut from well-publicized spectacular advances to more >cranks than just about any other scientific discipline; in that respect >it nicely brackets both CT and chemistry on both sides. Whether CT has >accumulated more cranks than chemists is an interesting question, which >brings to mind the category theory professors from the Mahareshi Yogi's >TM university in Fairfield buttonholing Bill Lawvere at an AMAST meeting >in Iowa a while back. Wish I could have video'd that. The thread I unintentionally initiated (with mixed results) did not express any concern about cranks, but about crackpots, whom I view as dangerous only if not spotted in time. I think that "cranks" means "eccentric" and, in it itself, it means nothing to me -- crankiness (if that is the correct adjective) can be: (a) the result of genuine absent-mindedness and total commitment to their activities as mathematicians/scientists, or (b) it can also be a pose by an insecure person who may have nothing else but his crankiness to be distinguished from the others. Some fields (like Physics) have both. Chemists are too serious (boring) to tolerate any cranks in their midst. CT? Yes, there are a few, but in my view, that is the least of our worries. Maybe by "crank" you meant something else ("crackpots"?), as the incident you recall (first time I hear about it) seems to indicate. In any case, the last thing anybody wants right now is to go back to discuss this sensitive issue. Best, Marta From rrosebru@mta.ca Thu Apr 20 10:23:22 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 20 Apr 2006 10:23:22 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1FWYyl-0002FD-IP for categories-list@mta.ca; Thu, 20 Apr 2006 10:13:51 -0300 Date: Wed, 19 Apr 2006 22:25:58 +0200 From: "Urs Schreiber" To: "Categories List" Subject: categories: lax functors and bimodules MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 58 Dear category theorists, let C be a monoidal category and S(C) the same category but regarded as a bicatgeory with a single object. Unless I am confused, a lax functor into S(C) is a lot like a sub-bicategory of the bicategory of bimodules internal to C. Identity morphisms a--Id-->a are sent by the lax functor to algebras A_a internal to C and morphisms a--->b to A_a-A_b bimodules. Composite morphisms a-->b-->c are sent to bimodule products over A_b. This, and in particular its precise formulation, must be well known. But I could not locate a reference for it. If anyone could provide any comments or point me to some literature, I'd be very grateful. P.S. This should play a role in defining the notion of background configurations is rational conformal field theory: http://golem.ph.utexas.edu/string/archives/000794.html From rrosebru@mta.ca Thu Apr 20 10:23:23 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 20 Apr 2006 10:23:23 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1FWZ3D-0002X9-Jc for categories-list@mta.ca; Thu, 20 Apr 2006 10:18:27 -0300 Subject: categories: What is Category Theory? From: "G. Sica" To: categories@mta.ca Content-Type: text/plain; charset=UTF-8 Date: Thu, 20 Apr 2006 14:53:21 +0200 Mime-Version: 1.0 Content-Transfer-Encoding: Quoted-Printable Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 59 Please allow me to bring to the attention of list members a recent publication about the foundations of Category Theory: WHAT IS CATEGORY THEORY? Editor: Giandomenico Sica http://www.polimetrica.com/polimetrica/389/ Price: 30 Euro. Forwarding and delivery charges are not included in the price. Publisher: Polimetrica Internatinal Scientific Publisher. Contributions and authors:=20 Abstract and Variable Sets in Category Theory (John L. Bell) Categories for Knotted Curves, Surfaces and Quandles (Scott Carter) Introducing Categories to the Practicing Physicist (Bob Coecke) Some Implications of the Adoption of Category Theory for Philosophy (David Corfield) Sets, Categories and Structuralism (Costas A. Drossos) A Theory of Adjoint Functors =E2=80=93 with some Thoughts about their Philosophical Significance (David Ellerman) Enriched Stratified Systems for the Foundations of Category Theory (Solomon Feferman) Category Theory, Pragmatism and Operations Universal in Mathematics (Ralf Kr=C3=B6mer) What is Category Theory?=20 (Jean-Pierre Marquis) Category Theory: an abstract setting for analogy and comparison=20 (Ronald Brown =E2=80=93 Tim Porter) On Doing Category Theory within Set Theoretic Foundations (Vidhy=C4=81n=C4=81th K. Rao) The best way to purchase this book is to buy it directly from the publisher's web-site: http://www.polimetrica.com .=20 I hope you can be interested in this information. If not, please accept my sincere apologies for the trouble: this is not a spam message. Many thanks. All the best, Giandomenico Sica From rrosebru@mta.ca Thu Apr 20 10:23:23 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 20 Apr 2006 10:23:23 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1FWYzp-0002JF-ST for categories-list@mta.ca; Thu, 20 Apr 2006 10:14:57 -0300 Date: Wed, 19 Apr 2006 16:32:01 -0400 (EDT) From: James Stasheff To: categories@mta.ca Subject: categories: Re: [Fwd: du Sautoy] MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 60 ah, linguistic problems not sure about British/Canadian English but in American cranks ae slightly worse than crackpots and not at all the same as being cranky Jim Stasheff jds@math.upenn.edu Home page: www.math.unc.edu/Faculty/jds On Wed, 19 Apr 2006, Marta Bunge wrote: > > Dear Vaughan, > > > >On the concern you raised a while back about perceptions of crankiness, > >physics runs the gamut from well-publicized spectacular advances to more > >cranks than just about any other scientific discipline; in that respect > >it nicely brackets both CT and chemistry on both sides. Whether CT has > >accumulated more cranks than chemists is an interesting question, which > >brings to mind the category theory professors from the Mahareshi Yogi's > >TM university in Fairfield buttonholing Bill Lawvere at an AMAST meeting > >in Iowa a while back. Wish I could have video'd that. > > > The thread I unintentionally initiated (with mixed results) did not express > any concern about cranks, but about crackpots, whom I view as dangerous only > if not spotted in time. > > I think that "cranks" means "eccentric" and, in it itself, it means nothing > to me -- crankiness (if that is the correct adjective) can be: (a) the > result