From cat-dist Mon Dec 1 14:01:58 1997 Received: (from cat-dist@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id OAA15034; Mon, 1 Dec 1997 14:00:31 -0400 (AST) Date: Mon, 1 Dec 1997 14:00:31 -0400 (AST) From: categories To: categories Subject: Workshop announcement Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-Status: Date: Mon, 01 Dec 1997 18:09:04 +0100 From: Bart Jacobs CALL FOR SUBMISSION: WORKSHOP ON COALGEBRAIC METHODS IN COMPUTER SCIENCE ======== == =========== ======= == ======== ======= (Lisbon, 28-29 March 1998 Satelite workshop to ETAPS'98) Organized by: Bart Jacobs, Larry Moss, Horst Reichel, Jan Rutten. Submissions: 7 January 1998: deadline for submissions 15 February 1998: notification 7 March 1998: final version Proceedings: ENTCS (Electronic Lecture Notes in Computer Science), and a special issue of TCS. For more information and instructions for submission see: http://www.cs.kun.nl/~bart/coalg_worksh.html. (We apologize for multiple copies.) From cat-dist Mon Dec 1 14:01:58 1997 Received: (from cat-dist@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id OAA14755; Mon, 1 Dec 1997 14:01:31 -0400 (AST) Date: Mon, 1 Dec 1997 14:01:31 -0400 (AST) From: categories To: categories Subject: Announcement PSSL'66 Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-Status: Date: Mon, 1 Dec 1997 17:18:36 +0000 (GMT) From: Neil Ghani The 66th meeting of the PSSL will be held at the University of Birmingham, England, over the weekend of 28-29 March 1998. Since its inception, the focus of the PSSL has broadened and now includes talks related to category theory, logic and theoretical computer science. The meetings are informal in nature and talks on work in progress is welcome. A more detailed announcement will be made in the new year Valeria De Paiva Neil Ghani From cat-dist Thu Dec 4 09:49:17 1997 Received: (from cat-dist@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id JAA14908; Thu, 4 Dec 1997 09:47:48 -0400 (AST) Date: Thu, 4 Dec 1997 09:47:48 -0400 (AST) From: categories To: categories Subject: preprints available Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: O X-Status: Date: Thu, 4 Dec 1997 11:54:52 +0100 From: Marco Grandis The following preprints are now accessible as ps-files, via web of ftp: http://www.dima.unige.it/STAFF/GRANDIS/ ftp://www.dima.unige.it/pub/STAFF/GRANDIS (1). "Limits in double categories", by Marco Grandis and Robert Pare Dbl.Dec97.ps (2). "Weak subobjects and weak limits in categories and homotopy categories", by M.G. Var1.Aug97.ps (3). "Weak subobjects and the epi-monic completion of a category", by M.G. Var2.Dec97.ps *** The first was announced on this mailing list, on 13 Nov 1997. (With respect to the printed preprint, this is a slightly revised version, containing a more detailed comparison with Bastiani-Ehresmann's "limits relative to double categories".) The second and third form an expanded version of a printed preprint ("Variables and weak limits in categories and homotopy categories", Dec 1996), announced on this list on 13 Dec 1996. Abstracts for (2) and (3) are given below. *** (2). Abstract. We introduce the notion of "variation", or "weak subobject", in a category, as an extension of the notion of subobject. The dual notion is called a covariation, or weak quotient. Variations are important in homotopy categories, where they are well linked to weak limits, much in the same way as, in "ordinary" categories, subobjects are linked to limits. Thus, "homotopy variations" for a space S, with respect to the homotopy category HoTop, form a lattice Fib(S) of "types of fibration" over S. Nevertheless, the study of weak subobjects in ordinary categories, like abelian groups or groups, is interesting in itself and relevant to classify variations in homotopy categories of spaces, by means of homology and homotopy functors. (To appear in: Cahiers Top. Geom. Diff. Categ.) (3). Abstract. Formal properties of weak subobjects are considered. The variations in a category X can be identified with the (distinguished) subobjects in the epi-monic completion of X, or Freyd completion FrX, the free category with epi-monic factorisation system over X, which extends the Freyd embedding of the stable homotopy category of spaces in an abelian category (P. Freyd, Stable homotopy, La Jolla 1965). If X has products and weak equalisers, as HoTop and various other homotopy categories, FrX is complete. If X has zero-object, weak kernels and weak cokernels, as the homotopy category of pointed spaces, then FrX is a "homological" category. Finally, if X is triangulated, FrX is abelian and the embedding X --> FrX is the universal homological functor on X, as in the original case. These facts have consequences on the ordered sets of variations. Marco Grandis Dipartimento di Matematica Universita' di Genova via Dodecaneso 35 16146 GENOVA, Italy e-mail: grandis@dima.unige.it tel: +39.10.353 6805 fax: +39.10.353 6752 http://www.dima.unige.it/STAFF/GRANDIS/ From cat-dist Thu Dec 4 09:49:20 1997 Received: (from cat-dist@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id