From rrosebru@mta.ca Fri Jul 2 07:47:32 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 02 Jul 2004 07:47:32 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BgLYe-0005gZ-00 for categories-list@mta.ca; Fri, 02 Jul 2004 07:46:16 -0300 Date: Thu, 1 Jul 2004 06:36:51 -0400 (EDT) From: Michael Barr X-X-Sender: barr@triples.math.mcgill.ca To: Subject: categories: Re: Grothendieck bio? In-Reply-To: <20040630174359.50998.qmail@web52607.mail.yahoo.com> Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 1 I do not think that anyone has written a biography of AG, but he has written an autobiography, called Recoltes et semailles (Reapings and Sowings--the order is intentionally backwards). It is not publicly available (not published) but someone has, I understand, done a Russian translation that is. There is also a (very) partial English translation that is an ongoing project that requires money to proceed. Thus if you want to read it, you have to send cash to the translator, Roy Lisker. See his web page, http://www.fermentmagazine.org/, for more details. I cannot vouch for the quality of the translation, but I disagree with him on how to translate the title. I think he called it Harvests and Sowings, which clanks on my ear. He says his French is better than mine, which I won't argue, but my wife agrees with me and she is a professional French to English translator. Besides we are not arguing over the meaning, but the best sounding English. Be that as it may, it is the best you can do unless you can read it in Russian (which I assume from your name you can). Sorry, I don't know a source for that. On Wed, 30 Jun 2004, Galchin Vasili wrote: > Hello, > > Does anybody know of a Grothendieck biography? For > me many times it is helpful to read a bio to the > historical development of a person's work. > > Thanks in advance, Bill Halchin > > From rrosebru@mta.ca Fri Jul 2 07:47:32 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 02 Jul 2004 07:47:32 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BgLXC-0005Yw-00 for categories-list@mta.ca; Fri, 02 Jul 2004 07:44:46 -0300 Date: Thu, 1 Jul 2004 11:12:43 +0100 From: Robin Houston To: Subject: categories: Re: Grothendieck bio? Message-ID: <20040701101243.GB1832@rpc142.cs.man.ac.uk> References: <20040630174359.50998.qmail@web52607.mail.yahoo.com> Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Disposition: inline In-Reply-To: <20040630174359.50998.qmail@web52607.mail.yahoo.com> User-Agent: Mutt/1.4i X-Spam-Score: -4.9 (----) X-Scanner: exiscan for exim4 (http://duncanthrax.net/exiscan/) *1BfyYe-0006ky-FP*2QK8Cy90Pic* Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 2 On Wed, Jun 30, 2004 at 10:43:59AM -0700, Galchin Vasili wrote: > Does anybody know of a Grothendieck biography? This question came up recently on sci.math.research, where there were several interesting responses. The thread is at http://groups.google.com/groups?threadm=0t3t3bw3rrcd%40legacy Robin From rrosebru@mta.ca Fri Jul 2 07:48:09 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 02 Jul 2004 07:48:09 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BgLaL-0005ma-00 for categories-list@mta.ca; Fri, 02 Jul 2004 07:48:01 -0300 Message-Id: <200407011701.i61H1SRH005609@coraki.Stanford.EDU> X-Mailer: exmh version 2.6.3 04/04/2003 with nmh-1.0.4 To: Subject: categories: Re: Questions on dinatural transformations. Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Date: Thu, 01 Jul 2004 10:01:28 -0700 From: Vaughan Pratt Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 3 >From: noson@sci.brooklyn.cuny.edu >I was hoping that the category of small categories, functors and >dinat transformations... There's a category problem already at this point. Dinats don't go between functors F,G:C->D, they go between sesquifunctors F:C^op x C->D and differ from n.t.'s of that type by only being defined on the diagonal of C^op x C. The off-diagonal and non-identity-morphism entries in F,G only participate in the dinaturality condition, not in the transformation itself. >a) It is well known that there is no vertical >composition of dinatural transformations. >How about horizontal composition? Before you can compose dinats horizontally you have to be able to compose the sesquifunctors they bridge. I don't know how others do this, but if I had to compose G:D^op x D -> E with F:C^op x C -> D, my inclination would be to restrict the evident composite G(F(a,b),F(c,d)) to a=d, b=c (i.e. where the variances match up). That is, GoF:C^op x C -> E is defined by G(F(c,c'),F(c',c)) on object pairs (c',c) of C^op x C, with the expected extension to morphism pairs (f',f) where f':c'->d' in C^op (i.e. f':d'->c' in C) and f:c->d in C, namely G(F(f,f'),F(f',f)): G(F(c,c'),F(c',c)) -> G(F(d,d'),F(d',d)). With that (or some) choice of sesquifunctor composition one can then ask about horizontal composition tos where s:F->F', t:G->G'. How would you whisker a dinatural on the left, i.e. apply the whisker G:D^op x D->E on the left to the dinat s:F->F' on the right where F,F':C^op x C->D? For natural transformations, G is just a functor G:D->E, so this is just a matter of applying G pointwise to each s_c. For dinaturals however, G is a sesquifunctor. What do you want a sesquifunctor to do to a morphism s_c? Maybe there's some span-like thing one can do here but I don't see it. For dinaturals, vertical composition may turn out to be easier than horizontal, in that it at least makes sense provided one solves the shape-matching problem somehow. In doing so one also solves another problem, that dinaturality is too weak a condition, typically admitting transformations on the internal hom that aren't Church numerals (Pare & Roman, JPAA 128 33-92 for Set, Pratt, TCS 294:3, bottom of p461, for Chu(Set,K) and chu(Set,K) which awkwardly seem to need different treatments). Mike Barr has a notion of strong dinatural (unpublished?), and the notion of binary (more generally n-ary) logical transformation also works well here when definable on the category of interest. Vaughan Pratt From rrosebru@mta.ca Sat Jul 3 12:21:03 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 03 Jul 2004 12:21:03 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BgmHC-0002AC-00 for categories-list@mta.ca; Sat, 03 Jul 2004 12:18:02 -0300 From: Robert Knighten MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Message-ID: <16612.43771.47234.143768@zeus.knighten.org> Date: Thu, 1 Jul 2004 17:23:23 -0700 To: Subject: categories: Grothendieck bio? In-Reply-To: <20040630174359.50998.qmail@web52607.mail.yahoo.com> References: <20040630174359.50998.qmail@web52607.mail.yahoo.com> X-Mailer: VM 7.17 under Emacs 21.3.2 Reply-To: Robert@Knighten.org (Robert L. Knighten) Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 4 Galchin Vasili writes: > Hello, > > Does anybody know of a Grothendieck biography? For > me many times it is helpful to read a bio to the > historical development of a person's work. > > Thanks in advance, Bill Halchin I'm pretty sure there is no book length biography, but there is some information at: http://www.math.jussieu.fr/~leila/biographic.php which is really the information from www.grothendieck-circle.org which appears to be off-line at the moment. -- Bob -- Robert L. Knighten Robert@Knighten.org From rrosebru@mta.ca Sat Jul 3 12:21:03 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 03 Jul 2004 12:21:03 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BgmJR-0002Ji-00 for categories-list@mta.ca; Sat, 03 Jul 2004 12:20:21 -0300 Message-ID: <40E563D3.E38A8097@bangor.ac.uk> Date: Fri, 02 Jul 2004 14:32:03 +0100 From: Ronnie Brown X-Mailer: Mozilla 4.79 [en] (Win98; U) X-Accept-Language: en MIME-Version: 1.0 To: categories@mta.ca Subject: categories: Re: Grothendieck bio? References: <20040630174359.50998.qmail@web52607.mail.yahoo.com> <20040701101243.GB1832@rpc142.cs.man.ac.uk> Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 5 People may like to look at the Spectator article: http://www.lewrockwell.com/spectator/spec262.html I thought Recollte et Semaille translated as `Reaping and sowing'? He was a great correspondent in the 1980s, and we have a mass of letters which will be transferred to an archive in good hands in due course (my administrative matters have got too much at present). This correspondence is relevant to Pursuing Stacks, which was written in English as a response to our correspondence in English, which he describes in `Esquisse d'un programme' (EdP) as `a baton rompu' (ranging over this and that). In fact EdP is available in French and English translation in books by Pierre Lochack and Leila Schneps (LMS Lecture notes series). Pursuing Stacks was to have been volume 1 of a series on `The long march towards Galois theory', written in a new informal style, as in Pursuing Stacks, where the thought is open to view. I suspect that writing R&S distracted him from this aim. I expect to explain the correspondence which led to Pursuing Stacks being sent to me, and Larry Breen, and then circulated from Bangor, in 1983, but have not yet got round to it. In any case, Pursuing Stacks seems to be increasingly influential, as does EdP. Ronnie Brown Robin Houston wrote: > > On Wed, Jun 30, 2004 at 10:43:59AM -0700, Galchin Vasili wrote: > > Does anybody know of a Grothendieck biography? > > This question came up recently on sci.math.research, where there were > several interesting responses. The thread is at > > http://groups.google.com/groups?threadm=0t3t3bw3rrcd%40legacy > > Robin -- Professor Emeritus R. Brown, Department of Mathematics, University of Wales, Bangor Dean St., Bangor, Gwynedd LL57 1UT, United