of genuine absent-mindedness and total commitment to their activities > as mathematicians/scientists, or (b) it can also be a pose by an insecure > person who may have nothing else but his crankiness to be distinguished from > the others. Some fields (like Physics) have both. Chemists are too serious > (boring) to tolerate any cranks in their midst. CT? Yes, there are a few, > but in my view, that is the least of our worries. Maybe by "crank" you meant > something else ("crackpots"?), as the incident you recall (first time I hear > about it) seems to indicate. In any case, the last thing anybody wants right > now is to go back to discuss this sensitive issue. > > Best, > Marta > > From rrosebru@mta.ca Thu Apr 20 10:23:23 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 20 Apr 2006 10:23:23 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1FWZ1l-0002QZ-4v for categories-list@mta.ca; Thu, 20 Apr 2006 10:16:57 -0300 From: Thomas Streicher Subject: categories: Re: [Fwd: du Sautoy] Date: Thu, 20 Apr 2006 02:51:12 +0200 (CEST) To: categories@mta.ca MIME-Version: 1.0 Content-Transfer-Encoding: 7bit Content-Type: text/plain; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 61 Dear Steve, > One of the basic expositional problems for teaching CT in computer > science is that our students do not have the body of mathematical > experience that Mac Lane presumed. I don't think that this is the problem. There are quite a few areas in CS (mainly semantics) where it is even impossible to formulate the problem when not having the language of CT available. Paradigmatic example being solution of recursive domain equations. In my regular course on semantics I introduce category theory by need and some of those people then attend my course on category theory and categorical logic (all available on my home page if you want to look). One certainly need not know a lot about algebra of geometry for these purposes. The problem rather is that most students of CS are not open to any theory whatsoever be it categorical or not. BTW another example are socalled "effects" (i.e. something fairly applied and "impure" if you want). For modelling them appropriately one needs either monads or cpo-enriched Lawvere theories. Maybe what you deplore is the absence of SIMPLE examples from CS. Well, I think one can use posets, graphs, monoids, abelian groups, fields etc. What's more problematic is the usual ignorance of simple topological examples. Maybe a bit of analysis (done properly) would do them good? Thomas From rrosebru@mta.ca Fri Apr 21 14:24:30 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 21 Apr 2006 14:24:30 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1FWz9k-0007h2-L4 for categories-list@mta.ca; Fri, 21 Apr 2006 14:10:56 -0300 Date: Fri, 21 Apr 2006 08:26:36 +0100 To: categories@mta.ca Subject: categories: Computability in Europe 2006 - Call for Participation MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit From: A.Beckmann@swansea.ac.uk (Arnold Beckmann) Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 62 [Apologies for multiple copies] CiE 2006 Computability in Europe 2006 : Logical Approaches to Computational Barriers 30 June - 5 July 2006 Swansea University, United Kingdom http://www.cs.swansea.ac.uk/cie06/ cie06@swansea.ac.uk CALL FOR PARTICIPATION Important deadlines: Informal Presentations 30 April, 2006 Early registration 15 May, 2006 * Some grants for UK students are still available * CiE 2006 is the second of a new conference series which serves as an interdisciplinary forum for researchers into all aspects of computability and the foundations of computer science. The scientific programme consists of two three-hour tutorials, nine plenary talks, six special sessions with four talks each, and over sixty contributed talks. For more details on the programme see the full list of talks below, or visit http://www.cs.swansea.ac.uk/cie06/ The conference venue and accommodation will be on the campus of Swansea University. Swansea lies at the southcoast of Wales, next to the beautiful Gower Peninsula. To register, submit an informal presentations, apply for a UK student grant, or to obtain any other information visit http://www.cs.swansea.ac.uk/cie06/ Contact: cie06@swansea.ac.uk ********* PROGRAMME ********* TUTORIALS Samuel R. Buss (San Diego, CA) Proof Complexity and computational hardness Julia Kempe (Paris) Quantum Algorithms PLENARY TALKS Jan Bergstra (Amsterdam) Elementary Algebraic Specifications of the Rational Function Field Luca Cardelli (Microsoft Research) Biological systems as reactive systems Martin Davis (New York, NY) The Church-Turing thesis: consensus and opposition John W Dawson (York, PA) Goedel and the origins of computer science Jan Krajicek (Prague) Forcing with random variables and proof complexity Elvira Mayordomo Camara (Zaragoza) The fractal dimension of complexity classes Istvan Nemeti (Budapest) Can general relativistic computers break the Turing barrier? Helmut Schwichtenberg (Munich) Program extraction from proofs in constructive analysis Andreas Weiermann (Utrecht) Phase transition thresholds in recursion theory SPECIAL SESSIONS PROOFS AND COMPUTATION organised by Alessandra Carbone and Thomas Strahm Kai Bruennler (Bern) Deep inference Roy Dyckhoff (St Andrews) LJQ: a focused calculus for intuitionistic logic Thomas Ehrhard (Marseille) About the Krivine machine and the Taylor expansion of lambda-terms Georges Gonthier (Microsoft Research) Using reflection to prove the Four Colour Theorem COMPUTABLE ANALYSIS organised by Peter Hertling and Dirk Pattinson Margarita Korovina (Aarhus) Complexity of bisimulations on Pfaffian hybrid systems Paulo Oliva (London) Computational interpretations of proofs in classical analysis Matthias Schroeder (Edinburgh) Admissible representations in computable analysis Xizhong Zheng (Cottbus) Computability theory of real numbers CHALLENGES IN COMPLEXITY organised by Klaus Meer and Jacobo Toran Johannes Koebler (Berlin) Complexity of graph isomorphism for restricted graph classes Sophie Laplante (Paris) Lower bounds using Kolmogorov complexity Janos A. Makowsky (Haifa) Computable graph invariants Mihai Prunescu (Freiburg) The fast elimination of quantifiers and some structures with P=NP according to the unit-cost model of computation FOUNDATIONS OF PROGRAMMING organised by Inge Bethke and Martin Escardo Erika Abraham (Freiburg) Fully abstract semantics of concurrent class-based