JAA15028; Thu, 4 Dec 1997 09:49:00 -0400 (AST) Date: Thu, 4 Dec 1997 09:48:59 -0400 (AST) From: categories To: categories Subject: e-prints Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-Status: Date: Wed, 3 Dec 1997 10:45:08 -0500 (EST) From: James Stasheff Dear colleagues, I'm writing to you about a proposed e-print archive in category theory, on behalf of a committee of mathematicians which is advocating the unification of various electronic preprint servers and archives into a single system with a common format. We want to invite Category Theorists to join this group. This invitation is being issued to 15 preprint servers (listed below) which together cover about half of the subject areas in mathematics. We are also trying to organize active groups in the remaining subject areas, so that the unified preprint server will soon cover all of mathematics. This organizational effort has already produced interested groups in combinatorics and geometric topology. Managing a preprint server can be a time-consuming task, but fortunately there is a similar preprint server in operation in physics, running at Los Alamos National Lab and funded by the National Science Foundation, whose staff is willing to take on the operation of a unified mathematics server. This will enable all of us to take advantage of their years of software development, as well as their efficient staff who monitor the (fully automated) operation. When scientific questions arise (such as the suitability of a particular paper for a particular archive), these staff members would consult with a designated "moderator" for each subject area. (The moderator also receives abstracts of papers as they are submitted, and can have the staff intervene in the rare instances of inappropriate papers or other difficulties.) Someone you designate collectively would serve in this capacity under the new system. The great advantage of a unified server is that all mathematicians will be able to participate in electronic preprint exchanges in a single, flexible system (which can distribute preprints in a variety of formats, including dvi, ps and pdf). The computer systems staff in a mathematics department can be asked to familiarize themselves with this system, which will be easy to support for users. Moreover, a central location for preprints (with dozens of mirror sites worldwide) together with a soon-to-be-familiar scheme for citing these preprints will mean that mathematicians in one field who see a citation to a preprint in another field will easily be able to locate it. We will also all gain the ability to simultaneously search through related archives, including full text searches. There is a common keyword index for the mathematical holdings, permitting simultaneous searching of all or designated related archives. A given paper could easily be relevant to users of more than one archive, so this would make information much easier to track. In order to take advantage of the system in place at Los Alamos Lab, we have agreed to follow the technical decisions they have made: authors are asked to submit tex source files, for example. Although this may be a change for users of your current system, we believe that the long-term advantages of unification outweigh the temporary disadvantages to users of an established archive. We propose to copy the contents of your archive (in its current form) into the unified archive, and suggest that you encourage all future submissions be made directly to the unified archive. Category theory is one of the subject areas in the unified archive and is intended as a continuation of your archive. It should be fairly easy to construct a kind of front-end on a web page at your site which will provide access to both old and new papers in your portion of the unified archive, giving your users a certain degree of continuity and allowing them to retain the feeling of belonging to a smaller community of users of a particular preprint archive. We will be happy to assist in the construction of such front-ends. A primitive prototype for such a front-end (in the area of combinatorics) can be viewed at http://eprints.math.duke.edu/archive/CO/ All but one of the links on that page take you directly into the archive at Los Alamos. A front-end for the entire unified archive is under construction at U.C. Davis by Greg Kuperberg: you can view it at http://front.math.ucdavis.edu You might also like to look at the Los Alamos Math Archive itself (partially functioning already), at http://xxx.lanl.gov/form/math You will see that the combinatorics and geometric topology sections are getting a good start this week. At the time of unification (probably Jan. 1) the four current math archives alg-geom, dg-ga, funct-an and q-alg at the Los Alamos site will be merged into the unified archive, becoming subject areas AG, DG, part of FA, and QA, respectively. Our committee has had Joe Christie, Greg Kuperberg, Dave Morrison, Dick Palais, Jim Stasheff and Mark Steinberger as its active participants, with occasional participation by a few