From cat-dist Sun Mar 2 15:20:00 1997 Received: by mailserv.mta.ca; id AA30807; Sun, 2 Mar 1997 15:18:55 -0400 Date: Sun, 2 Mar 1997 15:18:54 -0400 (AST) From: categories To: categories Subject: Intuitionism's Limits Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-Status: Date: Sun, 2 Mar 1997 15:07:12 +1030 (CST) From: William James Intuitionism's Limits: if C is a category sufficiently complex to demonstrate that some C-arrow f:a-->b is monic and B is a subcategory of C containing just f (and the requisite identity arrows), do we still know that f is monic? Should we? (Or, in other words, which view *should* dominate: Intuitionism, Realism, the category theoretic...?) What if C is something (semi?)fundamental like a category of all sets and functions, or a category of categories? I suppose the answer is that monicity is relative to a category, but what supports this as a claim? And doesn't it seem to contradict the reasonable realist claim that we can somehow know f in B to be monic? (Or am I missing something straightforward: that properties can be granted to f by its relationship to C via an inclusion functor?) This goes to the issue of the adequacy of category theory as a foundation in more than the simply technical sense. (I could be using the term "realism" incorrectly too: I take it to be a positon, in maths at least, that mathematical entities can have collections of properties beyond the constraints of a given theoretical context.) William James From cat-dist Sun Mar 2 15:20:11 1997 Received: by mailserv.mta.ca; id AA23305; Sun, 2 Mar 1997 15:20:01 -0400 Date: Sun, 2 Mar 1997 15:20:01 -0400 (AST) From: categories To: categories Subject: Book on semantics of computation Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-Status: Date: Sun, 02 Mar 1997 18:47:57 +0100 From: Andrew Pitts BOOK ANNOUNCEMENT Semantics and Logics of Computation Edited by Andrew M Pitts University of Cambridge and P Dybjer Chalmers University The aim of this volume is to present modern developments in semantics and logics of computation in a way that is accessible to graduate students. The book is based on a summer school at the Isaac Newton Institute and consists of a sequence of linked lecture courses. The authors are leaders in their fields and much of material they present was either not previously accessible, or not accessible in such a digestible form. Contents S. Abramsky, Semantics of interaction: an introduction to game semantics. T. Coquand, Computational content of classical logic M. Hofmann, Syntax and semantics of dependent types M. Hyland, Game semantics E. Moggi, Metalanguages and applications A. Pitts, Operationally-based theories of program equivalence G. Winskel and M. Nielsen, Categories in concurrency Hardback ISBN 0521580579 Published by Cambridge University Press January 1997 UKL 35.00 Ordering information at: http://www.cup.cam.ac.uk/order/ordertop.html (email: information@cup.cam.ac.uk). From cat-dist Mon Mar 3 10:36:18 1997 Received: by mailserv.mta.ca; id AA13693; Mon, 3 Mar 1997 10:35:21 -0400 Date: Mon, 3 Mar 1997 10:35:21 -0400 (AST) From: categories To: categories Subject: Re: Intuitionism's Limits Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-Status: Date: Sun, 2 Mar 1997 15:27:28 -0500 (EST) From: John Baez William James writes: > I suppose the answer is that monicity is relative to a category, > but what supports this as a claim? It seems to me that category theory takes the sensible viewpoint that mathematical entities (e.g. objects and morphisms) only become interesting through their relationship with other entities. Every arrow looks just like every other arrow if we consider it in isolation. Every arrow in a category C is an image of the what James Dolan calls the "walking arrow" --- the nonidentity morphism in the free category C0 on a single morphism --- under some functor F: C0 -> C. Studying an arrow in isolation is just like studying the walking arrow, which is completely dull. The fun begins only when we have a bunch of arrows and start composing them. This is one reason why I think n-category theory should be useful in physics problems like quantum gravity, where it only makes sense to speak of where or when an event occurs relative to other events, not with respect to some spacetime manifold of fixed geometry. For some of the technical apsects of how this might go, see: John Baez and James Dolan, Higher-dimensional algebra and topological quantum field theory, Jour. Math. Phys. 36 (1995), 6073-6105. Louis Crane, Clock and category: is quantum gravity algebraic?, J. Math. Phys. 36 (1995), 6180-6195. These both appeared in a special issue on diffeomorphism-invariant physics. From cat-dist Mon Mar 3 10:36:21 1997 Received: by mailserv.mta.ca; id AA21520; Mon, 3 Mar 1997 10:36:01 -0400 Date: Mon, 3 Mar 1997 10:36:01 -0400 (AST) From: categories To: categories Subject: Re: Intuitionism's Limits Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-Status: Date: Sun, 2 Mar 1997 15:52:17 -0500 (EST) From: Peter Freyd To William James, You must be using a non-standard (philosophical?) definition of "monic", since it is obvious using the standard (mathematical) definition that a monic remains a monic in any subcategory containing it (to get unnecessarily technical, because it's given by a universally quantified Horn sentence). Could you tell us your definition? (For the record: f: A -> B is monic iff for all x,x':X -> A it x f x' f is the case that X -> A -> B = X -> A -> B implies x = x'.) From cat-dist Mon Mar 3 10:36:52 1997 Received: by mailserv.mta.ca; id AA14670; Mon, 3 Mar 1997 10:36:46 -0400 Date: Mon, 3 Mar 1997 10:36:46 -0400 (AST) From: categories To: categories Subject: RE: Intuitionism's Limits Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-Status: Date: Sun, 2 Mar 97 21:09 EST From: Fred E J Linton <0004142427@mcimail.com> If a and b are *two* objects, then, in the category consisting solely of those two objects, their respective identity maps, and one further map from a to b (and nothing more), that map is both monic and epic. Once embedded in another category, however, that map may easily fail to remain monic, may easily fail to remain epic, may remain one but not the other -- there's no telling. And if a = b instead, and f and the identity on a are the only *two* maps there are, then clearly f *may* be idempotent, hence neither monic nor epic; then again, f *may* be involutory, hence a true isomorphism. I think true realism requires that one pay strict attention to the definitions, refraining from free-associations with the vibrations of the terms defined. Cheers, -- Fred From cat-dist Mon Mar 3 10:37:46 1997 Received: by mailserv.mta.ca; id AA13493; Mon, 3 Mar 1997 10:37:39 -0400 Date: Mon, 3 Mar 1997 10:37:39 -0400 (AST) From: categories To: categories Subject: Re: Intuitionism's Limits Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-Status: Date: Mon, 3 Mar 1997 18:40:30 +1030 (CST) From: William James > Intuitionism's Limits: if C is a category sufficiently complex to > demonstrate that some C-arrow f:a-->b is monic and B is a subcategory > of C containing just f (and the requisite identity arrows), do we > still know that f is monic? Should we? (Or, in other words, which > view *should* dominate: Intuitionism, Realism, the category > theoretic...?) What if C is something (semi?)fundamental like a > category of all sets and functions, or a category of categories? > Whoops! The question is trivialised by using monicity as the relevant property. Reconsider it in terms of say f as an isomorphism, or of f holding some property in C that B lacks the resources to demonstrate. I'm thinking aloud on this question: constructive maths should say that of f in B there is no demonstration forthcoming, so judgment will be withheld on whether or not f has the property; a category theorist might say that category theory does not dwell on elements and that, in context, B is no different from any isomorph of 2, so there positively is no further property of f to be had other than that which can be demonstrated in any isomorph of 2. This is more than Intuitionism will allow. Might I, then, go on to say that the philosophies of constructive mathematics and category theory really are different? William James (if I'm digging a hole, I want it to be big) From cat-dist Mon Mar 3 13:14:43 1997 Received: by mailserv.mta.ca; id AA05060; Mon, 3 Mar 1997 13:14:11 -0400 Date: Mon, 3 Mar 1997 13:14:11 -0400 (AST) From: categories To: categories Subject: Re: Intuitionism's (read "Philosophy's") Limits Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: O X-Status: Date: Mon, 3 Mar 1997 10:45:55 -0500 (EST) From: Peter Freyd William James continues to write: Might I, then, go on to say that the philosophies of constructive mathematics and category theory really are different? Constructive mathematics is a philosophy. Category theory is not. The question doesn't even type-check. Of course they're different. From cat-dist Tue Mar 4 22:42:20 1997 Received: by mailserv.mta.ca; id AA02802; Tue, 4 Mar 1997 22:41:13 -0400 Date: Tue, 4 Mar 1997 22:41:13 -0400 (AST) From: categories To: categories Subject: Re: Intuitionism's (read "Philosophy's") Limits Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: O X-Status: Date: Tue, 4 Mar 1997 18:19:51 +1030 (CST) From: William James > William James continues to write: > > Might I, then, go on to say that the philosophies of constructive > mathematics and category theory really are different? > > Constructive mathematics is a philosophy. Category theory is not. > The question doesn't even type-check. > > Of course they're different. Does category theory, being mathematics, have no associated philosophy? (I grant you the original question would have been more recognisable given better use of language: "...philosophies of constructive mathematics and *of* category theory...") William James From cat-dist Wed Mar 5 11:13:55 1997 Received: by mailserv.mta.ca; id AA20713; Wed, 5 Mar 1997 11:13:02 -0400 Date: Wed, 5 Mar 1997 11:13:00 -0400 (AST) From: categories To: categories Subject: Re: Intuitionism's (read "Philosophy's") Limits Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-Status: Date: Wed, 05 Mar 1997 00:56 -0500 (EST) From: Fred E J Linton <0004142427@mcimail.com> Any philosophy category theory may have would have at its core, I think, the notion that mathematical objects are known *not* in isolation but in the context of their comrades. The group of rational integers, accompanied *only* by its identity map, and the Thom space of the tangent bundle of some exotic manifold, accompanied once again *only* by its identity map, are, as categories, indistinguishable. Plucked out of their original contexts, there is no longer any social setting where one can find any difference between them that really *makes* a difference. According to some other views of mathematics, the group of rational integers, that particular Thom space, the real number {pi}, and my current left shoe, all have unique mathematical personalities that let them be "obviously" distinguished one from another, without any reference even to what I would call their "natural ambient environments". >From my perspective, admittedly that of a categorist, these views result from a simple failure to recognize that what passes for the "intrinsic structure" of a mathematical object is in fact nothing more (nor less) than a clear understanding of its relations with its mates, of roughly similar character, in some category (that "went without saying") they all jointly inhabit -- even the phrase "roughly similar character" is justifiable *only* by virtue of the fact that they *do* all inhabit some same category. I hope I'm actually making myself clear, and not just preaching to the converted. -- Fred From cat-dist Wed Mar 5 11:14:01 1997 Received: by mailserv.mta.ca; id AA17746; Wed, 5 Mar 1997 11:13:50 -0400 Date: Wed, 5 Mar 1997 11:13:50 -0400 (AST) From: categories To: categories Subject: Re: Intuitionism's (read "Philosophy's") Limits Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-Status: Date: Wed, 5 Mar 1997 10:54:19 +0000 From: Steve Vickers > Constructive mathematics is a philosophy. Category theory is not. > The question doesn't even type-check. > > Of course they're different. Philosophy is the love of wisdom; type-checking is not. Of course category theory has its philosophy. To me it's "all things are connected" - you cannot fully describe anything purely in itself but only by the way it connects with others. Category theory makes the connections explicit (as morphisms) and then characterizes things by their universal properties. The philosophy plays a real role in categorical practice: for instance, in the idea that isomorphism between objects is more important than equality, which is not something that can be meaningful just in terms of the formal mathematics. The philosophy also yields a criterion for evaluating the theory: Is categorical structure adequate for describing the connections that we actually find? The strength of the categorical view of "connection structure" is amply confirmed by the power of the universal properties it can express (compare it with, say, graph theory); but if it does fail us anywhere, how might it advance beyond its present formalization? (There is already a plausible answer here: topology has a different way of describing the connections between a point and its neighbours, and the categorical and topological approaches combine to make topos theory.) I hesitate to try to reduce the philosophy of constructive mathematics to a single pithy phrase, not least because there are different schools of constructivism with apparently different philosopies. I shall therefore duck the question of comparing "the philosopies of constructive mathematics and category theory", but I don't believe it's a meaningless one. Steve