Kingdom Tel. direct:+44 1248 382474|office: 382681 fax: +44 1248 361429 World Wide Web: home page: http://www.bangor.ac.uk/~mas010/ (Links to survey articles: Higher dimensional group theory Groupoids and crossed objects in algebraic topology) Centre for the Popularisation of Mathematics: http://www.cpm.informatics.bangor.ac.uk/ (reorganised site with new sculpture animations) From rrosebru@mta.ca Sat Jul 3 12:24:20 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 03 Jul 2004 12:24:20 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BgmNA-0002Tg-00 for categories-list@mta.ca; Sat, 03 Jul 2004 12:24:12 -0300 Message-ID: <40E5FBBB.4020701@cs.queensu.ca> Date: Fri, 02 Jul 2004 20:20:11 -0400 From: Claudio Hermida MIME-Version: 1.0 To: categories@mta.ca Subject: categories: Re: Questions on dinatural transformations. References: <200407011701.i61H1SRH005609@coraki.Stanford.EDU> In-Reply-To: <200407011701.i61H1SRH005609@coraki.Stanford.EDU> Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 6 Vaughan Pratt wrote: >>From: noson@sci.brooklyn.cuny.edu >>I was hoping that the category of small categories, functors and >>dinat transformations... >> >> > >There's a category problem already at this point. Dinats don't go between >functors F,G:C->D, they go between sesquifunctors F:C^op x C->D and differ >from n.t.'s of that type by only being defined on the diagonal of C^op x C. >The off-diagonal and non-identity-morphism entries in F,G only participate >in the dinaturality condition, not in the transformation itself. > > > >>a) It is well known that there is no vertical >>composition of dinatural transformations. >>How about horizontal composition? >> >> > >Before you can compose dinats horizontally you have to be able to compose >the sesquifunctors they bridge. I don't know how others do this, but if I >had to compose G:D^op x D -> E with F:C^op x C -> D, my inclination would >be to restrict the evident composite G(F(a,b),F(c,d)) to a=d, b=c (i.e. >where the variances match up). That is, GoF:C^op x C -> E is defined by >G(F(c,c'),F(c',c)) on object pairs (c',c) of C^op x C, with the expected >extension to morphism pairs (f',f) where f':c'->d' in C^op (i.e. >f':d'->c' in C) and f:c->d in C, namely > > G(F(f,f'),F(f',f)): G(F(c,c'),F(c',c)) -> G(F(d,d'),F(d',d)). > There is a `canonical' choice of composition for such `sesquifunctors' (what follows is presumably folklore and written up somewhere). Consider the category SDCat of *self-dual* categories: objects are categories C, equipped with a duality c: C -> C^op (with c^op c = id), and morphisms F: (C,c) -> (D,d) are functors F:C -> D such that F^op c = d F. The forgetful SDCat -> Cat admits both adjoints (and SDCat is actually both monadic and comonadic over Cat): the right adjoint takes a category A to (A^op x A, s) where s is the switch isomorphism (the second projection \pi' : A^op x A -> A is the counit of the adjunction). We thus get a comonad G on Cat, and sesquifunctors are the morphisms of the resulting Kleisli category Cat_G, which tells us how to compose G:D^op x D -> E with F:C^op x C -> D. The composite is G(F^op s, F)\delta, which agrees indeed with the formula above. (This is of course the composite in SDCat via the adjunction) > >With that (or some) choice of sesquifunctor composition one can then ask >about horizontal composition tos where s:F->F', t:G->G'. How would you >whisker a dinatural on the left, i.e. apply the whisker G:D^op x D->E >on the left to the dinat s:F->F' on the right where F,F':C^op x C->D? >For natural transformations, G is just a functor G:D->E, so this is just a >matter of applying G pointwise to each s_c. For dinaturals however, G is >a sesquifunctor. What do you want a sesquifunctor to do to a morphism s_c? >Maybe there's some span-like thing one can do here but I don't see it. > >For dinaturals, vertical composition may turn out to be easier than >horizontal, in that it at least makes sense provided one solves the >shape-matching problem somehow. In doing so one also solves another >problem, that dinaturality is too weak a condition, typically admitting >transformations on the internal hom that aren't Church numerals (Pare & Roman, >JPAA 128 33-92 for Set, Pratt, TCS 294:3, bottom of p461, for Chu(Set,K) and >chu(Set,K) which awkwardly seem to need different treatments). Mike Barr >has a notion of strong dinatural (unpublished?), and the notion of binary >(more generally n-ary) logical transformation also works well here when >definable on the category of interest. > >Vaughan Pratt > > The counterexamples mentioned in P. Scott's posting concern the lack of a well-defined *vertical* composition of dinaturals. If one persists on endowing them with such a composite, one possible approach is to accept the partiality of this composition and work with *paracategories*. Pushing this simple idea to its logical conclusion leads to a decent enough basic theory, which allows to make sense of the fact that `dinats into a ccc form a cartesian-closed paracat'. See Hermida, C; Mateus, P. Paracategories. II. Adjunctions, fibrations and examples from probabilistic automata theory. Theoret. Comput. Sci. 311 (2004), no. 1-3, 71--103. (also available at my homepage http://maggie.cs.queensu.ca/chermida) Making a 2-dimensional structure with dinats, using their partial vertical composition, leads to consider enrichment over ParCat (the cartesian closed category of paracategories). But whiskering (and therefore *horizontal* composition) is bound to be a partial operation as well, so one has to broaden/weaken ParCat to accommodate this fact. Ultimately, the kind of composite required in Yanosfky's posting: S,S':C^op x C---->B T,T':C^op x C ----> B^op U,U':B^op x B --->A \alpha: S--->S' dinat \alpha': T--->T' dinat \beta: U--->U' dinat ------------------------------------------------------------------- \beta \circ (\alpha',\alpha) suggests a *partial multicategory* structure (as introduced in the article above), with homs in ParCat. Claudio Hermida From rrosebru@mta.ca Sat Jul 3 16:37:38 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 03 Jul 2004 16:37:38 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BgqIg-00074Z-00 for categories-list@mta.ca; Sat, 03 Jul 2004 16:35:50 -0300 Message-Id: <5.2.0.9.0.20040703133831.01598070@pop.cwru.edu> X-Sender: cxm7@pop.cwru.edu (Unverified) X-Mailer: QUALCOMM Windows Eudora Version 5.2.0.9 Date: Sat, 03 Jul 2004 13:45:55 -0400 To: categories@mta.ca From: Colin McLarty Subject: categories: Quick surveys of categorical logic Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii"; format=flowed Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 7 For a philosophy article I need one or two comprehensive references to categorical logic, especially emphasizing the array of doctrines. I mean, from algebraic theories to left exact theories to coherent theories and such. I have hundreds of references. I need one or two. Very quick surveys are fine for this, even preferable. What is there? best, Colin From rrosebru@mta.ca Mon Jul 5 16:08:32 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 05 Jul 2004 16:08:32 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BhYlO-0007BJ-00 for categories-list@mta.ca; Mon, 05 Jul 2004 16:04:26 -0300 Date: Sat, 3 Jul 2004 17:29:20 -0400 (EDT) From: Robert Seely To: categories@mta.ca Subject: categories: Re: Quick surveys of categorical logic In-Reply-To: <5.2.0.9.0.20040703133831.01598070@pop.cwru.edu> Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 8 An old but still useful reference is Kock & Reyes' article in the Handbook of Mathematical Logic (of course, for a mid-70's paper, it's a bit dated by now!). Phil Scott has written some more recent ones, including "Some Aspects of Categories in Computer Science (Survey Article on Categorical Logic)" and "Category Theory for Linear Logicians" (with R. Blute), available on his website (he can provide the pub refs). -= rags =- On Sat, 3 Jul 2004, Colin McLarty wrote: > For a philosophy article I need one or two comprehensive references to > categorical logic, especially emphasizing the array of doctrines. I mean, > from algebraic theories to left exact theories to coherent theories and such. > > I have hundreds of references. I need one or two. Very quick surveys are > fine for this, even preferable. What is there? > > best, Colin > > > -- From rrosebru@mta.ca Mon Jul 5 16:08:32 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 05 Jul 2004 16:08:32 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BhYoG-0007Oc-00 for categories-list@mta.ca; Mon, 05 Jul 2004 16:07:24 -0300 Message-ID: <40E8F6B5.9010406@usyd.edu.au> Date: Mon, 05 Jul 2004 16:35:33 +1000 From: Max Kelly User-Agent: Mozilla/5.0 (Windows; U; Windows NT 5.0; en-US; rv:1.4) Gecko/20030624 Netscape/7.1 (ax) X-Accept-Language: en-us, en MIME-Version: 1.0 To: categories@mta.ca Subject: categories: Dinatural transformations Content-Type: text/plain; charset=us-ascii; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 9 Nason Yanofsky asked a question about composition of dinatural transformations, and there have been a number of replies - but none giving the reference I should have expected, namely [S.Eilenberg and G.M.Kelly, A generalization of the functorial calculus,, J.Algebra 3 (1966), 366 - 375] . What Sammy and I were concerned with were such families as the evaluationn e_A,B : [A,B] o A --> B , where o is a tensor product and [ , ] is an internal hom. Here e_A,B is natural in B in the usual sense; it is also natural, in our extended sense, in the variable A, which appears twice on one side of the arrow, but with two opposite