languages Roland Backhouse (Nottingham) Datatype-Generic Reasoning James Leifer (INRIA, Le Chesnay) Transactional atomicity in programming languages Alban Ponse (Amsterdam) Program and thread algebra MATHEMATICAL MODELS OF COMPUTERS AND HYPERCOMPUTERS organised by Joel D Hamkins and Martin Ziegler Jean-Charles Delvenne (Louvain-la-Neuve) Turing-universal dynamical systems Benedikt Loewe (Amsterdam) Infinite time complexity theory Klaus Meer (Odense) Optimization and approximation problems related to polynomial system solving Philip Welch (Bristol) Admissibility and infinite time computation GOEDEL CENTENARY: HIS LEGACY FOR COMPUTABILITY organised by Matthias Baaz and John W Dawson Arnon Avron (Tel Aviv) From constructibility and absoluteness to computability and safety Torkel Franzen (Lulea) What does the incompleteness theorem add to the unsolvability of the halting problem? Wilfried Sieg (Pittsburgh, PA) Goedel's Conflicting approaches to effective calculability Richard Zach (Calgary, AB) Kurt Goedel, logic, and theoretical computer science CONTRIBUTED TALKS Hajnal Andreka (Budapest) Relativity theory for logicians and new computing paradigms Marat Arslanov (Kazan) Generalized tabular reducibilities in infinite levels of Ershov hierarchy Josef Berger (Munich) The logical strength of the uniform continuity theorem Jens Blanck (Swansea) Note on Reducibility Between Domain Representations Paul Brodhead, Douglas Cenzer and Seyyed Dashti (Florida) Random Closed Sets Riccardo Bruni (Florence) Goedel, Turing, the Undecidability Results and the Nature of Human Mind Douglas Cenzer (Florida) and Zia Uddin (Lock Haven, PA) Logspace Complexity of Functions and Structures Alexey Chernov (Manno) and Juergen Schmidhuber (Munich) Prefix-like Complexities and Computability in the Limit Jose Felix Costa (Lisbon) and Jerzy Mycka (Lublin) The conjecture P =/= NP given by some analytic condition Paolo Cotogno (Brescia) Decidability of arithmetic through hypercomputation: a logical objection Fredrik Dahlgren (Uppsala) Partial Continuous Functions and Admissible Domain Representations Ugo Dal Lago and Simona Martini (Bologna) An Invariant Cost Model for the Lambda Calculus Stefan Dantchev (Durham) On the complexity of the Sperner Lemma Gregorio de Miguel Casado and Juan Manuel Garcia Chamizo (Alicante) The Role of Algebraic Models and TTE in Special Purpose Processor Design Paulin Jacobe de Naurois (Paris) A Measure of Space for Computing over the Reals Pavel Demenkov (Novosibirsk) Computer simulation replacements aminoacids in proteins David Doty (Iowa) Every Sequence is Decompressible from a Random One Jerome Durand-Lose (Orleans) Reversible conservative rational abstract geometrical computation is Turing-universal Birgit Elbl (Munich) On generalising predicate abstraction Willem Fouche (Pretoria) Brownian motion and Kolmogorov complexity Gassner Christine (Greifswald) A Structure with P = NP Alexander Gavryushkin (Novosibirsk) On Complexity of Ehrenfeucht Theories with Computable Model Annelies Gerber (Paris) Some mathematical properties of input resolution refutations with non-tautological resolvents Philipp Gerhardy (Darmstadt) Functional interpretation and modified realizability interpretation of the double-negation shift Guido Gherardi (Siena) An Analysis of the Lemmas of Urysohn and Urysohn-Tietze according to effective Borel measurability Lev Gordeev (Tuebingen) Toward combinatorial proof of P < NP. Basic approach Neal Harman (Swansea) Models of Timing Abstraction in Simultaneous Multithreaded and Multi-Core Processors Charles Milton Harris (Leeds) Enumeration reducibility with polynomial time bounds Eiju Hirowatari (Kitakyushu), Kouichi Hirata (Kyushu) and Tetsuhiro Miyahara (Hiroshima) Finite Prediction of Recursive Real-Valued Functions Tie Hou (Swansea) Coinductive Proofs for Basic Real Computation Iskander Kalimullin (Kazan, Russia) The Dyment reducibility on the algebraic structures and on the families of subsets of omega Dazhou Kang, Baowen Xu, Jianjiang Lu and Yanhui Li (Southeast University, China) Reasoning within the Extended Fuzzy Description Logics with Restricted Boxes Peter Koepke (Bonn) Infinite time register machines Peter Koepke (Bonn) and Ryan Siders (Helsinki) Computing the Recursive Truth Predicate on Ordinal Register Machines Ekaterina Komendantskaya and Anthony Seda (Cork) Bilattice-based Logic Programs: Automated Reasoning and Neural Computation Shankara Narayanan Krishna (Bombay) Upper and Lower Bounds for the Computational Power of P Systems with Mobile Membranes Lars Kristiansen (Oslo) Complexity-Theoretic Hierarchies Oleg Kudinov and Victor Selivanov (Novosibirsk) Undecidability in the Homomorphic Quasiorder of Finite Labeled Forests Andrew Edwin Marcus Lewis (Siena) The jump classes of minimal covers Chung-Chih Li (Beaumont, TX) Clocking Type-2 Computation in The Unit Cost Model John Longley (Edinburgh) On the calculating power of Laplace's demon Maria Lopez-Valdes (Zaragoza) Scaled Dimension of Individual Strings Barnaby Martin and Florent Madelaine (Durham) Towards a Trichotomy for Quantified H-Coloring Klaus Meer (Odense) and Martin Ziegler (Paderborn) Uncomputability below the Real Halting Problem Greg Michaelson (Edinburgh) and Paul Cockshott (Glasgow) Constraints on hypercomputation Philippe Moser (Maria de Luna) Martingale Families and Dimension in P Benedek Nagy and Sandor Valyi (Debrecen) Solving a PSPACE-complete problem by a linear interval-valued computation Keng Meng Ng (Wellington), Frank Stephan (Singapore) and Gouhua Wu (Singapore) Degrees of Weakly Compact Reals Peter Peshev and Dimiter Skordev (Sofia) A Subrecursive Refinement of the Fundamental Theorem of Algebra Petrus Hendrik Potgieter (Pretoria) Hypercomputing the Mandelbrot Set? Vadim Puzarenko (Novosibirsk) Definability of the Field of Reals in Admissible Sets Rose Hafsah Abdul Rauf (Swansea) Integrating Functional Programming Into C++: Implementation and Verification Mihai Prunesco (Bucharest/Freiburg) Fast quantifier elimination means P = NP Peter Schuster and Julia Zappe (Munich) Do Noetherian modules have Noetherian basis functions? Anton Setzer (Swansea) Partial Recursive Functions in Martin-Loef Type Theory Merlijn Sevenster (Amsterdam) and Tero Tulenheimo (Helsinki) Partially ordered connectives and Sigma-1-1 on finite models Alan Skelley (Prague) Third-Order Computation and Bounded Arithmetic Boris Solon (Ivanovo) Co-total enumeration degrees