Vickers. From cat-dist Wed Mar 5 11:14:37 1997 Received: by mailserv.mta.ca; id AA17758; Wed, 5 Mar 1997 11:14:35 -0400 Date: Wed, 5 Mar 1997 11:14:35 -0400 (AST) From: categories To: categories Subject: Re: Intuitionism's (read "Philosophy's") Limits Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-Status: Date: Wed, 5 Mar 1997 12:46:26 +0000 (GMT) From: Dusko Pavlovic According to William James : > > Does category theory, being mathematics, have no associated philosophy? I'm afraid, William, that this presumed association of mathematics and philosophy is actually a bit of a sad romance: while some philosophies do like to be associated with mathematics, mathematics (it doesn't even have a proper plural) mathematics, most of the time, can't care less. While philosophy spends a lot of time defining itself and its relationship with the world, mathematics tends to be a kind of work some people like to do, taking up the world whichever way it comes to them: as a model of a process, as a game of signs or pictures, as a funny language shared between them and theri colleagues... Most mathematicians just smirk not only on philosophy, but even on category theory, or anything else deeply concerned with its own identity. They just like to solve their problems, and sometimes solve other people's problems, thereby gaining everyone's respect and admiration. At least, that's the way I have seen it. Perhaps it helps with your questions a bit. -- Dusko Pavlovic From cat-dist Wed Mar 5 17:20:12 1997 Received: by mailserv.mta.ca; id AA06945; Wed, 5 Mar 1997 17:19:30 -0400 Date: Wed, 5 Mar 1997 17:19:30 -0400 (AST) From: categories To: categories Subject: Re: Intuitionism's (read "Philosophy's") Limits Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: O X-Status: Date: Wed, 5 Mar 1997 11:27:42 -0500 (EST) From: James Stasheff this seems to ignore the distinction between neighbors (aka comrades) and parts (elements) The group of rational integers, with its non-identity automrophisms can, i thought, be distinguished from the Thom space of the > tangent bundle of some exotic manifold with its non-identity automrophisms without comparison to other sets of `numbers' or less exotic manifolds .oooO Jim Stasheff jds@math.unc.edu (UNC) Math-UNC (919)-962-9607 \ ( Chapel Hill NC FAX:(919)-962-2568 \*) 27599-3250 http://www.math.unc.edu/Faculty/jds May 15 - August 15: 146 Woodland Dr Lansdale PA 19446 (215)822-6707 On Wed, 5 Mar 1997, categories wrote: > Date: Wed, 05 Mar 1997 00:56 -0500 (EST) > From: Fred E J Linton <0004142427@mcimail.com> > > Any philosophy category theory may have would have at its core, I think, > the notion that mathematical objects are known *not* in isolation but > in the context of their comrades. The group of rational integers, > accompanied *only* by its identity map, and the Thom space of the > tangent bundle of some exotic manifold, accompanied once again *only* > by its identity map, are, as categories, indistinguishable. > > Plucked out of their original contexts, there is no longer any social setting > where one can find any difference between them that really *makes* a > difference. > > According to some other views of mathematics, the group of rational integers, > that particular Thom space, the real number {pi}, and my current left shoe, > all have unique mathematical personalities that let them be "obviously" > distinguished one from another, without any reference even to what I would > call their "natural ambient environments". > > >From my perspective, admittedly that of a categorist, these views result > from a simple failure to recognize that what passes for the "intrinsic > structure" of a mathematical object is in fact nothing more (nor less) > than a clear understanding of its relations with its mates, of roughly > similar character, in some category (that "went without saying") they all > jointly inhabit -- even the phrase "roughly similar character" is justifiable > *only* by virtue of the fact that they *do* all inhabit some same category. > > I hope I'm actually making myself clear, and not just preaching to the converted. > > -- Fred > > > From cat-dist Wed Mar 5 17:20:37 1997 Received: by mailserv.mta.ca; id AA07116; Wed, 5 Mar 1997 17:20:35 -0400 Date: Wed, 5 Mar 1997 17:20:35 -0400 (AST) From: categories To: categories Subject: Re: Intuitionism's (read "Philosophy's") Limits / flame on Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: O X-Status: Date: Wed, 05 Mar 1997 09:55:51 -0800 From: John C. Mitchell >Philosophy is the love of wisdom; type-checking is not. Well that's a bizarre statement. Not that I want to get into this discussion or anything, but can't a love of wisdom be consistent with type checking? John Mitchell From cat-dist Wed Mar 5 17:23:01 1997 Received: by mailserv.mta.ca; id AA09096; Wed, 5 Mar 1997 17:22:55 -0400 Date: Wed, 5 Mar 1997 17:22:55 -0400 (AST) From: categories To: categories Subject: From moderator Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-Status: The philosophy of the categories list is to allow wide latitude for discussion, but the current discussion of philosophy is getting rather far afield. Therefore further contributions are discouraged, and will not be accepted beyond 5pm GMT on Friday, March 7. Best wishes Bob Rosebrugh, Moderator categories From cat-dist Thu Mar 6 13:31:29 1997 Received: by mailserv.mta.ca; id AA01309; Thu, 6 Mar 1997 13:30:40 -0400 Date: Thu, 6 Mar 1997 13:30:39 -0400 (AST) From: categories To: categories Subject: Change of e-mail Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-Status: Date: Thu, 6 Mar 1997 12:11:56 +0100 (MET) From: Pierre DAMPHOUSSE This short e-mail is to inform my colleagues that my new e-mail address is pdmphss@cauchy.math.univ-tours.fr The former e-mail "damphous@balzac.univ-tours.fr" may still be used, but for a short time only ... until I cancel my account on "balzac". Regards to all. Pierre. Pierre DAMPHOUSSE D\'epartement de Math\'ematiques Facult\'e des Sciences de Tours Parc de Grandmont 37200 Tours, FRANCE ................................................... T\'el : (33)-02-47-36-72-62 (bureau) (33)-02-47-36-69-25 (secr\'etariat) Fax : (33)-02-47-36-70-68 (fax for the department; mention my name) When faxing or telephoning from abroad, drop the the 0 (zero) in 33-02-... ....................