variances. Similar for d_A,B : A --> [B, AoB]. In certain circumstances one can compose such "natural transformations" to form new ones:one example is the composite AoB ---------> [B, AoB] o B ----------> AoB d_A,B o B e_B, AoB which is in fact the identity natural transformation. Sammy and I gave a general treatment in the article above. Later, others generalised our "extended naturals" to get the notion of dinatural transformation. Since these do not compose except in some very special cases, I find them to be of limited interest. In contrast, I find that I still use the Eilenberg-Kellycalculus from time to time. Max Kelly. From rrosebru@mta.ca Mon Jul 5 16:08:33 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 05 Jul 2004 16:08:33 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BhYor-0007Q7-00 for categories-list@mta.ca; Mon, 05 Jul 2004 16:08:01 -0300 Date: Mon, 5 Jul 2004 12:24:17 +0200 Message-Id: <200407051024.i65AOH925697@www.lmcs-online.org> From: Logical Methods in CS Subject: categories: New Journal To: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 10 NEW JOURNAL----NEW JOURNAL----NEW JOURNAL----NEW JOURNAL----NEW JOURNAL -------------------------EXCUSE MULTIPLE COPIES----------------------- L O G I C A L M E T H O D S I N C O M P U T E R S C I E N C E Dear Colleague: We are writing to inform you about a new open-access, online, refereed journal: "Logical Methods in Computer Science". As an open-access publication, the journal will be freely available on the web. This new journal will be devoted to all theoretical and practical topics in computer science related to logic in a broad sense. You can find the homepage at http://www.lmcs-online.org The journal will open to submissions on September 1, 2004. It will be published under the auspices of The International Federation for Computational Logic: http://www.colognet.org/IFCoLog/. The journal will technically be published as an overlay of the Computing Research Repository (CoRR), see http://arxiv.org/archive/cs/intro.html. On the homepage you find a flier and a leaflet containing the basic information about the new journal. We would appreciate your posting and distributing the information, and encouraging potential authors to submit to Logical Methods in Computer Science. You may have heard about the various developments in the past couple of years in regard to the Open Access movement, see, e.g.,: http://www.zim.mpg.de/openaccess-berlin/berlindeclaration.html http://www.plos.org/ http://www.earlham.edu/~peters/fos/overview.htm and the link "Landscape..." at the jornal website. The open-access idea is that knowledge, including scientific knowledge, should be widely and readily available to society, in a stable and long-term form. The Internet and electronic publishing provides an evident means to that end. Not unrelated are concerns arising from the increasingly high prices charged commercially. There are already a few open-access journals in Computer Science, e.g.: http://www.theoryofcomputing.org/ http://www.jair.org/ and http://www.ai.mit.edu/projects/jmlr/. We are convinced that now is the time to start one in our area of logic and computer science. Yours Sincerely, Jiri Adamek, Gordon D. Plotkin, Dana S. Scott and Moshe Y. Vardi From rrosebru@mta.ca Mon Jul 5 16:08:33 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 05 Jul 2004 16:08:33 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BhYpG-0007RP-00 for categories-list@mta.ca; Mon, 05 Jul 2004 16:08:26 -0300 Date: Mon, 5 Jul 2004 18:20:00 +0200 (CEST) From: Simeoni Marta To: categories@mta.ca Subject: categories: ICGT 2004: call for participation Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 11 [Apologies for multiple copies of this announcement] CALL FOR PARTICIPATION ICGT 2004 2nd International Conference on Graph Transformation Roma (Italy), September 28 - October 2, 2004 The second International Conference on Graph Transformation ICGT 2004, along with several satellite events, will be held in Roma at the end of September 2004. It follows the first ICGT 2002 (Barcelona, October 2002) and a series of six international workshops on graph transformation with applications in computer science held from 1978 to 1998 in Europe and the USA. The conference takes place under the auspices of EATCS, EASST, and IFIP WG 1.3. The proceedings will appear in the Lecture Notes in Computer Science series by Springer-Verlag. The conference is co-located with IEEE Symposium on Visual Languages and Human Centric Computing (VL/HCC), September 26-29, 2004, allowing its participants to have a closer look at this important, related field. Scope. Graphical structures of various kinds (like graphs, diagrams, visual sentences and others) are very useful to describe complex structures and systems in a direct and intuitive way. These structures are often augmented by formalisms which add to the static description a further dimension modelling the evolution of systems via any kind of transformation of such graphical structures. The field of Graph Transformation is concerned with the theory, applications and implementation issues of all these formalisms. The theory is strongly related to areas such as graph theory and graph algorithms, formal language and parsing theory, theory of concurrency and distributed systems, formal specification and verification, logic and semantics. The application areas include all those fields of Computer Science, Information Processing, Engineering and Natural Sciences where static and dynamic modeling by graphical structures and graph transformations, respectively, play an important role. Invited speakers. Andy Evans (York, UK), Ravi Sandhu (Fairfax, VA USA), Margaret-Anne Storey (Victoria, BC Canada) (joint speaker with VL/HCC) Program committee. M.Bauderon (FR), D.Blostein (CA), A.Corradini (IT), H.Ehrig (DE), G.Engels (co-chair; DE), R.Heckel (DE), D.Janssens (BE), H.-J.Kreowski (DE), B.Koenig (DE), B.Meyer (AU), U.Montanari (IT), M.Nagl (DE), F.Orejas (ES), F.Parisi-Presicce (co-chair; USA/IT), M.Pezze` (IT), J.Pfaltz (USA), R.Plasmeijer (NL), D.Plump (UK), L.Ribeiro (BR), G.Rozenberg (NL), A.Schuerr (DE), G.Taentzer (DE), G.Tortora (IT), G.Valiente (ES) Important dates. Main conference: September 29 -- October 1, 2004 Conference including satellite events: September 28 -- October 2, 2004 General organizing committee. Paolo Bottoni (Roma, Italy), Hartmut Ehrig (chair; Berlin, Germany), Gregor Engels (Paderborn, Germany), Francesco Parisi-Presicce (Roma, Italy), Grzegorz Rozenberg (Leiden, The Netherlands) Local organizing committee. Paolo Bottoni (chair), Francesco Parisi-Presicce, Marta Simeoni (publicity chair) Conference address. ICGT 2004 Francesco Parisi-Presicce / Paolo Bottoni Universita` degli Studi di Roma La Sapienza Dipartimento di Informatica Via Salaria 113 (III piano), I-00198 Roma, Italy Tel: +39 06 4991-8426, Fax: +39 06 8541842 email: icgt2004@dsi.uniroma1.it web: http://icgt2004.dsi.uniroma1.it Satellite events. For most of the following satellite events, the submission of contributions is still open. Please, check the relevant dates on the corresponding web pages. GRA-TRA TUTORIAL Tutorial on Foundations and Applications of Graph Transformation Date: Sept. 28 (afternoon) Organizers, contact and further information: Luciano Baresi (Milano, Italy, baresi@elet.polimi.it), Reiko Heckel (Paderborn, Germany, reiko@upb.de) http://www.upb.de/cs/ag-engels/Conferences/ICGT04/Tutorial DNA & GRA-TRA 2004 Tutorial on DNA Computing and Graph Transformation Date: Sept. 28 (all day) Organizers: Tero Harju (Turku, Finland), Ion Petre (Turku, Findland), Grzegorz Rozenberg (Leiden, The Netherlands) Contact and further information: rozenber@liacs.nl http://users.utu.fi/harju/tutorial.htm PNGT 2004 Workshop on Petri Nets and Graph Transformations Date: Oct. 2 Organizers: Grzegorz Rozenberg (Leiden, The Netherlands), Hartmut Ehrig (Berlin, Germany), Julia Padberg (Berlin, Germany) Contact and further information: padberg@cs.tu-berlin.de TERMGRAPH 2004 International Workshop on Term Graph Rewriting Date: Oct. 2 Organizers, contact and further information: Maribel Fernandez (London, UK, maribel@dcs.kcl.ac.uk), Andrea Corradini (Pisa, Italy, andrea@di.unipi.it) http://www.dcs.kcl.ac.uk/staff/maribel/TERMGRAPH.html GraBaTs 2004 International Workshop on Graph-Based Tools Date: Oct. 2 Organizers: Tom Mens (Brussels, Belgium), Andy Schuerr (Munich, Germany), Gabriele Taentzer (Berlin, Germany) Contact and further information: gabi@cs.tu-berlin.de http://tfs.cs.tu-berlin.de/grabats LOGIC, GRAPH TRANSFORMATIONS, FINITE AND INFINITE STRUCTURES Workshop with invited lectures and short contributions Date: Oct. 1 (morning) - Oct. 2 Organizers: Bruno Courcelle (Bordeaux, France), David Janin (Bordeaux, France) Contact and further information: courcell@labri.fr http://www.labri.fr/Perso/~courcell/LogicIcgt.html SETra 2004 2nd Workshop on Software Evolution through Transformations: Model-based vs. Implementation-level Solutions Date: Oct. 2 Organizers: Reiko Heckel (Paderborn, Germany), Tom Mens (Brussels, Belgium) Contact and further information: reiko@upb.de http://www.upb.de/cs/ag-engels/Conferences/ICGT04/SET04/ From rrosebru@mta.ca Tue Jul 6 15:40:59 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 06 Jul 2004 15:40:59 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1Bhup1-0006Y5-00 for categories-list@mta.ca; Tue, 06 Jul 2004 15:37:39 -0300 MIME-Version: 1.0 X-MimeOLE: Produced By Microsoft Exchange V6.5.6944.0 Subject: categories: Universal Logic 05 Date: Tue, 6 Jul 2004 19:54:23 +0200 Message-ID: From: "COSTA LEITE Alexandre" To: "COSTA LEITE Alexandre" Content-Type: text/plain;charset="us-ascii" Content-Transfer-Encoding: quoted-printable Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 12 1st World Congress and School on Universal Logic (UNILOG 2005) =20 http://www.uni-log.org =20 Montreux - Switzerland, School : March 26-30 ; Congress : March 31 - April 3, 2005=20 This event will focus on:=20 1) Techniques that can be used for a general theory of logics (Labelled deductive systems, Kripke structures, Logical matrices, etc.) ;=20 2) Studies of classes of logics (Substructural logics, Non monotonic logics, Paraconsistent logics, etc.)