Ivan Soskov (Sofia) Extensions of the semi-lattice of the enumeration degrees Alexandra Soskova (Sofia) Relativized Degree Spectra Alexey Stukachev (Novosibirsk) On inner constructivizability of admissible sets Andreas Weiermann and Arnoud den Boer (Utrecht) A sharp phase transition threshold for elementary descent recursive functions Albert Ziegler (Munich) Some Reflections on the Principle of Image Collection Jeffery Zucker (McMaster) Primitive Recursive Selection Functions over Abstract Algebras PROGRAMME COMMITTEE Samson Abramsky (Oxford), Benedikt Loewe (Amsterdam), Klaus Ambos-Spies (Heidelberg), Yuri Matiyasevich (St. Petersburg), Arnold Beckmann (co-chair), Dag Normann (Oslo), Ulrich Berger (Swansea), Giovanni Sambin (Padova), Olivier Bournez (Nancy), Uwe Schoening (Ulm), Barry Cooper (Leeds), Andrea Sorbi (Siena), Laura Crosilla (Florence), Ivan Soskov (Sofia), Costas Dimitracopoulos (Athens), Leen Torenvliet (Amsterdam), Abbas Edalat (London), John Tucker (Swansea, co-chair), Fernando Ferreira (Lisbon), Peter van Emde Boas (Amsterdam), Ricard Gavalda (Barcelona), Klaus Weihrauch (Hagen), Giuseppe Longo (Paris) ORGANISERS Arnold Beckmann, Ulrich Berger, S Barry Cooper, Phil Grant, Oliver Kullmann, Benedikt Loewe, Faron Moller, Monika Seisenberger, Anton Setzer, John V Tucker CiE 2006 received financial support by the Department of Computer Science at Swansea, the British Logic Colloquium (BLC), the British Engineering and Physical Sciences Research Council (EPSRC), the Kurt Goedel Society (KGS) in Vienna, the London Mathematical Society (LMS), the Welsh Development Agency (WDA) and IT Wales. Other sponsors are the Association for Symbolic Logic (ASL), the British Computer Society (BCS) and the European Association for Theoretical Computer Science (EATCS). From rrosebru@mta.ca Mon Apr 24 23:17:26 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 24 Apr 2006 23:17:26 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1FYCxb-0004vN-7e for categories-list@mta.ca; Mon, 24 Apr 2006 23:07:27 -0300 From: "Ernesto Pimentel" To: "Ernesto Pimentel" Date: Mon, 24 Apr 2006 13:54:58 +0200 MIME-Version: 1.0 Subject: categories: ESSLLI 2006: Call for participation Content-Type: text/plain;charset="us-ascii" Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 63 ESSLLI 2006 ESSLLI 2006 ESSLLI 2006 ESSLLI 2006 ESSLLI 2006 ESSLLI 2006 CALL FOR PARTICIPATION 18TH EUROPEAN SUMMER SCHOOL OF LOGIC, LANGUAGE AND INFORMATION July 31 - August 11, 2006 Malaga, Spain (Extended Early registration deadline: May 14, 2006) ESSLLI 2006 is organized by the Software Engineering Group of the University of Malaga, under the auspices of FoLLI, the European Association for Logic, Language and Information. The main focus of ESSLLI is on the interface between linguistics, logic and computation. The school has developed into an important meeting place and forum for discussion for students, researchers and IT professionals interested in the interdisciplinary study of Logic, Language and Information. The 18th edition of ESSLLI is offering 48 courses, organized into three interdisciplinary areas (Language & Computation, Language & Logic, and Logic & Computation), at a variety of levels (foundational, introductory, advanced), as well as seven workshops. All the information may be found at: http://esslli2006.lcc.uma.es Foundational courses aim to provide truly introductory courses into a field. The courses presuppose absolutely no background knowledge. In particular, they should be accessible to people from other disciplines. Introductory courses are intended to equip students and young researchers with a good understanding of a field's basic methods and techniques, and to allow experienced researchers from other fields to acquire the key competences of neighboring disciplines, thus encouraging the development of a truly interdisciplinary research community. Advanced courses are intended to enable participants to acquire more specialized knowledge about topics they are already familiar with. Workshops are intended to encourage collaboration and the cross-fertilization of ideas by stimulating in-depth discussion of issues which are at the forefront of current research in the field. In these workshops, students and researchers can give presentations of their research. In addition to courses and workshops a student session is being also organized, with the aim of providing Masters and PhD students with an opportunity to present their own work to a professional audience, thereby getting informed feedback on their own results. Unlike workshops, the student session is not tied to any specific theme. If you are interested in presenting a paper to any of the ESSLLI workshops, you can access to their call for papers through the following link http://esslli2006.lcc.uma.es. The early (extended) registration deadline is May 14, 2006. Ernesto Pimentel Local Organizing Committee Chair University of Malaga esslli2006@lcc.uma.es ESSLLI 2006 ESSLLI 2006 ESSLLI 2006 ESSLLI 2006 ESSLLI 2006 ESSLLI 2006 From rrosebru@mta.ca Mon Apr 24 23:17:26 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 24 Apr 2006 23:17:26 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1FYCvp-0004rh-1C for categories-list@mta.ca; Mon, 24 Apr 2006 23:05:37 -0300 From: SOS 2006 Organisers To: categories@mta.ca, Date: Mon, 24 Apr 2006 16:54:31 +1000 Subject: categories: SOS 2006 - Call for Papers Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: RO X-Status: X-Keywords: X-UID: 64 Second Call for Papers: Structural Operational Semantics 2006 A Satellite Workshop of CONCUR 2006 August 26, 2006, Bonn, Germany http://www.cse.unsw.edu.au/~rvg/SOS2006 Aim: Structural operational semantics (SOS) provides a framework for giving operational semantics to programming and specification languages. A growing number of programming languages from commercial and academic spheres have been given usable semantic descriptions by means of structural operational semantics. Because of its intuitive appeal and flexibility, structural operational semantics has found considerable application in the study of the semantics of concurrent processes. Moreover, it is becoming a viable alternative to denotational semantics in the static analysis of programs, and in proving compiler correctness. Recently, structural operational semantics has been successfully applied as a formal tool to establish results that hold for classes of process