^.............................. From cat-dist Thu Mar 6 13:31:31 1997 Received: by mailserv.mta.ca; id AA26186; Thu, 6 Mar 1997 13:29:47 -0400 Date: Thu, 6 Mar 1997 13:29:47 -0400 (AST) From: categories To: categories Subject: Re: Intuitionism's Limits Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-Status: Date: Wed, 05 Mar 1997 22:36:19 -0800 From: Vaughan Pratt Date: Tue, 4 Mar 1997 18:19:51 +1030 (CST) From: William James (I grant you the original question would have been more recognisable given better use of language: "...philosophies of constructive mathematics and *of* category theory...") Your original question was "Which view should dominate?", where "the category theoretic view" was one of your options. (You had several questions but this one seemed the most central.) If you are asking whether the primary expression of structure should be in terms of relations between elements or transformations of objects, then I would answer this as follows. The analogous question for physics is whether energy and matter consist of particles or waves. The consensus in physics today is that both energy and matter can be viewed more or less equally accurately, if not equally insightfully, as either particles or waves. Which offers more insight depends on the circumstances. The corresponding position for mathematics would be that structure can be expressed more or less equally well in elementary or transformational terms, and that which approach gives more insight depends on the circumstances. The extent to which this is not the consensus in mathematics today is less a reflection on either approach than on the conceptual health of mathematics relative to that of physics. Vaughan Pratt From cat-dist Fri Mar 7 15:45:28 1997 Received: by mailserv.mta.ca; id AA32198; Fri, 7 Mar 1997 15:43:26 -0400 Date: Fri, 7 Mar 1997 15:43:26 -0400 (AST) From: categories To: categories Subject: non philosophy Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-Status: Date: Fri, 7 Mar 1997 14:24:15 -0500 (EST) From: Peter Freyd William James answered his own question when he asked: Does category theory, being mathematics, have no associated philosophy? Yes, category theory is mathematics. Therefore its associated philosophy is whatever philosophy one chooses to associate with mathematics. As for the latter, Dusko provided a pretty good answer. I would modify it only to reflect that mathematics (which, as always in the absence of a qualifier, means pure mathematics) is a subject matter. Most mathematicians are sufficiently confident about their subject matter that they feel no need for a semantics, much less a stated philosophy. (Yes, it has been notoriously difficult to define intensionally, but that's not special to mathematics. What's the subject matter of physics? If either mathematicians or physicists were -- using Dusko's language -- to spend a lot of time defining their subject, there never would have been much mathematics or physics.) Steve thinks that the existence of a philosophy of category theory is an "of course". In one of the public meanings of the word "philosophy" he's certainly correct but not, I think, in the sense that would include something like constructivism. (The public meaning in question has even less than type-checking to do with either love or wisdom. Well, maybe it has something to do with love.) May I suggest that the applied mathematician may have a very different understanding of category theory from the mathematician. Steve says that category theory is "all things are connected". But that's an article of faith for almost any mathematician. He goes on to say, "you cannot fully describe anything purely in itself but only by the way it connects with others." This assertion about what "you cannot" do sounds like it could be a good way of describing *applied* mathematicians. To begin with, Eilenberg and Mac Lane defined categories in order to define functors and they defined functors in order to define natural transformations. Immediately it was noted that a new tool existed to pin down -- in a formal way -- how it is that some of the all things are connected. It should be noted that categories -- and more to the point, functors -- have always been considered tools for studying the subject matter of mathematics. Tools, not the subject matter itself. I am on record that the language of categories began to become respectable when Frank Adams was able to count the number of independent vector fields on each sphere using a construction that quantified over functors: it produced an n-ary transformation on the K-functor for every n-ary endofunctor on the category of finite dimensional vector spaces (which he assembled into what are now known as the Adams operations). One of the better successes since then has been the use of categories in finding connections between various foundational systems. Because some of these systems are constructivist it has apparently caused some to think that categories are intrinsically constructivist. Strange. There's another important aspect of category theory. Most categories, in the beginning at least, were categories that naturally arose from existing branches of mathematics. Some of these categories, though, had never been lived in before they were invented as categories. Joel Cohen named one of these the "Freyd Category" (named not after Peter but Jennifer): its an abelian category whose full subcategory of projectives is the stable-homotopy category; all the other objects have no easy description; the category can be described as the target of the universal homology theory. But a much better example is in Serre's dissertation. This work, hailed by many as the single most substantive dissertation ever written, contends with the two abelian categories that result when one starts with the category of abelian groups and identifies with the zero group all finite groups in one case, or all finitely generated groups in the second case. Most remarkably, Serre did all this without using category theory. (The fact that the first non-trivial construction of a category occured without benefit of category theory must be reckoned an embarrassment for category theorists.) But in recent applications I think a very different type of question is being asked: "Is it possible that there is a category in which ... can take place?" These questions are at the heart of many approaches to programming semantics. And they are at the heart of many of the uses of categories in theoretical physics. But the first serious example came, in fact, a long time ago. In the late 60's Lawvere's approach to differential geometry asked just this type of question. Elementary topoi made their first appearance as just a preliminary part of the answer. So what's this all have to do with philosophy? Not much, of course. From cat-dist Mon Mar 10 14:32:58 1997 Received: by mailserv.mta.ca; id AA18125; Mon, 10 Mar 1997 14:31:17 -0400 Date: Mon, 10 Mar 1997 14:31:17 -0400 (AST) From: categories To: categories Subject: Research Associate Position Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: O X-Status: Date: Mon, 10 Mar 97 18:14:51 GMT From: Roy L. Crole UNIVERSITY OF LEICESTER Department of Mathematics and Computer Science RESEARCH ASSOCIATE Applications are invited for a post of Research Associate available for up to three years to work on an EPSRC funded project entitled "The Complexity of Problems in Infinite Groups". The aims of the project are to further develop and extend links between Theoretical Computer Science and Mathematics. Candidates should possess, or