others. If you are interested in having a representative of category theory joining this committee, we would love to have one. Our tasks after this unification will be developing the remaining subject areas, and publicizing this archive among mathematicians. Short of that, as individuals, all you need to do right now is write back and say you think the category theory category is a good idea, or better yet, to pledge some number of e-prints to be submitted soon after the category starts. Those already archived other than on your own server should be offered with a copy of the offer going to the archive administrator. Of course we are most eager to have your present and future e-prints added to the unified server. (For e-print versions of papers for which you no longer have the copyright, permission from the copyright holder will be needed.) I am very optimistic that this effort will eventually lead to a complete transition to efficient electronic distribution of new results in category theory. The xxx archives has 3,000 math e-prints in the four existing mathematics categories and 50,000 physics e-prints. As you might guess from these numbers, xxx has already effected the electronic transition in several areas of physics. The category theory category will be of great benefit to us all. Please help get it started; the more who join, the better. Best regards, Jim Stasheff P.S. Here is the list of 15 preprint servers which we propose to merge. If you have other suggestions for inclusion on this list, please let us know. 1. Algebraic Geometry (http://eprints.math.duke.edu/archive/alg-geom/) 2. Algebraic Number Theory Archives (http://www.math.uiuc.edu/Algebraic-Number-Theory/) 3A. Banach Spaces & Functional Analysis (ftp://ftp.math.okstate.edu/pub/banach/) 3B. Functional Analysis (http://xxx.lanl.gov/archive/funct-an/) 4. Combinatorial and Geometric Group Theory (MAGNUS) (http://zebra.sci.ccny.cuny.edu/web/html/magnus.html) 5. Conservation Laws Preprint Server (http://www.math.ntnu.no/conservation/) 6. Differential Geometry (http://www.msri.org/preprints/dg-ga.html) 7. Dynamical Systems Electronic Preprint Server (http://www.math.sunysb.edu/dynamics/preprints/preprints.html) 8. Hopf Topology Archive (http://hopf.math.purdue.edu/pub/hopf.html) 9. K-theory Preprint Archives (http://www.math.uiuc.edu/K-theory/) 10. Logic Eprints (http://www.math.ufl.edu/~logic/) 11. Mathematical Physics Preprint Archive at the University of Texas, Austin (http://www.ma.utexas.edu/mp_arc/mp_arc-home.html) 12. Quantum Algebra and Topology (http://eprints.math.duke.edu/archive/q-alg/) 13. Representations and Cohomology of Groups (http://www.math.uga.edu/~djb/archive.html) 14. Several Complex Variables (ftp://iu-math.math.indiana.edu/pub/scv/) ************************************************************ Until August 10, 1998, I am on leave from UNC and am at the University of Pennsylvania Jim Stasheff jds@math.upenn.edu 146 Woodland Dr Lansdale PA 19446 (215)822-6707 Jim Stasheff jds@math.unc.edu Math-UNC (919)-962-9607 Chapel Hill NC FAX:(919)-962-2568 27599-3250 From cat-dist Thu Dec 4 14:20:56 1997 Received: (from cat-dist@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id OAA10730; Thu, 4 Dec 1997 14:20:45 -0400 (AST) Date: Thu, 4 Dec 1997 14:20:45 -0400 (AST) From: categories To: categories Subject: Sheaves and Logic Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-Status: Date: Thu, 4 Dec 1997 12:17:39 -0300 (EST) From: Regivan Hugo Nunes Santiago Dear friends, I am a PhD Student in Computer Science at Departamento de Informatica, UFPE, Brazil, and I need to study the theory of sheaves and its conexion with logic. However I am finding some dificulties concerning matterials who have an intuitive explanation of the subject. I am reading Michael Fourman and D. Scott's Sheaves and Logic paper. It would be helpful if you could give me an intuition about the following questions: Is there any intuition about the notions of global and local objects? What is the connection between global and local objects, and, for example, partial and total functions? Is there any intuition about the existence predicate E:|A|->\omega? What is a singleton? In the paper "Identity and Existence", in the same proceedings, Scott formalized the notion of partial objects (e.g.partial functions). If we are modelling the standard intuitionistic logic, the local objects makes sense? Let me explain what I want to get. Is sheaves an adequate model for intuitionistic logic just when we want to formalize the notion of partial objects? And if we are working with standard intuitionistic logic, does the category of structure generated by a first order theory contain strutures with, for example, partial functions? Is there any intuitive written material about the subject? My best regards Regivan --------------------------- Regivan H. N. Santiago http://www.di.ufpe.br/~rhns Recife-Pernambuco/Brazil --------------------------- From cat-dist Thu Dec 4 16:43:42 1997 Received: (from cat-dist@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id