=20 3) Scope of validity and domain of application of fundamental theorems of logic (Completeness, Deduction, Cut-elimination, etc.) 4) Philosophical considerations about the nature of logic and the universality of some logical laws or axioms=20 The school is intended for advanced students and young researchers. There will be about 20 tutorials on many subjects: combination of logics, multiple conclusion logic, combinatory logic, logics and games, abstract model theory, logic as language vs. logic as calculus, category theory for logics, etc. Invited speakers of the congress will include A.Avron, D.Batens, J.Corcoran, M.Dunn, D.Gabbay, R.Jansana, A.Koslow, V.de Paiva, K.Segerberg. Contributed papers for the congress can be submitted before October 30, 2004.=20 More information on the website: http://www.uni-log.org =20 =20 =20 =20 =20 From rrosebru@mta.ca Wed Jul 7 17:16:08 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 07 Jul 2004 17:16:08 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BiIlN-0003nO-00 for categories-list@mta.ca; Wed, 07 Jul 2004 17:11:29 -0300 Message-ID: <20040707133255.14362.qmail@web52703.mail.yahoo.com> Date: Wed, 7 Jul 2004 06:32:55 -0700 (PDT) From: Roy Lisker Subject: categories: Grothendieck Bio To: categories@mta.ca In-Reply-To: <200407071116.i67BGL3S000138@saul.cis.upenn.edu> MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 13 My translation of Harvests and Sowings (Alexandre's own notion of how the title should be translated by the way)is in fact available for free from my website. I just stopped doing the translation after the Introduction and Preface because I didn't have time to continue it unless there was some money to pay for it. However, at , there are dozens of pages of biographical material about AG, his mother and his father. Every now and then Leila Schneps adds to it. Incidentally, I've finally found the time to edit and revise the Ferment series "Quest for Grothendieck". It was hastily put together in 1989 and needs considerable work to bring it up to book quality. I estimate that the work will take about a year .Roy L. ===== Ferment and Ferment Press Dr.Roy Lisker Ferment, Ferment Press 8 Liberty Street #306 Middletown, CT 06457 From rrosebru@mta.ca Fri Jul 9 14:41:30 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 09 Jul 2004 14:41:30 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BizIt-0005xF-00 for categories-list@mta.ca; Fri, 09 Jul 2004 14:36:55 -0300 Message-ID: <40EC61AA.5040306@kestrel> Date: Wed, 07 Jul 2004 13:48:42 -0700 From: Dusko Pavlovic User-Agent: Mozilla/5.0 (X11; U; Linux i686; en-US; rv:1.2.1) Gecko/20030225 X-Accept-Language: en-us, en MIME-Version: 1.0 To: categories@mta.ca Subject: categories: Re: Grothendieck Bio References: <20040707133255.14362.qmail@web52703.mail.yahoo.com> In-Reply-To: <20040707133255.14362.qmail@web52703.mail.yahoo.com> Content-Type: text/plain; charset=us-ascii; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 14 a good occasion to say: thanks for doing this! (in the name of several readers) -- dusko Roy Lisker wrote: > My translation of Harvests and Sowings (Alexandre's >own notion of how the title should be translated by >the way)is in fact available for free from my website. >I just stopped doing the translation after the >Introduction and Preface because I didn't have time to >continue it unless there was some money to pay for it. > However, at , >there are dozens of pages of biographical material >about AG, his mother and his father. Every now and >then Leila Schneps adds to it. > Incidentally, I've finally found the time to edit >and revise the Ferment series "Quest for >Grothendieck". It was hastily put together in 1989 and >needs considerable work to bring it up to book >quality. I estimate that the work will take about a >year .Roy L. > >===== >Ferment and Ferment Press >Dr.Roy Lisker >Ferment, Ferment Press > >8 Liberty Street #306 >Middletown, CT 06457 > > > > > > From rrosebru@mta.ca Fri Jul 9 14:41:30 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 09 Jul 2004 14:41:30 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BizJY-0005zY-00 for categories-list@mta.ca; Fri, 09 Jul 2004 14:37:36 -0300 Message-ID: <40ECEB18.7020407@usyd.edu.au> Date: Thu, 08 Jul 2004 16:35:04 +1000 From: Max Kelly User-Agent: Mozilla/5.0 (Windows; U; Windows NT 5.0; en-US; rv:1.4) Gecko/20030624 Netscape/7.1 (ax) X-Accept-Language: en-us, en MIME-Version: 1.0 To: categories@mta.ca Subject: categories: Grothendieck's writings Content-Type: text/plain; charset=us-ascii; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 15 Recent communications about Grothendieck's "Recoltes et semelles" refer to the partial translation by Roy Lisker - but none, as far as I recall, gives an electronic reference to the French original. Is it not available in this form? Max Kelly. From rrosebru@mta.ca Fri Jul 9 14:41:30 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 09 Jul 2004 14:41:30 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BizMM-00069W-00 for categories-list@mta.ca; Fri, 09 Jul 2004 14:40:30 -0300 From: Thomas Streicher Message-Id: <200407090843.i698hiYM031677@fb04209.mathematik.tu-darmstadt.de> Subject: categories: Domains VII (call for participation) To: types@cis.upenn.edu, categories@mta.ca Date: Fri, 9 Jul 2004 10:43:44 +0200 (CEST) X-Mailer: ELM [version 2.4ME+ PL100 (25)] MIME-Version: 1.0 Content-Transfer-Encoding: 7bit Content-Type: text/plain; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 16 Call for Participation DOMAINS VII Darmstadt, August 29 - September 2, 2004 The WORKSHOP DOMAINS series is aimed at computer scientists and mathematicians alike who share an interest in the mathematical foundations of computation. It focuses on domains, their applications and related topics. The series was conceived and first realised by Klaus Keimel in Darmstadt in 1994. This seventh workshop returns to Darmstadt on the occasion of his 65th birthday. LOCATION The Workshop will take place at Technische Universitaet Darmstadt located in the centre of the city of Darmstadt: Hochschulstrasse 1 (Altes Hauptgebaeude) Room S1 03/123 See: www.tu-darmstadt.de/lageplaene/ follow the links ``Stadtmitte'', ``Abschnitt S1'', in particular www.tu-darmstadt.de/lageplaene/darmstadt/stadtmitte/s1.tud WORKSHOP SCHEDULE August 29 is the arrival day and September 2 departure day. There will be a barbecue at 6 pm on Sunday 29. Thus, plan to arrive in good time. The talks will take place from 9am on Monday, August 30, until 5pm on Wednesday, September 1. PARTICIPATION If you would like to participate in the workshop, please send a message to domains7@mathematik.tu-darmstadt.de It may still be possible to accommodate a few more talks. Please send us title and abstract if you would like to speak. ACCOMODATION Participants will have to arrange accommodation by themselves. For hotel reservations go to www.proregio-darmstadt.de/tagungen/tagungen.asp\\ phone ++49 6151 132782 fax ++49 6151 132783 There you will find a link for our Workshop Domains 7; on the workshop page follow the link for reservation (=``Buchung''). A certain number of rooms in several hotels are available for participants of the Workshop. They are guaranteed until July 15. But reservation will still be possible later (don't be disturbed by the misleading text at the bottom of the booking). If you go to www.proregio-darmstadt.de/uebernachten/hotel.asp you will find a list of hotels. Closest to the University you have Bockshaut, Ernst Ludwig, Zentral Hotel, Alpha-City-Hotel, Best Western Parkhaus Hotel, Pallas Hotel, Zum Rosengarten, Ibis, Etap (ordered roughly with respect to closeness to the University.) You can in any case contact the hotels directly, if you prefer. If you have problems with arranging accomodation, please contact domains7@mathematik.tu-darmstadt.de FEES The Workshop is organized without institutional financial support. There will be a registration fee of 50 Euros to covering expenses to be paid in cash at registration. (Students need not pay this fee.) Programme and organizing committee Achim Jung University of Birmingham Klaus Keimel Technische Universitaet Darmstadt Thomas Streicher Technische Universitaet Darmstadt INVITED SPEAKERS P.-L. Curien PPS, CNRS, University Paris 7, France Sequentiality : A Survey Yu.L. Ershov Sib. Branch of the Russian Academy of Science, Novosibirsk, Russia Two right topologies for spectral theory of semitopological semilattices J.D. Lawson Louisiana State University, Baton Rouge, USA Sober spaces: some old and some new M. Mislove Tulane University, New Orleans, USA Probability and Domain Theory J.