description languages. This has allowed for the generalisation of well-known results in the field of process algebra, and for the development of a meta-theory for process calculi based on the realization that many of the results in this field only depend upon general semantic properties of language constructs. This workshop aims at being a forum for researchers, students and practitioners interested in new developments, and directions for future investigation, in the field of structural operational semantics. One of the specific goals of the workshop is to establish synergies between the concurrency and programming language communities working on the theory and practice of SOS. Moreover, it aims at widening the knowledge of SOS among postgraduate students and young researchers worldwide. Specific topics of interest include (but are not limited to): * programming languages * process algebras * higher-order formalisms * rule formats for operational specifications * meaning of operational specifications * comparisons between denotational, axiomatic and SOS * compositionality of modal logics with respect to operational specifications * congruence with respect to behavioural equivalences * conservative extensions * derivation of proof rules from operational specifications * software tools that automate, or are based on, SOS. Papers reporting on applications of SOS to software engineering and other areas of computer science are welcome. History: The first SOS Workshop took place in August 2004 in London as one of the satellite workshops of CONCUR 2004, and was attended by over 30 participants [http://www.cs.aau.dk/~luca/SOS-WORKSHOP/]. The second SOS Workshop occurred in July 2005 in Lisbon as a satellite workshop of ICALP 2005, and attracted 19 submissions [http://www.cs.le.ac.uk/events/SOS2005/]. INVITED SPEAKERS: * Robin Milner (Cambridge, UK; joint invited speaker with EXPRESS 2006) * Bartek Klin (Sussex, UK) PAPER SUBMISSION: We solicit unpublished papers reporting on original research on the general theme of SOS. Prospective authors should register their intention to submit a paper by uploading a title and abstract via the workshop web page by: *** Friday 26 May 2006. *** Papers should take the form of a dvi, postscript or pdf file in ENTCS format [http://www.entcs.org/], whose length should not exceed 15 pages (not including an optional "Appendix for referees" containing proofs that will not be included in the final paper). We will also consider 5-page papers describing tools to be demonstrated at the workshop. Submissions from PC members are allowed. Proceedings: Preliminary proceedings will be available at the meeting. The final proceedings of the workshop will appear as a volume in the ENTCS series. If the quality and quantity of the submissions warrant it, the co-chairs plan to arrange a special issue of an archival journal devoted to full versions of selected papers from the workshop. IMPORTANT DATES: * Submission of abstract: Friday 26 May 2006 * Submission: Sunday 4 June 2006, midnight GMT * Notification: Wednesday 28 June 2006 * Final version: Friday 14 July 2006 * Workshop: Saturday 26 August 2006 * Final ENTCS version: Friday 29 September 2006. PROGRAMME COMMITTEE Rocco De Nicola (Florence, IT) Wan Fokkink (Amsterdam, NL) Rob van Glabbeek (NICTA, AU, co-chair) Reiko Heckel (Leicester, UK) Matthew Hennessy (Sussex, UK) Ugo Montanari (Pisa, IT) Peter Mosses (Swansea, UK, co-chair) MohammadReza Mousavi (Eindhoven, NL) David Sands (Chalmers, SE) Irek Ulidowski (Leicester, UK) Shoji Yuen (Nagoya, JP) CONTACT: sos2006@cs.stanford.edu WORKSHOP ORGANISERS: Rob van Glabbeek National ICT Australia Locked Bag 6016 University of New South Wales Sydney, NSW 1466 Australia Peter D. Mosses Department of Computer Science Swansea University Singleton Park Swansea SA2 8PP United Kingdom From rrosebru@mta.ca Mon Apr 24 23:17:26 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 24 Apr 2006 23:17:26 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1FYCwR-0004ss-DR for categories-list@mta.ca; Mon, 24 Apr 2006 23:06:15 -0300 Date: Mon, 24 Apr 2006 10:30:14 +0200 (CEST) Subject: categories: algebra and coalgebra: positions for 3 PhDs and 1 postdoc From: "Yde Venema" To: categories@mta.ca MIME-Version: 1.0 Content-Type: text/plain;charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 65 ----------------------------------------------------- ALGEBRA & COALGEBRA: POSITIONS FOR 3 PhDs & 1 POSTDOC ----------------------------------------------------- As of September 2006, funding for 3 PhD studants and 1 postdoc will be available at the Universiteit van Amsterdam in the area of Logic and Theoretical Computer Science. The appointees will join the NWO sponsored research project ALGEBRA AND COALGEBRA (the mathematical environments of modal logic) which is funded by the Dutch research organisation NWO and directed by Dr. Yde Venema. Successful candidates will be working at the Institute fo= r Logic, Language and Computation. The PhD students will concentrate on one of the following projects: =95 Modal fixpoint logic =95 Partially ordered algebra =95 Universal coalgebra The post-doc will perform research preferably in the following area: =95 Coalgebra automata. More information on the positions is available on http://www.uva.nl/vacatures/object.cfm/objectid=3DA44F58E5-560B-489C-B= 1DCE7856F46F88B or via the web page of Dr. Venema: http://staff.science.uva.nl/~yde -------------------------------------------------------------------------= ----- From rrosebru@mta.ca Wed Apr 26 10:01:12 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 26 Apr 2006 10:01:12 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1FYjQv-0001Ve-Cq for categories-list@mta.ca; Wed, 26 Apr 2006 09:47:53 -0300 Mime-Version: 1.0 (Apple Message framework v749.3) Content-Transfer-Encoding: 7bit From: Michael Mislove Subject: categories: MFPS 22 Program online Date: Tue, 25 Apr 2006 16:07:36 -0500 To: categories@mta.ca Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 66 Dear Colleagues, The Program for the Twenty-second Conference on the Mathematical Foundations of Programming Semantics is now available online. It can be found on the MFPS 22 web page, http://www.math.tulane.edu/~mfps/ mfps22.htm Information about registration and accommodation for the meeting is also available on that site. It should be noted that the Astor hHotel in Nervi that will house conference participants has extended the deadline for obtaining the conference rate. If you register this week, the conference rate will be honored. Best regards, Mike Mislove Co-Oranizer MFPS =============================================== Professor Michael Mislove Phone: +1 504 862-3441 Department of Mathematics FAX: +1 504 865-5063 Tulane University URL: http://www.math.tulane.edu/~mwm New Orleans, LA 70118 USA =============================================== From rrosebru@mta.ca Wed Apr 26 18:00:25 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 26 Apr 2006 18:00:25 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1FYr45-0006Dc-3G for categories-list@mta.ca; Wed, 26 Apr 2006 17:56:49 -0300 Date: Wed, 26 Apr 2006 09:58:56 -0700 From: Vaughan Pratt MIME-Version: 1.0 To: categories list Subject: categories: Does duality categorify? Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 67 Does duality categorify? If so, how? If not, why not? For example distributive lattices categorify to distributive algebras. The dual of a distributive lattice is a partially ordered Stone space. What does categorification do here? (Apologies if this is an old chestnut.) Vaughan Pratt From rrosebru@mta.ca Thu Apr 27 14:49:37 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 27 Apr 2006 14:49:37 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1FZAQH-000151-B7 for categories-list@mta.ca; Thu, 27 Apr 2006 14:37:01 -0300 Date: Thu, 27 Apr 2006 18:19:16 +0100 From: Robin Houston To: categories@mta.ca Subject: categories: Re: Products in a compact closed category Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Disposition: inline Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 68 On Thu, Mar 23, 2006 at 12:17:05PM +0000, Robin Houston wrote: > I recently proved that [finite] products (or coproducts) in a compact > closed category are necessarily biproducts, and I'm wondering whether > this is a known theorem. Since a couple of you have been asking about this, I thought I should post a quick followup message. I had several private replies, almost all of them asking to see the proof. None of my respondents knew of an existing proof. A preliminary paper, describing the proof, in far more detail than most of the people on this list would need, is available from http://www.arxiv.org/abs/math.CT/0604542 (If any of you have any comments on it, I'd be interested in hearing them.) Yours, Robin From rrosebru@mta.ca Sat Apr 29 10:31:54 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 29 Apr 2006 10:31:54 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1FZpNp-0002v8-As for categories-list@mta.ca; Sat, 29 Apr 2006 10:21:13 -0300 Subject: categories: Does duality categorify? To: categories@mta.ca (categories) Date: Thu, 27 Apr 2006 20:00:13 -0700 (PDT) From: "John Baez" MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 69 Vaughn Pratt asks: > Does duality categorify? If so, how? If not, why not? Of course this is a huge question, but the answer is: surely it must! My own favorite duality is between compact Hausdorff spaces and commutative C*-algebras, because my advisor was Irving Segal. Elements of such a C*-algebra can be thought of as continuous functions on its "spectrum", which is a compact Hausdorff space. This map from the algebra to function on its spectrum is called the "Gelfand transform"; you can think of the Fourier transform as a special case. If you categorify this you get something called the Doplicher-Robert theorem, which is a duality between certain "compact groupoids" and certain "symmetric monoidal C*-categories". I tried to explain this here: http://front.math.ucdavis.edu/q-alg/9609018 However, if I really wanted to categorify dualities in general, I'd start with less complicated examples. > For example distributive lattices categorify to distributive algebras. > The dual of a distributive lattice is a partially ordered Stone space. > What does categorification do here? Unfortunately I don't know what a distributive algebra is or in what sense it's a categorified distributive lattice. If I had to think about this, I'd probably start with something I understand ever so slightly better, like the duality between finite posets and finite distributive lattices. Best, jb PS - there's some nice feedback on our questions about the algebraic closure of the rationals here: http://groups.google.com/group/sci.math.research/browse_thread/thread/61e30c22ee6c27b6/f647aee0763a349c?&hl=en#f647aee0763a349c Briefly, while the existence of an algebraic closure of Q can be shown without choice, it uniqueness-up-to-isomorphism seems to require choice. Also, while arithmetic operations in Qbar are computable, they seem to present interesting challenges. Quoting David Madore: The usual manner is to represent a real element of Qbar by * its minimal polynomial over Q (or perhaps, some polynomial, not necessarily minimal, but probably at least separable, of which it is a root), * an interval which isolates the root from all other roots (or the number of the root in the usual order on the reals). Basically the trick is that sums and products can be computed by universal rules (if P1 and P2 are polynomials over Q, there is a polynomial, which can be given universally in function of the coefficients of P1 and P2, whose roots are the sums of roots of P1 and P2, and ditto for the product), and roots can always be isolated using Sturm-Liouville (in other words, you can narrow the interval as much as you want since Sturm-Liouville lets you count the number of roots in any given interval). This is for real algebraics; for the full Qbar, you just represent a complex number by its real and imaginary parts (both of which are algebraic if the complex is algebraic). Actually programming this is *unbelievably* painful. As for the algorithmic complexity, I think it's not that bad, in the sense that if x and y have small height (for any reasonable definition of "height") then computing x+y can be done in a reasonable time, but there's a catch: the height of x+y grows considerably larger than that of x or y, so any actual computation can become terribly difficult. (The same problem happens for rationals: computing r+s where r and s are rationals is polynomial in the height of r and s, but try computing something like 1/2+1/3+1/5+1/7+1/11+1/13+1/17...) From rrosebru@mta.ca Sat Apr 29 10:31:54 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 29 Apr 2006 10:31:54 