be completing, a PhD in Mathematics or Theoretical Computer Science. Salary will be towards the lower end of the R&A 1A Scale (14,732 - 22,143 GBpounds pa) depending on qualifications and experience. Further information can be obtained from Dr R. M. Thomas (rmt@mcs.le.ac.uk) or Prof I. A. Stewart (i.a.stewart@mcs.le.ac.uk); particulars are also available on the web (http://www.mcs.le.ac.uk/~rthomas/Particulars). Application forms and further particulars are available from the Personnel and Planning Office (Research Appointments), University of Leicester, University Road, Leicester LE1 7RH. Tel (0116) 223 1341. Please quote reference number R7025/Web. Closing date for receipt of applications is 4th April 1997. From cat-dist Wed Mar 12 14:15:17 1997 Received: by mailserv.mta.ca; id AA13440; Wed, 12 Mar 1997 14:13:48 -0400 Date: Wed, 12 Mar 1997 14:13:48 -0400 (AST) From: categories To: categories Subject: AMS Special session in categories Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-Status: Date: Wed, 12 Mar 1997 10:47:41 -0500 From: Robert A. G. Seely It has been pointed out to me that there was some ambiguity about some of the details I posted recently concerning the Special Session on category theory at the September AMS meeting in Montreal. After confirming the following with Mike Barr, here are the additional details: ] Notice of AMS Meeting September 26-28, 1997 Montreal, Quebec Canada ] (1997 Fall Eastern Sectional Meeting) ] Meeting # 924, Notices Program Issue: October 1997 ] Deadline for Contributed Papers for consideration in Special Sessions: ] May 1, 1997 This means _titles_ of papers, not the actual papers themselves. ] Deadline for Abstract Submission: June 26, 1997 This means what it says. But note that submissions (of titles and abstracts) are to be made to the AMS (although if you send them to one of the organizers I imagine they will be able to forward them to the right place...) ] Special Session on Category Theory and Its Applications ] Organizers: ] Michael Barr, McGill University barr@triples.math.mcgill.ca ] Ieke Moerdijk, University of Utrecht. Netherlands moerdijk@math.ruu.ne ] Myles Tierney, Rutgers University tierney@math.rutgers.edu This session is in honour of Bill Lawvere. From cat-dist Sat Mar 15 09:49:50 1997 Received: by mailserv.mta.ca; id AA16894; Sat, 15 Mar 1997 09:49:02 -0400 Date: Sat, 15 Mar 1997 09:49:02 -0400 (AST) From: categories To: categories Subject: a characterisation of factorisation systems Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: O X-Status: Date: Fri, 14 Mar 1997 15:26:15 GMT From: Paul-Andre Mellies Dear categorists, I have recently proved an (E,M)-factorisation theorem in the framework of axiomatic rewriting systems: every derivation X -> Y factorises (up to Levy permutation equivalence) into a head reduction X -> Z followed by a non-head reduction Z -> Y. One special difficulty in my case is that I do not define the class M of non-head reductions as a category. So, I need a characterisation of factorisation system (E,M) without any assumption of categoricity of E or M. Here is the statement of the theorem I finally proved: ----------------------------------------------------------------------------- Let E and M be two classes of morphisms in a category C. (E,M) is a factorisation system of C if and only if the four following properties hold: 1. every morphism f in C can be factored as f=me with m in M and e in E, 2. if e is a morphism in E and m is a morphism in M then e is orthogonal to m, 3. if i is an iso left composable to e in E, then ie is in E, 4. if i is an iso right composable to m in M, then mi is in M. ----------------------------------------------------------------------------- I do not know if this characterisation already exists in the litterature on factorisation systems. If it does, please send me the reference to integrate in my paper. People interested in the paper can load it there: http://www.dcs.ed.ac.uk/home/paulm/ From cat-dist Mon Mar 17 14:51:40 1997 Received: by mailserv.mta.ca; id AA00191; Mon, 17 Mar 1997 14:49:26 -0400 Date: Mon, 17 Mar 1997 14:49:26 -0400 (AST) From: categories To: categories Subject: Re: a characterisation of factorisation systems Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-Status: Date: Mon, 17 Mar 1997 10:01:13 -0500 From: Walter Tholen With regard to the message below, it should be pointed out that the history of factorization systems is almost as old as category theory itself, going back at least to Mac Lane's "Groups, categories and duality" of 1948 (Proc. Nat. Acad. Sci. U.S.A. 34, 263-267). The paper most often referred to in conjunction with factorization systems (P. Freyd and G.M. Kelly. JPAA 2 (1972) 169-191) requires the classes E and M to be closed under composition, a requirement that also occurs in many other papers. But that, in the presence of the conditions 1-4 below, this is a redundant requirement was known to at least some people at the time. The statement below appears explicitly in my Ph.D. thesis of 1974 (as Theorem 3.11 - even more generally, since I deal with "factorizations along a functor" there, which give the usual thing if you then consider the identity functor). But I certainly do not claim to have been the first to observe this. I am almost certain that the theorem below was known to O. Wyler in 1968 who has an unpublished paper with H. Ehrbar of 1968 (which he recalls in a 1987 paper in the Cahiers 28 , 143-159). Another often neglected reference is C.M. Ringel, Math. Z. 112 (1970) 248-266. I would also think that John Isbell , J. Kennison, Horst Herrlich, D. Pumpluen and Louis Nel were aware of the theorem at about that time. If all this does not sound clear-cut, then look at Theorem 1.8 in my book with D. Dikranjan on the "Categorical Structure of Closure Operators" (Kluwer, 1995); see also the Notes to Chapter 1 which give other useful references. Best regards to all, Walter Tholen. On Mar 15, 9:49am, categories wrote: > Subject: a characterisation of factorisation systems > Date: Fri, 14 Mar 1997 15:26:15 GMT > From: Paul-Andre Mellies > > > Dear categorists, > > I have recently proved an (E,M)-factorisation theorem > in the framework of axiomatic rewriting systems: > every derivation X -> Y factorises (up to Levy permutation equivalence) > into a head reduction X -> Z followed by a non-head reduction Z -> Y. > > One special difficulty in my case is that I do not define > the class M of non-head reductions as a category. > So, I need a characterisation of factorisation system (E,M) > without any assumption of categoricity of E or M. > Here is the statement of the theorem I finally proved: > > ----------------------------------------------------------------------------- > Let E and M be two classes of morphisms in a category C. > (E,M) is a factorisation system of C if and only if > the four following properties hold: > > 1. every morphism f in C can be factored as f=me with