-E. Pin LIAFA, CNRS, University Paris 7, France Topological methods in automata theory D.S. Scott Carnegie Mellon University, Pittsburgh, USA Domains and Logic (Tentative title) CONTRIBUTED TALKS (subject to changements) A. Bauer University of Ljubljana, Slowenia Synthetic Proof of Kreisel-Lacombe-Shoenfield Theorem Ch. Berline PPS, CNRS, Universit\'e Paris 7, France The graph semantics of lambda-calculus, or: The power set domain in its full lambda-glory Yixiang Chen Shanghai Teachers University, Shanghai, China Interval-valued CCS M. Droste Universitaet Leipzig, Germany Almost any domain is universal A. Edalat Imperial College, London, England Inverse and Implicit Function Theorems: A Domain-theoretic Treatment M. Escardo University of Birmingham, England Finitary approximations of Markov processes R. Heckmann AbsInt Angewandte Informatik GmbH, Saarbruecken, Germany A cartesian closed category containing the category of locales M. Huth Imperial College, London, England A domain for refinement of modal transition systems Hui Kou Sichuan University, Chengdu, China Constructing semantic domains by fixed ponits of self-maps A. Jung University of Birmingham, England Domain environments for real numbers Jihua Liang Sichuan University, Chengdu, China Convex Powerdomains and Vietoris Spaces T. Loew Technische Universitaet Darmstadt, Germany A universal model for an infinitary CPS target language J. Marcial University of Birmingham, England Semantics of a sequential language for exact real-number computation A. Moshier Chapman University, California, USA Gelfand Duality for Stably Compact Spaces P. Maneggia University of Birmingham, England Domain theoretical models of linear polymorphism J. Paseka University of Brno, Tcheque Republic Points in quantales and cm-lattices A. Schalk University of Manchester, England Concrete data structures as games V. Schmitt University of Leicester, England Flatness, preorders and general metric spaces V. Selivanov Siberian Division of the Russian Academy of Sciences, Novosibirsk, Russia Variations on wadge reducibility D. Spreen Universitaet Siegen, Germany Domains with approximation structure and their canonical quasi-metrics H. Tsuiki Kyoto University, Japan Topological dimension of domain environments P. Waszkiewicz Jagiellonian University, Krakow, Poland A domain-theoretic metrization theorem From rrosebru@mta.ca Sat Jul 10 14:24:59 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 10 Jul 2004 14:24:59 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BjLXY-0003pH-00 for categories-list@mta.ca; Sat, 10 Jul 2004 14:21:32 -0300 X-Authentication-Warning: triples.math.mcgill.ca: barr owned process doing -bs Date: Fri, 9 Jul 2004 14:33:07 -0400 (EDT) From: Michael Barr X-X-Sender: barr@triples.math.mcgill.ca To: categories@mta.ca Subject: categories: Re: Grothendieck's writings In-Reply-To: <40ECEB18.7020407@usyd.edu.au> Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 18 To reiterate what I said in my original posting on the subject: No. A Russian translation does exist, but the original does not. And Roy's very small beginning is the only one available in English AFAIK. Let me take this opportunity to describe the experience I had trying to get permission from Grothendieck. Some made the suggestion that TAC reprint the Tohoku paper. I had recently met one Jean Malgoire (not Magloire, incidentally) who claimed to be the unique mathematician who is in communication with Grothendieck. I started by writing the editors of Tohoku since in my experience these rights were kept by the journal. They told me that the rights were held by Grothendieck. So I wrote to Malgoire. He replied that it was so unlikely that Grothendieck would agree that he would not ask him. Later someone told me that in fact, Malgoire had full authority as Grothendieck's literary executor. I don't know if this in fact true, but even so he may well have felt that going against Grothendieck's known wishes was inadvisable (although he could have explained that to me, instead, apparently, of lying). So I assume that Grothendieck didn't want the original posted. By the way, the third word of the title is "semailles" (sowings, not seeds). On Thu, 8 Jul 2004, Max Kelly wrote: > Recent communications about Grothendieck's "Recoltes et semelles" refer > to the partial translation by Roy Lisker - but none, as far as I recall, > gives an electronic reference to the French original. Is it not > available in this form? > > Max Kelly. > > > > From rrosebru@mta.ca Sat Jul 10 14:28:33 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 10 Jul 2004 14:28:33 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BjLdL-0003ym-00 for categories-list@mta.ca; Sat, 10 Jul 2004 14:27:31 -0300 From: Robert Knighten MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Message-ID: <16622.59286.407431.567286@zeus.knighten.org> Date: Fri, 9 Jul 2004 11:44:38 -0700 To: categories@mta.ca Subject: categories: Grothendieck's writings In-Reply-To: <40ECEB18.7020407@usyd.edu.au> References: <40ECEB18.7020407@usyd.edu.au> X-Mailer: VM 7.17 under Emacs 21.3.2 Reply-To: Robert@Knighten.org (Robert L. Knighten) Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 19 [note from moderator: http://www.grothendieck-circle.org mentioned earlier by the poster, is currently on-line and has many links, including scans of `Recoltes et semailles'.] Max Kelly writes: > Recent communications about Grothendieck's "Recoltes et semelles" refer > to the partial translation by Roy Lisker - but none, as far as I recall, > gives an electronic reference to the French original. Is it not > available in this form? > > Max Kelly. > > http://mapage.noos.fr/recoltesetsemailles/TdM.htm -- Bob -- Robert L. Knighten Robert@Knighten.org From rrosebru@mta.ca Mon Jul 12 12:26:42 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 12 Jul 2004 12:26:42 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1Bk2dj-0000q0-00 for categories-list@mta.ca; Mon, 12 Jul 2004 12:22:47 -0300 Date: Sun, 11 Jul 2004 15:26:30 -0400 (EDT) From: Peter Freyd Message-Id: <200407111926.i6BJQULF027532@saul.cis.upenn.edu> To: categories@mta.ca Subject: categories: Roy Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 20 The Grothendieck discussion has moved a bit far from the main reason for this list but, if I may, a couple of points: First -- in answer to Max's query -- Roy Lisker tells me that almost all of Grothendieck's autobiography in the original French has been transcribed onto www.grothendieck-circle.org. Second, who is Roy Lisker? I've valued him as a resource for over 40 years. He was a student at Penn and a few years later I was a character witness in his trial for draft-card burning. Yep. And he served a 6 month sentence. Among other mathematicians who support his efforts are Lou Kauffman and Mike Barr (Mike has known him longer than I have). Take a look at www.fermentmagazine.org. First you might want to read: Commonweal 02/09/2001 Stop the Presses by Richard Alleva I enter the Russell Public Library of Middletown, Connecticut, just around the corner from Wesleyan University. Walking past the circulation desk, I turn left and enter a publisher's office. No, wait, it's not a publisher's office but the library's reference department. But, behold, in one corner, publishing is indeed in progress. Crouched over a computer keyboard is a middle-aged man with a pate appropriately monkish and a face appropriately gnomic, for like any good writer he coaxes his thoughts onto the page with the humble intensity of a monk decorating a manuscript or the greedy intensity of a gnome counting his gold. He has slipped his complete works onto some disks which he carries to and from the library. With the aid of a benevolent library computer technician, he has installed a wide variety of typefonts on the hard drive which not only he but any other library patron can employ (thereby making our writer not only the beneficiary but the benefactor of the library), and once he has written at least a couple of drafts in longhand, he chooses the most appropriate font for the story or essay in progress, types it, revises again and again until satisfied, prints, photocopies, turns the results over to a bindery, and winds up with the latest of several handsome booklets with blue or purple or red covers, puckishly decorated by their author. Presto, a twenty-first-century descendant of the Elizabethan chapbook. The contents? Modern variations of Greek and Indian myths, "cynical" (but actually quite poignant) Christmas stories, short fiction about Americans in Paris in the 1960s, factual reports on scientific conferences, ruminations on the state of current academia, horror stories of the homeless, book reviews, farces, musings on the latest developments in physics, and one of the most unsparing and tacitly poignant autobiographies I have ever read. Whose autobiography? That of Roy Lisker, onetime math prodigy, ex-wandering musician, contributor to JeanPaul Sartre's Les Temps Modernes, and local character in a succession of places (mostly university communities), political protestor and prankster, and indefatigable self-publisher. Unless you are Noam Chomsky or historian Howard Zinn or composers Milton Babbitt and John Harbison or one of the other subscribers to Lisker's monthly publication, Ferment, you will have to take my word for it that Roy is worth reading for the way he can make a fictional character as rooted in the real world as the subject of a New Yorker profile, while endowing a real-life academic with the fabulousness of a character in Dickens. If there were any literary justice in the world, Linker's story, "Sam, The Messiah Man," about a violinist who devotes his entire career to perfecting the violin passages of a Handel oratorio, would be as renowned as Borges's fable about another artistic specialist, "Pierre Menard, Author of the Quixote." But what really concerns me here is to point out how tenaciously Lisker reverts to the seemingly outmoded notion of the writer