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1FZpOd-0002x2-Gc for categories-list@mta.ca; Sat, 29 Apr 2006 10:22:03 -0300 Date: Sat, 29 Apr 2006 13:27:20 +0930 From: David Roberts To: categories@mta.ca Subject: categories: gr-stacks in the literature MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 70 Dear all, after a bit of searching, I cannot find much in the literature about gr- stacks, more specifically, charts and presentations thereof reflecting (in a non-technical sense) the group-like structure. Also, aside from self equivalences of gerbes and quotients of groups (G/H for non-normal H), I cannot dream up other "interesting" examples - and these are the opposite ends of the spectrum I want to consider. All pointers welcome. -- David Roberts Pure Mathematics University of Adelaide South Australia, 5005 From rrosebru@mta.ca Sun Apr 30 13:28:23 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 30 Apr 2006 13:28:23 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1FaEb2-0002eH-CY for categories-list@mta.ca; Sun, 30 Apr 2006 13:16:32 -0300 Date: Sat, 29 Apr 2006 13:52:55 -0400 From: Ettore Aldrovandi To: categories@mta.ca Subject: categories: Re: gr-stacks in the literature Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Disposition: inline Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 71 Greetings: I take this chance to post my first message to this list... On Sat, Apr 29, 2006 at 01:27:20PM +0930, David Roberts wrote: > Dear all, > > after a bit of searching, I cannot find much in the literature about gr- > stacks, more specifically, charts and presentations thereof reflecting (in a > non-technical sense) the group-like structure. Also, aside from self > equivalences of gerbes and quotients of groups (G/H for non-normal H), I > cannot dream up other "interesting" examples - and these are the opposite ends > of the spectrum I want to consider. Another example would be stack associated to the presheaf of groupoids defined by a crossed module d: G --> H. You end up with the stack of G-torsors equipped with a trivialization of the associated H-torsor via the homomorphism d. But because you have a crossed module, the trivialization can be used to induce a G-bitorsor structure compatible with the section giving the trivialization above. The bitorsor product will give the gr-stack structure. This is spelled out in some detail in L. Breen's "Bitorseurs et cohomologie non ab\'elienne," in The Grothendieck Festschrift, Vol. I. Also, Aut(x) for x an object in a 2-gerbe gives an example. Hope this helps a bit, -- Ettore Aldrovandi Department of Mathematics http://www.math.fsu.edu/~ealdrov Florida State University aldrovandi at math.fsu.edu Tallahassee, FL 32306-4510, USA +1 (850) 644-9717 (FAX: 4053) From rrosebru@mta.ca Sun Apr 30 13:28:23 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 30 Apr 2006 13:28:23 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1FaEYr-0002SH-6K for categories-list@mta.ca; Sun, 30 Apr 2006 13:14:17 -0300 Date: Sat, 29 Apr 2006 10:14:14 -0400 (EDT) From: Peter Freyd Message-Id: <200604291414.k3TEEEPt012831@saul.cis.upenn.edu> To: categories@mta.ca Subject: categories: dualities Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 72 On the subject of favorite dualities: Surely the most important are the self-dualities and the most important of these (so important we stop noticing it as we age) is the category of finite-dimensional vector spaces over a given field. Next is Pontryagin's: the category of locally compact groups. The original Pontryagin duality easily generalizes: the category of locally compact modules over a given commutative ring is self-dual. (In the non-commutative case one also obtains a duality but not a self-duality -- unless, of course, the ring is self-dual.) A corollary is that the category of discrete left R-modules is dual to the category of compact right R-modules. (For 50 years I've been trying to turn this into an exercise in abelian categories. There's a nice reduction down to the proposition that R/Z is a cogenerator for the category of compact abelian groups, but that fact seems to require some non-trivial functional analysis.) Strange that two of the most important "dualities" are both Pontryagin's. The other is in algebraic topology theory. Then, of course there's my present favorite: the category of finitely presented group-valued functors from the category of finitely presented modules over a commutative ring. From rrosebru@mta.ca Sun Apr 30 13:28:23 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 30 Apr 2006 13:28:23 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1FaEaG-0002ZT-10 for categories-list@mta.ca; Sun, 30 Apr 2006 13:15:44 -0300 Date: Sat, 29 Apr 2006 10:37:16 -0700 From: Vaughan Pratt MIME-Version: 1.0 To: categories Subject: categories: Re: Does duality categorify? Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 73 John Baez wrote: > Vaughn Pratt asks: >>For example distributive lattices categorify to distributive algebras. >>The dual of a distributive lattice is a partially ordered Stone space. >>What does categorification do here? > > Unfortunately I don't know what a distributive algebra is > or in what sense it's a categorified distributive lattice. Sorry, I meant to write distributive category, a la Chapter 3 of Bob Walters' book "Categories and Computer Science". (I just finished writing an article on algebra, I seem to have algebras on the brain.) > If I had to think about this, I'd probably start with something > I understand ever so slightly better, like the duality between > finite posets and finite distributive lattices. Right, that was the example I had in mind. Distributive lattices:posets :: distributive categories:? As an initial guess: "categories", with dualizer Set, which is both a category and a distributive category. So is CAT(C,Set) a distributive category? And if so, is DCAT(CAT(C,Set),Set) equivalent to C? And what about the enriched case V-DCAT(V-CAT(C,V),V)? Vaughan From rrosebru@mta.ca Mon May 1 15:18:14 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 01 May 2006 15:18:14 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1FacnK-0005I2-9F for categories-list@mta.ca; Mon, 01 May 2006 15:06:50 -0300 From: "Mamuka Jibladze" To: "Peter Freyd" , Subject: categories: Re: dualities Date: Sun, 30 Apr 2006 20:56:34 +0400 MIME-Version: 1.0 Content-Type: text/plain;format=flowed;charset="Windows-1252";reply-type=original Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 