m in M and e in E, > 2. if e is a morphism in E and m is a morphism in M then e is orthogonal to m, > 3. if i is an iso left composable to e in E, then ie is in E, > 4. if i is an iso right composable to m in M, then mi is in M. > ----------------------------------------------------------------------------- > > I do not know if this characterisation already exists in the litterature > on factorisation systems. If it does, please send me the reference > to integrate in my paper. > From cat-dist Tue Mar 18 10:29:38 1997 Received: by mailserv.mta.ca; id AA23682; Tue, 18 Mar 1997 10:28:09 -0400 Date: Tue, 18 Mar 1997 10:28:09 -0400 (AST) From: categories To: categories Subject: 2-Tangles Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: O X-Status: Date: Tue, 18 Mar 1997 00:09:18 -0500 (EST) From: John Baez Here is a short paper summarizing some work done by my student Laurel Langford. ----------------------------------------------------------------------- 2-Tangles John C. Baez and Laurel Langford Just as links may be algebraically described as certain morphisms in the category of tangles, compact surfaces smoothly embedded in R^4 may be described as certain 2-morphisms in the 2-category of `2-tangles in 4 dimensions'. In this announcement we give a purely algebraic characterization of the 2-category of unframed unoriented 2-tangles in 4 dimensions as the `free semistrict braided monoidal 2-category with duals on one unframed self-dual object'. A forthcoming paper will contain a proof of this result using the movie moves of Carter, Rieger and Saito. We comment on how one might use this result to construct invariants of 2-tangles. One can get a Postscript version of this paper at http://math.ucr.edu/home/baez/2tang.ps or by anonymous ftp to math.ucr.edu, where it's in the directory pub/baez, as the file 2tang.ps From cat-dist Tue Mar 18 10:29:38 1997 Received: by mailserv.mta.ca; id AA19515; Tue, 18 Mar 1997 10:29:00 -0400 Date: Tue, 18 Mar 1997 10:29:00 -0400 (AST) From: categories To: categories Subject: Re: a characterisation of factorisation systems Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: O X-Status: Date: 18 Mar 97 12:42:34 +0200 From: Hans Porst >Date: Fri, 14 Mar 1997 15:26:15 GMT >From: Paul-Andre Mellies Your definition >Let E and M be two classes of morphisms in a category C. >(E,M) is a factorisation system of C if and only if >the four following properties hold: > >1. every morphism f in C can be factored as f=me with m in M and e in E, >2. if e is a morphism in E and m is a morphism in M then e is orthogonal >to m, >3. if i is an iso left composable to e in E, then ie is in E, >4. if i is an iso right composable to m in M, then mi is in M. seems to be precisely the definition used in Adamek, Herrlich, Strecker: Abstract and Concrete Categories. Check their Chapter 14! AHS 14.6 shows in particular that E and M will be closed under composition. --------------------------------------------------------- Hans-E. Porst e-mail: porst@mathematik.uni-bremen.de FB 3: Mathematik Phone: +49 421 2182276 University of Bremen +49 421 2184971 D-28334 Bremen Fax: +49 421 2184856 --------------------------------------------------------- From cat-dist Tue Mar 18 10:29:45 1997 Received: by mailserv.mta.ca; id AA16797; Tue, 18 Mar 1997 10:29:42 -0400 Date: Tue, 18 Mar 1997 10:29:42 -0400 (AST) From: categories To: categories Subject: BRICS International PhD School: Call for Applications Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: O X-Status: Date: Tue, 18 Mar 1997 15:12:12 +0100 (MET) From: Uffe Henrik Engberg BRICS International PhD School in Computer Science University of Aarhus, Denmark Announcement and Call for Applications An international PhD School in computer science is opening at the University of Aarhus. This is its initial call for admissions and grant applications. The School is an integrated part of the BRICS (Basic Research in Computer Science) Research Centre, and both are funded by the Danish National Research Foundation. The school admits 10-12 students annually, and provides a substantial number of grants for Danish as well as foreign students. The PhD School wishes to recruit foreign PhD students of the highest international standards. It provides an excellent research environment and scientific training facilities, and aims at making its PhD graduates attractive for a wide spectrum of employers - in private and public research and development institutions, both in Denmark and abroad. So, if you are a computer science student and soon to complete at least four years of full-time study, highly motivated for a PhD study in a truly international environment, please send us an application following the instructions below. For more details please visit http://www.brics.dk, or contact us by e-mail at phdschool@brics.dk. Also, we would appreciate your passing on this information to interested students and colleagues at your university or research institute. BRICS The Research Centre BRICS (Basic Research In Computer Science) was founded in 1994 by the Danish National Research Foundation at the University of Aarhus in association with the University of Aalborg. BRICS supports basic research in Algorithmics, Logic and Semantics, mainly through an extensive programme of short- and long-term visiting scientists. Research Areas The core areas of the PhD School are: Semantics of Computation; Logic in Computer Science; Computational Complexity; Design and Analysis of Algorithms; Programming Languages; Distributed Computing; Verification; and Data Security and Cryptology. The school will provide its students with a solid background in the theoretical foundation centred around BRICS activities. From this foundation, the students may either continue in one of the core areas or venture into areas of a more applied or experimental nature as possible areas of thesis specialisation. Admission Prerequisites and Study Structure Admission is based on knowledge corresponding to four years of full-time studies, including basic courses in programming and programming languages, algorithms and data structures, computer architecture, computability and mathematics. (This list is based on the current undergraduate education at the University of Aarhus, and will be interpreted in a flexible way.) The time allocated for the PhD studies is a further four years, where the first two years include some mandatory course work and introductory research, concluded by a qualifying examination, whereas the last two years are dedicated to the writing of the thesis, finishing with a defence. All students admitted to the school will enter this study structure. We may, however, take into account merits from previous study. Students are normally admitted for the semester start September 1st, but admission may take place throughout the year. PhD Student Grants The school offers student grants of different types covering tuition waivers and/or living expenses. School Start The BRICS International PhD School formally started January 1st 1997. The first school students will be admitted by September 1st 1997. The school will admit approximately 10-12 students per year, of which half are expected to be foreign. How to apply 1. Fill in the application form on http://www.brics.dk/PhDSchool/Application.html Alternatively, send an e-mail to phdschool@brics.dk with subject "Application" including: - your full name, personal address and phone number, college / university, URL of home page (if applicable), e-mail address, - type of application, i.e. a combination of: admission; tuition waiver; studentship covering living expenses (for details see http://www.brics.dk). 