as local character and streetcorner vendor of news, satire, and fantasy. To be sure, Lisker has been conventionally published (his academic satire, Getting That Meal Ticket, was published in Paris by Rend Juliard in 1972), but he now confines his energies to using his private printing press in the Russell Library, hawking his wares on the Wesleyan campus, giving readings at local bookstores, and mailing his publications to subscribers who are all over the country because Roy, in his youth, had been all over the country befriending and bugging people while enacting his role of academic-mathematician- wandering minstrel. [For the whole thing: www.fermentmagazine.org/Commonweal.html] From rrosebru@mta.ca Mon Jul 12 12:26:42 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 12 Jul 2004 12:26:42 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1Bk2cX-0000lZ-00 for categories-list@mta.ca; Mon, 12 Jul 2004 12:21:33 -0300 Message-Id: Date: Sun, 11 Jul 2004 11:32 +0200 From: femke@few.vu.nl (Femke van Raamsdonk) To: categories@mta.ca Subject: categories: RTA'05: call for papers Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 21 ****************************** * * * RTA'05 CALL FOR PAPERS * * * ****************************** http://www-i2.informatik.rwth-aachen.de/RTA05/ April 19--21, 2005 Nara, Japan The 16th Int. Conf. on Rewriting Techniques and Applications (RTA'05) will collocate with the 7th International Conference on Typed Lambda Calculi and Applications (TLCA'05) as part of the Federated Conference on Rewriting, Deduction and Programming (RDP'05). IMPORTANT DATES: Nov 12, 2004: Deadline for electronic submission of title and abstract Nov 19, 2004: Deadline for electronic submission of papers Jan 14, 2005: Notification of acceptance of papers Feb 4, 2005: Deadline for final versions of accepted papers Apr 19-21, 2005: Conference RTA is the major forum for the presentation of research on all aspects of rewriting. Typical areas of interest include (but are not limited to): * APPLICATIONS: case studies; rule-based (functional and logic) programming; symbolic and algebraic computation; theorem proving; system synthesis and verification; proof checking. * FOUNDATIONS: matching and unification; narrowing; completion techniques; strategies; constraint solving; explicit substitutions; tree automata. * FRAMEWORKS: string, term, and graph rewriting; lambda-calculus and higher-order rewriting; proof nets; constrained rewriting/deduction; categorical and infinitary rewriting. * IMPLEMENTATION: compilation techniques; parallel execution; rewriting tools. * SEMANTICS: equational logic; rewriting logic. INVITED TALKS will be given at RTA'05 by: * Amy Felty (Ottawa) * Yoshihito Toyama (Sendai) * Philip Wadler (Edinburgh) BEST PAPER AWARDS: An award of 100,000 Yen will be given to the best paper or papers as decided by the PC. RTA'04 PROGRAM COMMITEE: * Franz Baader (Dresden) * Mariangiola Dezani (Torino) * Juergen Giesl (Aachen, Chair) * Bernhard Gramlich (Vienna) * Florent Jacquemard (Cachan) * Claude Kirchner (Nancy) * Pierre Lescanne (Lyon) * Aart Middeldorp (Innsbruck) * Hitoshi Ohsaki (Amagasaki) * Vincent van Oostrom (Utrecht) * Christine Paulin-Mohring (Orsay) * Frank Pfenning (Pittsburgh) * Femke van Raamsdonk (Amsterdam) * Mark-Oliver Stehr (Urbana) * Rakesh Verma (Houston) * Andrei Voronkov (Manchester) RTA'05 SUBMISSIONS: Submissions must be original and not submitted for publication elsewhere. Submission categories include regular research papers and system descriptions. Also problem sets and submissions describing interesting applications of rewriting techniques will be very welcome. The page limit is 15 pages (10 pages for system descriptions). As usual, accepted papers will appear in the Springer-Verlag Lecture Notes in Computer Science series. More information about paper submission is available at the RTA'05 web page. http://www-i2.informatik.rwth-aachen.de/RTA05/ LOCATION, TRAVEL, ACCOMODATION, AND REGISTRATION The conference takes place in Nara park, which is one of the most important cultural sights of Japan with some of the oldest and most impressive temples and shrines. Airfares from Europe or the US to Japan are not expensive in mid-April and the conference will offer reasonably priced accommodation and low registration fees. RTA'05 PROGRAM CHAIR: Juergen Giesl LuFG Informatik II RWTH Aachen Ahornstr. 55 52074 Aachen Germany giesl@informatik.rwth-aachen.de RTA'05 CONFERENCE CHAIR: Hitoshi Ohsaki AIST Japan ohsaki@ni.aist.go.jp From rrosebru@mta.ca Fri Jul 16 10:10:43 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 16 Jul 2004 10:10:43 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BlSQU-0004O5-00 for categories-list@mta.ca; Fri, 16 Jul 2004 10:06:58 -0300 Message-ID: <20040715164456.30718.qmail@web52608.mail.yahoo.com> Date: Thu, 15 Jul 2004 09:44:56 -0700 (PDT) From: Galchin Vasili Subject: categories: relationship between existential/universal quantifiers and adjoints?? To: cat group MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 22 Hello Cat Community, I would like a clear exposition of the relationship between quantifiers and their corresponding adjoints (so I can understand this relationship). In particular, I would to understand how Lawvere came to this insight. Which book, publication. etc. will best help me to understand this very important relationship? Regards, Bill Halchin From rrosebru@mta.ca Fri Jul 16 10:10:43 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 16 Jul 2004 10:10:43 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BlSPg-0004IA-00 for categories-list@mta.ca; Fri, 16 Jul 2004 10:06:08 -0300 Mime-Version: 1.0 X-Sender: awodey@cyrus.andrew.cmu.edu Message-Id: Date: Wed, 14 Jul 2004 13:45:47 -0400 To: categories@mta.ca From: Steve Awodey Subject: categories: algebraic set theory site Content-Type: text/plain; charset="us-ascii" ; format="flowed" Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 23 Dear Colleagues, This is to inform you that a small website has been created for the purpose of collecting and distributing research devoted to algebraic set theory. Following on the Joyal & Moerdijk monograph by the same name, people in several different locations have begun pursuing related research. It is hoped that linking these efforts will encourage collaboration and make it easier for those new to the field to gain easy access. The site is located at: http://www.phil.cmu.edu/projects/ast/ We hope to make more of the papers listed in the bibliography available on the site soon, and to augment the listings with brief descriptions. Please contact me or "webmaster" Michael Warren if you would like to have your name, homepage, and/or research listed. See (some of) you in Vancouver! Steve Awodey From rrosebru@mta.ca Tue Jul 20 18:57:45 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 20 Jul 2004 18:57:45 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1Bn2YR-0000Dn-00 for categories-list@mta.ca; Tue, 20 Jul 2004 18:53:43 -0300 Date: Mon, 19 Jul 2004 13:05:33 +0100 From: Robin Houston To: categories@mta.ca Subject: categories: Proof nets Message-ID: <20040719120533.GC26804@rpc142.cs.man.ac.uk> Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Disposition: inline User-Agent: Mutt/1.4i X-Spam-Score: -4.9 (----) X-Scanner: exiscan for exim4 (http://duncanthrax.net/exiscan/) *1BmWth-0005je-Hl*ERrT.CvyFHs* Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 24 Dear categorists, The category of ordinary MLL proof nets (where an object is a term, and a morphism X -> Y is a cut-free proof net for |- X^, Y) is the free unitless *-autonomous category generated by the literals. Does the corresponding result hold for MALL? The Hughes-van Glabeek notion of MALL proof net has the ring of truth about it, and indeed they claim to have proven (theorem 4.22) that "two cut-free MALL proofs translate to the same proof net iff they can be converted into each other by a series of rule commutations". Of course the category of MALL proof nets is a unitless *-autonomous category with binary products and coproducts, but nowhere (to my knowledge) is it described as the *free* such category. Is that because it isn't, or merely because it isn't (yet) known to be? Enlightenment will be much appreciated. Yours, Robin From rrosebru@mta.ca Wed Jul 28 10:27:23 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 28 Jul 2004 10:27:23 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BpoP1-0001rw-00 for categories-list@mta.ca; Wed, 28 Jul 2004 10:23:27 -0300 Message-Id: <5.2.0.9.0.20040727090329.03dad588@pop.cwru.edu> X-Sender: cxm7@pop.cwru.edu (Unverified) X-Mailer: QUALCOMM Windows Eudora Version 5.2.0.9 Date: Tue, 27 Jul 2004 09:34:41 -0400 To: categories@mta.ca From: Colin McLarty Subject: categories: Whitehead's problem Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii"; format=flowed Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 25 Does anyone here know the origin of the "Whitehead conjecture"? I mean the one saying every group G with Ext(G,Z)=0 is free. Did Whitehead himself consider this, or did it arise by generalizing his ideas? Did he expect it to be true, or just wonder about it? best, Colin From rrosebru@mta.ca Wed Jul 28 10:27:23 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 28 Jul 2004 10:27:23 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BpoPm-0001vt-00 for categories-list@mta.ca; Wed, 28 Jul 2004 10:24:14 -0300 Message-ID: <4106D44F.E8DD4597@mathstat.yorku.ca> Date: Tue, 27 Jul 2004 15:16:47 -0700 From: Walter Tholen X-Mailer: Mozilla 4.72 [en] (Win98; U) X-Accept-Language: en MIME-Version: 1.0 To: categories@mta.ca Subject: categories: Proceedings, Fields Inst Meeting Dept 2002 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 26 The proceedings of the conference held in September 2002 at the Fields Institute in Toronto are now available with the AMS. The 570-page volume is entitled "Galois Theory, Hopf Algebras, and Semiabelian Categories" (edited by George Janelidze, Bodo Pareigis, and Walter Tholen). See http://www.ams.org/bookstore?fn=20&arg1=whatsnew&item=FIC-43 for more information. A much smaller collection of papers especially devoted to categorical descent theory will appear (hopefully later this year) as an issue of "Applied Categorical Structures" (Kluwer). Walter Tholen. From rrosebru@mta.ca Thu Jul 29 12:00:33 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 29 Jul 2004 12:00:33 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BqCK6-0007aP-00 for categories-list@mta.ca; Thu, 29 Jul 2004 11:55:58 -0300 From: iu3@mcs.le.ac.uk To: categories@mta.ca Subject: categories: SOS2004: Call for Participation Date: 27 Jul 2004 11:18:57 +0100 X-Mailer: Prayer v1.0.7 X-Originating-IP: [143.210.72.63] Mime-Version: 1.0 Content-Type: text/plain; format=flowed; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Message-Id: <20040727101857.81D422F673A@scyros.mcs.le.ac.uk> Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 27 CALL FOR PARTICIPATION =09 Structural Operational Semantics http://www.cs.auc.dk/~luca/SOS-WORKSHOP/ A Satellite Workshop of CONCUR 2004 30 August, 2004, London, United Kingdom EARLY REGISTRATION DEADLINE: 30th July 2004. Please refer to http://www.doc.ic.ac.uk/concur2004/registrationindex.html STUDENT GRANT DEADLINE: 6th August 2004. Please see below. The SOS workshop aims to be a forum for researchers, students=20 and practitioners interested in new developments and directions=20 for future investigation in the field of structural operational=20 semantics. One of the specific goals of the workshop is=20 to establish synergies between the concurrency and programming=20 language communities working on the theory and practice of SOS.=20 The workshop will also mark the publication of a special issue of=20 the Journal of Logic and Algebraic Programming, devoted to SOS.=20 Together with original research papers on SOS, this special issue=20 will feature a definitive version of Gordon Plotkin's 1981 DAIMI memo=20 on SOS, together with a piece by Plotkin on the origins of SOS.=20 Preliminary Scientific Programme: * Andrew Pitts: Equivariant and Nominal SOS (invited talk) =20 * David Sands Representing and Manipulating Contexts: a Tool for=20 Operational Reasoning (tutorial) =20 * Matthias Mann Congruence of Bisimulation in a Non-Deterministic=20 Call-By-Need Lambda Calculus =20 * Bartek Klin Congruence Formats from Bialgebraic Semantics =20 * Rob van Glabbeek The Meaning of Negative Premises: Part II=20 (tutorial) * Olivier Tardieu A Deterministic Logical Semantics for Esterel =20 * Peter Mosses Modular Structural Operational Semantics =20 * Marija Kulas Toward the Concept of Backtracking Computation =20 * Ralf Laemmel Evolution Scenarios for Language-based Functionality =20 Sponsorship:=20 The workshop is partly sponsored by the Engineering and Physical=20 Sciences Research Council (EPSRC).=20 Student Grants:=20 Thanks to the support of the EPSRC, we have fifteen small grants available to the U.K.-based PhD students to attend the SOS workshop. A typical grant will cover the costs of travel and subsistence, and=20 in special cases the accommodation for one night in London. Full details on how to apply will soon appear on the workshop Web pages but, in short, if you are a PhD student researching at the U.K.-based=20 academic institution, you can apply for the grant by emailing=20 Irek Ulidowski (iu3 AT mcs.le.ac.uk) the following information: 1. Full name 2. Affiliation 3. Topic of research 4. Supervisor's details 5. Estimate of cost of travel and accommodation (if really necessary) 6. Short statement on how the SOS Workshop will benefit your present and future research We also recommend that you supply us with a short supporting letter=20 from your supervisor.=20 The student GRANT DEADLINE is 6th August 2004. =20 Please, copy your email to Luca Aceto (luca AT cs.auc.dk) and Wan Fokkink (wan AT cwi.nl). Program Committee: Luca Aceto (BRICS, Aalborg, Denmark, co-chair) Wan Fokkink (CWI, The Netherlands, co-chair) Rob van Glabbeek (NICTA, Sydney, Australia) Ralf Laemmel (CWI, The Netherlands) Peter Mosses (BRICS, Aarhus, Denmark) David Sands (Chalmers, Sweden) Alex Simpson (Edinburgh, United Kingdom) Simone Tini (Insubria, Italy) Irek Ulidowski (Leicester, United Kingdom, co-chair) Erik de Vink (Eindhoven, The Netherlands) Organizing Committee: Luca Aceto, email: luca AT cs.auc.dk, (BRICS, Aalborg, Denmark) Wan Fokkink, email: wan AT cwi.nl,=20 (CWI, The Netherlands) Irek Ulidowski, email iu3 AT mcs.le.ac.uk (Leicester, United Kingdom) From rrosebru@mta.ca Thu Jul 29 12:00:33 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 29 Jul 2004 12:00:33 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BqCNS-0007nF-00 for categories-list@mta.ca; Thu, 29 Jul 2004 11:59:26 -0300 From: Robert Knighten MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Message-ID: <16648.52785.228811.155889@zeus.knighten.org> Date: Thu, 29 Jul 2004 03:15:13 -0700 To: categories@mta.ca Subject: categories: re: Whitehead's problem In-Reply-To: <5.2.0.9.0.20040727090329.03dad588@pop.cwru.edu> References: <5.2.0.9.0.20040727090329.03dad588@pop.cwru.edu> X-Mailer: VM 7.17 under Emacs 21.3.2 Reply-To: Robert@Knighten.org (Robert L. Knighten) Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 28 Colin McLarty writes: > Does anyone here know the origin of the "Whitehead conjecture"? I mean the > one saying every group G with Ext(G,Z)=0 is free. Did Whitehead himself > consider this, or did it arise by generalizing his ideas? Did he expect it > to be true, or just wonder about it? > > best, Colin > This isn't definitive, but I think it is approximately correct. The connection between Ext(G,Z)=0 and G being free seems to have first appeared as a reformulation by Henri Cartan of a result of Karl Stein which arose from his work on the "second Cousin problem" in several complex variables. The reference to the paper and review is: @article {MR13:224f, AUTHOR = {Stein, Karl}, TITLE = {Analytische {F}unktionen mehrerer komplexer {V}er\"anderlichen zu vorgegebenen {P}eriodizit\"atsmoduln und das zweite {C}ousinsche {P}roblem}, JOURNAL = {Math. Ann.}, VOLUME = {123}, YEAR = {1951}, PAGES = {201--222}, MRCLASS = {30.0X}, MRNUMBER = {13,224f}, MRREVIEWER = {H. Cartan}, } Whitehead appears to have first posed the question (it doesn't seem to have been a conjecture) at a conference in Warsaw in 1952. The Whitehead problem seems to have been first published by A. Ehrenfeucht in 1955: @article {MR16:994b, AUTHOR = {Ehrenfeucht, A.}, TITLE = {On a problem of {J}. {H}. {C}. {W}hitehead concerning {A}belian groups}, JOURNAL = {Bull. Acad. Polon. Sci. Cl. III.}, VOLUME = {3}, YEAR = {1955}, PAGES = {127--128}, MRCLASS = {20.0X}, MRNUMBER = {16,994b}, MRREVIEWER = {P. A. Smith}, } -- Bob -- Robert L. Knighten Robert@Knighten.org From rrosebru@mta.ca Fri Jul 30 17:20:39 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 30 Jul 2004 17:20:39 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BqdnY-000798-00 for categories-list@mta.ca; Fri, 30 Jul 2004 17:16:12 -0300 Message-ID: <32774.62.252.132.5.1091147728.squirrel@mail.maths.gla.ac.uk> Date: Fri, 30 Jul 2004 01:35:28 +0100 (BST) Subject: categories: Book: Higher Operads, Higher Categories From: "Tom Leinster" To: X-Priority: 3 Importance: Normal Cc: X-Mailer: SquirrelMail (version 1.2.10) MIME-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 29 Fifteen months ago I announced to the list that my book, Higher Operads, Higher Categories, was available on the web. It is now out in traditional form too, in the blue-green LMS Lecture Note Series (Cambridge University Press). Details of both versions can be found at http://www.maths.gla.ac.uk/~tl/book.html The free web version will remain available permanently. Those of you who came to my talk at CT04 will know that there is a mistake on the front cover: take out your blue-green Tippex and paint over the words "Edited by". Tom From rrosebru@mta.ca Fri Jul 30 17:20:39 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 30 Jul 2004 17:20:39 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1Bqdol-0007Cv-00 for categories-list@mta.ca; Fri, 30 Jul 2004 17:17:27 -0300 Message-ID: <32776.62.252.132.5.1091147833.squirrel@mail.maths.gla.ac.uk> Date: Fri, 30 Jul 2004 01:37:13 +0100 (BST) Subject: categories: Limit of finite sets From: "Tom Leinster" To: X-Priority: 3 Importance: Normal Cc: X-Mailer: SquirrelMail (version 1.2.10) MIME-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 30 I've recently come across the following curious little result. I know how to prove it and have a use for it, but my question is: can anyone supply a wider context or explanation? The result is that the limit in Set of any diagram ... ---> S_3 ---> S_2 ---> S_1 of finite nonempty sets is nonempty. Note that finiteness cannot be dropped: for instance, take each S_n to be the natural numbers and each map to be addition of 1. Thanks, Tom From rrosebru@mta.ca Sat Jul 31 19:38:45 2004 -0300 Status: X-Status: X-Keywords: Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 31 Jul 2004 19:38:45 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1Br2QB-0005m4-00 for categories-list@mta.ca; Sat, 31 Jul 2004 19:33:43 -0300 Date: Fri, 30 Jul 