74 > Next is Pontryagin's: the category of locally compact groups. The > original Pontryagin duality easily generalizes: the category of > locally compact modules over a given commutative ring is self-dual. > (In the non-commutative case one also obtains a duality but not a > self-duality -- unless, of course, the ring is self-dual.) A corollary > is that the category of discrete left R-modules is dual to the > category of compact right R-modules. (For 50 years I've been trying to > turn this into an exercise in abelian categories. There's a nice > reduction down to the proposition that R/Z is a cogenerator for the > category of compact abelian groups, but that fact seems to require > some non-trivial functional analysis.) This reminded me of a long-standing torture: does anybody know an elementary proof at least of the particular case when the base ring - thus the dualizer too - has only two elements? (Demanded by Guram Bezhanishvili; I agreed to try thinking on this one as it seemed somehow close to Boolean algebras, but...) > Then, of course there's my present favorite: the category of finitely > presented group-valued functors from the category of finitely > presented modules over a commutative ring. Yes, yes? From rrosebru@mta.ca Mon May 1 15:18:14 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 01 May 2006 15:18:14 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1FacwC-0005nA-QN for categories-list@mta.ca; Mon, 01 May 2006 15:16:00 -0300 Date: Sun, 30 Apr 2006 08:17:30 -0400 From: jim stasheff MIME-Version: 1.0 To: categories@mta.ca Subject: categories: Re: gr-stacks in the literature Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 75 You've seen Larry Breen's Asterisque vol and others of his papers? David Roberts wrote: > Dear all, > > after a bit of searching, I cannot find much in the literature about gr- > stacks, more specifically, charts and presentations thereof reflecting (in a > non-technical sense) the group-like structure. Also, aside from self > equivalences of gerbes and quotients of groups (G/H for non-normal H), I > cannot dream up other "interesting" examples - and these are the opposite ends > of the spectrum I want to consider. > > All pointers welcome. > > From rrosebru@mta.ca Mon May 1 15:18:43 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 01 May 2006 15:18:43 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1Facy1-0005uw-SA for categories-list@mta.ca; Mon, 01 May 2006 15:17:53 -0300 Date: Sun, 30 Apr 2006 12:28:44 -0700 From: Vaughan Pratt MIME-Version: 1.0 To: categories@mta.ca Subject: categories: Re: dualities Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 76 In addition to Peter's nice collection of self-dualities there are the Kleisli and Eilenberg-Moore categories of "the" covariant power-set monad (there are really two such monads but either will do), respectively Rel and complete semilattices, both self-dual. One that Mike Barr introduced me to is the subcategory of Rel whose morphisms are the partial injections, those binary relations such that if (x,y) and (x,z) are both present then y = z and likewise for their converses. My personal favorites are finite chains with bottom (showing that \Delta, as the base category of the presheaf category of simplicial sets, comes very close to being self-dual; had \Delta itself been self-dual, Set^{\Delta\op} and Set^\Delta would have been the same thing), and semilattices with a top and all nonempty sups (my candidate for a self-dual system of event/state structures before I replaced it with Chu spaces). One should also mention the topological vector spaces in Barr's book on *-autonomous categories, whose self-duality does for the finite-dimensional vector spaces mentioned by Peter what Pontryagin duality does for finite abelian groups. A feature of Chu spaces I particularly like is that each of the above, as well as finite-dimensional vector spaces and finite abelian groups, can be described as that full subcategory of Chu(Set,K) (K = 2 except for vector spaces and abelian groups) consisting of biextensional Chu spaces whose rows and columns satisfy the same closure conditions. For example the category of finite-dimensional vector spaces over GF(2) (a sneaky way to stick to Chu(Set,2)) embeds in Chu(Set,2) as precisely those finite biextensional Chu spaces whose rows and columns, viewed as bit vectors in the sense a machine-language programmer understands the concept, are both closed under bitwise XOR. This example is given as an exercise at the end of Chapter 2 of http://boole.stanford.edu/pub/coimbra.pdf, my notes for the July 1999 Coimbra School cotaught with John Baez and Cristina Pedicchio. Proposition 2.2 in the same chapter obtains complete semilattices (of any cardinality) as those Chu spaces whose rows and columns are closed under bitwise OR, with the self-duality of CSLat as the immediate Corollary 2.3. This shows that the self-dualities CSLat and Vct_{GF(2)}, at least for finite objects, arise identically except for how they combine their bit-vectors, namely with respectively OR and XOR. Vaughan Peter Freyd wrote: > On the subject of favorite dualities: > > Surely the most important are the self-dualities and the most > important of these (so important we stop noticing it as we age) is the > category of finite-dimensional vector spaces over a given field. > > Next is Pontryagin's: the category of locally compact groups. The > original Pontryagin duality easily generalizes: the category of > locally compact modules over a given commutative ring is self-dual. > (In the non-commutative case one also obtains a duality but not a > self-duality -- unless, of course, the ring is self-dual.) A corollary > is that the category of discrete left R-modules is dual to the > category of compact right R-modules. (For 50 years I've been trying to > turn this into an exercise in abelian categories. There's a nice > reduction down to the proposition that R/Z is a cogenerator for the > category of compact abelian groups, but that fact seems to require > some non-trivial functional analysis.) Strange that two of the most > important "dualities" are both Pontryagin's. The other is in algebraic > topology theory. > > Then, of course there's my present favorite: the category of finitely > presented group-valued functors from the category of finitely > presented modules over a commutative ring. > >