2. Send by ordinary mail to the address below - a covering letter, including the information from your application form/e-mail, - a short curriculum vitae, - complete official transcripts from colleges or univer- sities, documenting minimally four years of full time study, - names of three people whom we may ask for letters of recommendation, - an indication of applicant's motivation for a PhD study, and particular research area of initial interest (max 2 pages). There are no general deadlines, but applications for admission September 1st, 1997 should be sent as soon as possible and preferably before April 15th. Further Information For further information, please e-mail phdschool@brics.dk or visit http://www.brics.dk Address BRICS PhD School Department of Computer Science University of Aarhus Ny Munkegade, Bldg. 540 DK-8000 Aarhus C. Denmark Phone: +45 8942 3264 From cat-dist Tue Mar 18 11:25:03 1997 Received: by mailserv.mta.ca; id AA23665; Tue, 18 Mar 1997 11:24:20 -0400 Date: Tue, 18 Mar 1997 11:24:17 -0400 (AST) From: categories To: categories Subject: Morphisms of diagrams Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: O X-Status: Date: Tue, 18 Mar 1997 10:20:19 -0500 From: Charles Wells Let C be a category and I and I' graphs (or categories if you prefer). Define a morphism of diagrams psi:(delta:I-->C)-->(delta':I'-->C) to be a graph morphism (or functor if you prefer) psi:I-->I' together with a natural transformation alpha:delta' o psi-->delta. This definition turns Lim into a contravariant functor from the category of diagrams to C (when C is complete, anyway). I believe this construction has been familiar since the early days of category theory, but I don't know a reference and would be glad to learn of any. By the way, Barr in SLN 236 (page 52) defines an entirely different notion of morphism of diagrams which Tholen and Tozzi develop extensively in "Completions of Categories and Initial Completions", Cahiers 1989, pages 127-156. This makes Lim a covariant functor. Charles Wells, 105 South Cedar Street, Oberlin, Ohio 44074, USA. (I am on sabbatical until 20 August 1997 and cannot easily be reached at Case Western Reserve University.) EMAIL: cfw2@po.cwru.edu. HOME PHONE: 216 774 1926. FAX: Same as home phone. HOME PAGE: URL http://www.cwru.edu/CWRU/Dept/Artsci/math/wells/home.html "Some have said that I can't sing. But no one will say that I _didn't_ sing." --Florence Foster Jenkins From cat-dist Wed Mar 19 11:20:07 1997 Received: by mailserv.mta.ca; id AA32430; Wed, 19 Mar 1997 11:18:56 -0400 Date: Wed, 19 Mar 1997 11:18:56 -0400 (AST) From: categories To: categories Subject: good news! Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: O X-Status: Date: Wed, 19 Mar 1997 07:09:01 -0500 (EST) From: Peter Freyd It's official: Peter Johnstone becomes a Reader in Maths. Three categorical readers at Cambridge -- not bad that. From cat-dist Thu Mar 20 13:34:10 1997 Received: by mailserv.mta.ca; id AA12015; Thu, 20 Mar 1997 13:33:43 -0400 Date: Thu, 20 Mar 1997 13:33:43 -0400 (AST) From: categories To: categories Subject: Readership Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-Status: Date: Thu, 20 Mar 97 09:50 GMT From: Dr. P.T. Johnstone Many thanks to all of you who have sent good wishes to me on my promotion. I apologise for not replying individually, but there really are too many of you! Peter Johnstone From cat-dist Thu Mar 20 13:34:12 1997 Received: by mailserv.mta.ca; id AA28798; Thu, 20 Mar 1997 13:31:45 -0400 Date: Thu, 20 Mar 1997 13:31:44 -0400 (AST) From: categories To: categories Subject: Re: Morphisms of diagrams Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: O X-Status: Date: Thu, 20 Mar 1997 14:53:31 +1100 (EST) From: Steve Lack > Date: Tue, 18 Mar 1997 11:24:35 -0400 (AST) > From: categories > > Date: Tue, 18 Mar 1997 10:20:19 -0500 > From: Charles Wells > > Let C be a category and I and I' graphs (or categories if > you prefer). Define a morphism of diagrams > psi:(delta:I-->C)-->(delta':I'-->C) to be a graph morphism (or > functor if you prefer) psi:I-->I' together with a natural > transformation alpha:delta' o psi-->delta. This definition > turns Lim into a contravariant functor from the category of > diagrams to C (when C is complete, anyway). > > I believe this construction has been familiar since the early > days of category theory, but I don't know a reference and would > be glad to learn of any. The dual construction (i.e. for colimits) appears in Rene Guitart, ``Remarques sur les machines et les structures'', Cahiers XV-2 (1974); and its sequel Rene Guitart and Luc Van den Bril, ``Decompositions et lax-completions'', Cahiers XVIII-4 (1977); where further references are also given. Steve Lack. From cat-dist Fri Mar 21 14:02:59 1997 Received: by mailserv.mta.ca; id AA19740; Fri, 21 Mar 1997 14:00:01 -0400 Date: Fri, 21 Mar 1997 14:00:01 -0400 (AST) From: categories To: categories Subject: Re: Morphisms of diagrams Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: O X-Status: Date: Fri, 21 Mar 97 15:15:56 +1100 From: Max Kelly Charles Wells asked the following: __________ Let C be a category and I and I' graphs (or categories if you prefer). Define a morphism of diagrams psi:(delta:I-->C)-->(delta':I'-->C) to be a graph morphism (or functor if you prefer) psi:I-->I' together with a natural transformation alpha:delta' o psi-->delta. This definition turns Lim into a contravariant functor from the category of diagrams to C (when C is complete, anyway). I believe this construction has been familiar since the early days of category theory, but I don't know a reference and would be glad to learn of any. ______________ Steve Lack replied with the folowing information: ____________ The dual construction (i.e. for colimits) appears in Rene Guitart, ``Remarques sur les machines et les structures'', Cahiers XV-2 (1974); and its sequel Rene Guitart and Luc Van den Bril, ``Decompositions et lax-completions'', Cahiers XVIII-4 (1977); where further references are also given. _____________ I am writing at the university, with my files at home; but my memory is that the construction was introduced by Eilenberg and Mac Lane in 1945, in a paper called something like "On a general theory of natural equivalences". Max Kelly. From cat-dist Mon Mar 24 10:41:19 1997 Received: by mailserv.mta.ca; id AA22548; Mon, 24 Mar 1997 10:40:24 -0400 Date: Mon, 24 Mar 1997 10:40:23 -0400 (AST) From: categories To: categories Subject: Lectureships at Edinburgh CS Dept. Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: O X-Status: Date: Mon, 24 Mar 1997 14:38:16 +0100 From: Gordon Plotkin Two Lectureships are available at the Department of Computer Science of the University of Edinburgh. One is strongly LFCS (Laboratory for the Foundations of Computer Science) related, and the other is general. For details, see http://www.dcs.ed.ac.uk/jobs/ Gordon Plotkin From cat-dist Thu Mar 27 11:27:35 1997 Received: by mailserv.mta.ca; id AA28660; Thu, 27 Mar 1997 11:24:37 -0400 Date: Thu, 27 Mar 1997 11:24:37 -0400 (AST) From: categories To: categories Subject: JFP Editorial Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-Status: Date: Wed, 26 Mar 1997 16:25:43 -0500 From: Philip Wadler The following editorial will appear in the next issue of the Journal of Functional Programming. It reiterates our scope, and announces some changes in our editorial staff. Our web address appears below, and e-mail addresses for the people mentioned below appear above. I look forward to seeing your submissions to JFP! -- P A HOT opportunity The Java phenomenon means that programmers that once laughed at garbage collection and strong typing have started to use it daily, and this opens up a wonderful opportunity for the functional programming community. Bob Harper coined the acronym HOT to summarise much of what functional programmers have to offer the world: expertise in languages that are Higher-Order and Typed. Bob argued for a broad interpretation of these terms, so that Higher-Order includes languages where objects contain methods (even though functions are not first-class citizens), and Typed includes both static and dynamic typing. By these criteria Java is HOT, and so are Haskell, ML, and Scheme. Not all functional languages of interest are all that HOT. Ericsson is using the functional and concurrent language Erlang to build phone switches containing hundreds of thousands of lines of code. Erlang is a first-order language with dynamic types (though recent work has added higher-order, and static types are in the offing). The key to Erlang's success is similar to Java's: both have thrived by focussing on an application area, the web for Java, telephony for Erlang. Those who strive to eke another five percent speed-up out of their compilers should note another similarity between Java and Erlang: both achieved their initial success based on byte code interpreters of modest efficiency (though fast native code compilers for both are coming along). We should continue to seek ``killer apps'' for functional programming. The Journal of Functional Programming encourages all attempts at outreach, from our area to others, from theory to practice. JFP has published papers on the higher-order and typed aspects of Modula-3, Algol, and Actors. We have run (or are about to run) papers on applications to animation, artificial intelligence, music, protein analysis, scientific programming, and text processing. We have had a special issue devoted to type systems for object-oriented programming, and another to applications. As always, we remain a broad church. Send us your HOT papers, your application papers, your papers on links to other areas. Send us papers about languages typed or untyped, strict or lazy, pure or stateful, sequential or concurrent. --- On the home front, there are some changes to announce. Sad to say, Henk Barendregt, due to pressures of work, has resigned as an editor of JFP. However, we are delighted that he has agreed to remain as editor of our Theoretical Pearls column. So continue to send Henk any beautiful and brief candidates for his column, but please send other submissions to one of the other JFP editors. Please join us in thanking Henk for his help in founding JFP, and for his seven years of devoted service. And please join us in welcoming our new editor, Thierry Coquand. Thierry brings special expertise in the HOT area of type theory, and is generally knowledgeable in all things theoretical. To give Thierry the warmest welcome, send him a paper today; submission details are on the inside back cover, addresses on the inside front. The theory editor is dead, long live the Thierry editor! Please also join us in welcoming Simon Thompson as book review editor. Publishers are keen to give away books in return for reviews, we are keen to run discriminating reviews, and the reviewer gets to keep the book. Let Simon know if you'd like to register as a reviewer, if there's some book you want to review, or if there's a book you'd like to see us review. His address is inside the front cover. This is also a good point to thank Richard Bird for his continuing effort as editor of Functional Pearls. If you have a contribution that is small, rounded, and pleasant, you'll find his address, too, on the inside front. Richard continues to contribute regular columns, setting a high standard for the rest of us. And when you do send a paper, just how long will it take to get a response? Answer: about three months, on average. We at JFP have no patience for journals that sit on papers for years. The editors all aim to reach a decision (accept, revise, or reject) on each paper within four months of receipt, a goal which Simon, Paul, and John met for every paper processed in the last year, and which Phil failed to meet just once (by four days). To achieve this, we ask our reviewers to acknowledge papers immediately and to provide reviews promptly, typically within a month. And we get back to them if we don't hear from them. This leads us to our penultimate thank you: to the reviewers who make the process work. Without them, our science would grind to a halt. --- A venerable curse reads ``May you live in interesting times''. The written word is increasingly viewed on the screen rather than on the page, and our web site at www.dcs.glasgow.ac.uk/jfp is increasingly a part of what we do. Nonetheless, we intend to publish as atoms rather than as bits for a while longer. Atoms or bits, journals will remain at the core of scientific progress. Their key ingredients are not ink and pulp, nor Latex and HTML, but writers, reviewers, and readers. Our final thank you is to you, for your contribution to JFP. We look forward to taking, with you, our next step into interesting times. -- Philip Wadler, for the editors of JFP ----------------------------------------------------------------------- Philip Wadler wadler@research.bell-labs.com Bell Laboratories http://cm.bell-labs.com/cm/cs/who/wadler/ Lucent Technologies office: +1 908 582 4004 700 Mountain Ave, Room 2T-304 fax: +1 908 582 5857 Murray Hill, NJ 07974-0636 USA home: +1 908 626 9252 -----------------------------------------------------------------------