2004 22:29:58 +0100 (BST) From: "Prof. Peter Johnstone" Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-DPMMS-Scan-Signature: 52b2ec4a892cc9295ce0dcc23e061bcd Sender: cat-dist@mta.ca Precedence: bulk On Fri, 30 Jul 2004, Tom Leinster wrote: > I've recently come across the following curious little result. I know > how to prove it and have a use for it, but my question is: can anyone > supply a wider context or explanation? > > The result is that the limit in Set of any diagram > > ... ---> S_3 ---> S_2 ---> S_1 > > of finite nonempty sets is nonempty. Note that finiteness cannot be > dropped: for instance, take each S_n to be the natural numbers and > each map to be addition of 1. > I'm not sure whether this counts as an explanation, but it's certainly a wider context: the result is a special case of the fact that a (cofiltered) inverse limit of locales and proper maps maps properly to each of the vertices of the diagram. See C3.2.11 in the Elephant, and also C1.1.12. (And note that the result fails for spaces: thus a key part of the argument in the finite case is that the inverse limit in Loc is a spatial locale.) Peter Johnstone From rrosebru@mta.ca Sat Jul 31 19:38:45 2004 -0300 Status: X-Status: X-Keywords: Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 31 Jul 2004 19:38:45 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1Br2Qz-0005nX-00 for categories-list@mta.ca; Sat, 31 Jul 2004 19:34:33 -0300 X-Authentication-Warning: triples.math.mcgill.ca: barr owned process doing -bs Date: Fri, 30 Jul 2004 22:00:55 -0400 (EDT) From: Michael Barr X-X-Sender: barr@triples.math.mcgill.ca To: categories@mta.ca Subject: categories: Re: Limit of finite sets In-Reply-To: <32776.62.252.132.5.1091147833.squirrel@mail.maths.gla.ac.uk> Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk It is purely a property of compactness. Take the product of compact spaces. The condition of an element of the product being in the limit is the conjunction of infinitely many conditions each of which says that two coordinates agree and if it is a chain (or, in fact, an inverse filtered diagram) of non-empty compact sets, each of those finitely many conditions defines a closed non-empty subset with the finite intersection property. So the general context is that an inverse filtered limit of non-empty compact Hausdorff spaces is non-empty. Although I don't seem to have used Hausdorffness, it is required to show those sets are closed. And without it, you could get the example Tom described using the trivial topology, which is certainly compact. I guess you could use the finite complement topology to get a T1 counterexample. Michael On Fri, 30 Jul 2004, Tom Leinster wrote: > I've recently come across the following curious little result. I know > how to prove it and have a use for it, but my question is: can anyone > supply a wider context or explanation? > > The result is that the limit in Set of any diagram > > ... ---> S_3 ---> S_2 ---> S_1 > > of finite nonempty sets is nonempty. Note that finiteness cannot be > dropped: for instance, take each S_n to be the natural numbers and > each map to be addition of 1. > > Thanks, > Tom > > > > > From rrosebru@mta.ca Sat Jul 31 19:38:45 2004 -0300 Status: X-Status: X-Keywords: Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 31 Jul 2004 19:38:45 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1Br2RT-0005pA-00 for categories-list@mta.ca; Sat, 31 Jul 2004 19:35:03 -0300 Message-ID: <32775.62.252.132.163.1091275347.squirrel@mail.maths.gla.ac.uk> Date: Sat, 31 Jul 2004 13:02:27 +0100 (BST) Subject: categories: Re: limits of finite sets From: "Tom Leinster" To: X-Priority: 3 Importance: Normal X-Mailer: SquirrelMail (version 1.2.10) MIME-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit Sender: cat-dist@mta.ca Precedence: bulk I asked for an explanation of the following result: > the limit in Set of any diagram > > ... ---> S_3 ---> S_2 ---> S_1 > > of finite nonempty sets is nonempty Thanks very much to all who replied. I'll summarize some of the points made to me in private replies: 1. This is called Koenig's Lemma, and is usually stated in the form "any finitely-branching infinite tree contains an infinite (positively oriented) path". 2. This also follows from a general result in topology by regarding each S_n as a discrete space. The general result is that any "suitably-shaped" limit of nonempty compact Hausdorff spaces is nonempty. For Bourbaki (General Topology), "suitably-shaped" means indexed by a directed poset. More generally still, it could be any componentwise cofiltered limit, i.e. any limit for which each connected-component of the indexing category I is cofiltered (or equivalently, every finite connected diagram in I admits a cone). The proof of the general topological result specializes to give a nice topological proof of Koenig. For each n, let V_n be the subset of the product \prod_n S_n consisting of those sequences whose first n terms are compatible; then \lim_n S_n is the intersection of the (V_n)s. But with the discrete topology on each S_n, Tychonoff says that \prod_n S_n is compact, and (V_n) is a nested sequence of nonempty closed subsets so has nonempty intersection. Tom From rrosebru@mta.ca Sat Jul 31 19:38:45 2004 -0300 Status: X-Status: X-Keywords: Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 31 Jul 2004 19:38:45 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1Br2Te-0005tv-00 for categories-list@mta.ca; Sat, 31 Jul 2004 19:37:18 -0300 In-Reply-To: <32776.62.252.132.5.1091147833.squirrel@mail.maths.gla.ac.uk> References: <32776.62.252.132.5.1091147833.squirrel@mail.maths.gla.ac.uk> Mime-Version: 1.0 (Apple Message framework v618) Content-Type: text/plain; charset=US-ASCII; format=flowed Message-Id: <079399ED-E30C-11D8-AEF5-000393C440BC@math.tulane.edu> Content-Transfer-Encoding: 7bit From: Michael Mislove Subject: categories: Re: Limit of finite sets Date: Sat, 31 Jul 2004 11:09:41 -0500 To: X-Mailer: Apple Mail (2.618) Sender: cat-dist@mta.ca Precedence: bulk Tom, The classical context I know is that in the category of compact Hausdorff spaces and continuous maps, limits exist, and are non-empty if each component space is non-empty. This uses the Axiom of Choice (and the Tychonoff Theorem) to show that the product of the component spaces $S_i$ is non-empty and compact. The generalization just embeds Set in Top by regarding sets as discrete spaces, so all sets are locally compact, and the compact sets are exactly the finite ones. The limit can be defined as the family $ L = \{ (s_i) \mid p_ji(s_j) = s_i, for i \leq j \in I\}. $ This limit is then the filtered intersection of the sets $T_F = \prod_{i \not\in F} S_i \times \{(s_i)_{i \in F} \mid p_{ji}(s_j) = s_i, i \leq j \in F\},$ where $F\subseteq I$ is finite. The Axiom of Choice implies $F, \prod_{i \not\in F} S_i$ is non-empty, and it's easy to show that $\{(s_i)_{i \in F} \mid p_{ji}(s_j) = s_i, i \leq j \in F\}$ is non-empty since $F$ is finite, so $T_F$ is non-empty. Since the bonding maps $p_{ji} \colon S_j \to S_i$ are continuous, the set $T_F$ is closed, so it's a non-empty closed subset of the compact Hausdorff space $\prod_i S_i$. Since the family is filtered, its intersection is non-empty. This generalization also suggests why the sets have to be finite - limits of non-empty locally compact spaces and continuous maps can be empty, because the limit object may be empty. Indeed, the same construction as given above defines the limit object L, but L may be empty because the filtered intersection of a family of closed, non-empty subsets of a locally compact space may be empty. Best regards, Mike On Jul 29, 2004, at 7:37 PM, Tom Leinster wrote: > I've recently come across the following curious little result. I know > how to prove it and have a use for it, but my question is: can anyone > supply a wider context or explanation? > > The result is that the limit in Set of any diagram > > ... ---> S_3 ---> S_2 ---> S_1 > > of finite nonempty sets is nonempty. Note that finiteness cannot be > dropped: for instance, take each S_n to be the natural numbers and > each map to be addition of 1. > > Thanks, > Tom > > From rrosebru@mta.ca Sat Jul 31 19:38:46 2004 -0300 Status: X-Status: X-Keywords: Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 31 Jul 2004 19:38:46 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1Br2ST-0005rZ-00 for categories-list@mta.ca; Sat, 31 Jul 2004 19:36:05 -0300 From: Peter Selinger Message-Id: <200407311257.i6VCvhh28559@quasar.mathstat.uottawa.ca> Subject: categories: Re: Limit of finite sets To: categories@mta.ca Date: Sat, 31 Jul 2004 08:57:43 -0400 (EDT) In-Reply-To: <32776.62.252.132.5.1091147833.squirrel@mail.maths.gla.ac.uk> from "Tom Leinster" at Jul 30, 2004 01:37:13 AM X-Mailer: ELM [version 2.5 PL3] MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk This seems to me to be equivalent to Koenig's lemma: every infinite, finitely branching tree has an infinite branch. The set of vertices is the disjoint union of all the S_n, and there is an edge from (a,i) to (b,i+1) if f_i(b)=a. Conversely, let S_n be the set of vertices at depth n. -- Peter Tom Leinster wrote: > > I've recently come across the following curious little result. I know > how to prove it and have a use for it, but my question is: can anyone > supply a wider context or explanation? > > The result is that the limit in Set of any diagram > > ... ---> S_3 ---> S_2 ---> S_1 > > of finite nonempty sets is nonempty. Note that finiteness cannot be > dropped: for instance, take each S_n to be the natural numbers and > each map to be addition of 1. > > Thanks, > Tom > > > > >