QAA05271; Thu, 4 Dec 1997 16:43:35 -0400 (AST) Date: Thu, 4 Dec 1997 16:43:34 -0400 (AST) From: categories To: categories Subject: Re: e-prints Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-Status: Date: Thu, 4 Dec 1997 16:25:28 GMT From: Michael Barr I am all in favor of Jim Stasheff's proposal, but what does one do about the fact that I, for example, have my own personal macros files and my TeX files cannot be compiled without them. If this is to be a straitjacket, I would just as soon maintain our own server with dvi and ps files. I am also just a bit wary of distributing the tex source, since it is so easily changed. Not that dvi and ps files can't be changed, but it is certainly a good deal harder. Michael From cat-dist Fri Dec 5 08:45:02 1997 Received: (from cat-dist@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id IAA07448; Fri, 5 Dec 1997 08:44:34 -0400 (AST) Date: Fri, 5 Dec 1997 08:44:34 -0400 (AST) From: categories To: categories Subject: CONCUR'98: 2nd cfp Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: O X-Status: Date: Thu, 4 Dec 1997 10:55:01 +0100 (MET) From: Davide.Sangiorgi@sophia.inria.fr [Apologies if you receive multiple copies] Second Call for Papers CONCUR'98 9th International Conference on Concurrency Theory Nice, France, September 8-11, 1998 Important dates ~~~~~~~~~~~~~~~ Paper submissions: March 10, 1998 Notifications: May 8, 1998 Final versions: June 10, 1998. CONCUR 98: Purpose and Scope ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The purpose of the CONCUR conferences is to bring together researchers, developers, and students in order to advance the theory of concurrency, and promote its applications. Interest in this topic is continuously growing, as a consequence of the importance of concurrent systems and their applications, and of the scientific relevance of their foundations. The scope of CONCUR'98 covers all areas of semantics, logics, and verification techniques for concurrent systems. A list of specific topics includes (but is not limited to) concurrency related aspects of models of computation and semantic domains, process algebras, Petri nets, event structures, real-time systems, hybrid systems, decidability, model-checking, verification techniques, refinement techniques, term and graph rewriting, distributed programming, logic constraint programming, object-oriented programming, typing systems and algorithms, case studies, tools and environments for programming and verification. Submissions: ~~~~~~~~~~~~~ Submissions should consist of a 100-200 word ASCII abstract and a summary (up to 15 pages, typeset 12 points; about 7000 words, excluding bibliography and figures). Simultaneous submissions to other conferences or journals are not allowed. Electronic submissions are strongly encouraged; instructions may be found at the CONCUR'98 web page, or obtained by sending an email with subject ``submission information'' to the address c98-subm@sophia.inria.fr. If surface mail is used, then five (5) copies of the paper should be sent to the following address: Concur'98, INRIA Sophia-Antipolis, BP 93, F-06902 Sophia-Antipolis Cedex, France. Program Committee ~~~~~~~~~~~~~~~~~~~ M. Abadi (Digital,Systems Research Center) A. Asperti (University of Bologna) J. Bradfield (University of Edinburgh) E. Clarke (Carnegie Mellon University) R. de Simone (INRIA Sophia-Antipolis, co-chair) J. Esparza (Technische Universitat Munchen) P. Gastin (University of Paris 7) R. van Glabbeek (Stanford University) G. Gonthier (INRIA Rocquencourt) M. Hennessy (Sussex University) O. Maler (Verimag Grenoble) F. Moller (Uppsala University) U. Montanari (University of Pisa) M. Mukund (SMI Madras) M. Nielsen (University of Aarhus) P. Panangaden (Mc Gill University) J. Parrow (Royal Institute of Technology, Stockholm) A. Rensink (University of Hildesheim) D. Sangiorgi (INRIA Sophia-Antipolis, co-chair) C. Talcott (Stanford University) J. Winkowski (Polish Academy of Sciences) Invited Speakers and Tutorials: ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ (in square brackets, the topic of the talk) Invited Speakers: T. Henzinger (University of California at Berkeley, USA) [Hybrid systems]; U. Herzog (Erlangen, Germany) [Process algebra for performance evaluation]; J. Rutten (CWI, Netherlands) [Coalgebraic models of computation]; J.-B. Stefani (CNET, France Telecom) [Open distributed systems]; M. Vardi (Rice University, USA) [Branching and linear time temporal logics]. Invited Tutorials : G. Berry (CMA Ecole des Mines, France) [Synchronous reactive programming and Esterel]; J.F. Groote (CWI, Netherlands) [Theorem provers in concurrency]; B. Pierce (Indiana U., USA) [Types in concurrency]. Satellite events ~~~~~~~~~~~~~~~~~ COTIC'98: 2nd international workshop on Concurrent Constraint Programming for Time Critical Applications EXPRESS'98: 5th international workshop on Expressiveness in Concurrency HLCL'98: 3rd international workshop on High-Level Concurrent Languages PAPM'98: 6th international workshop on Process Algebra and Performance Modeling CONFER W.G.: 4th workshop of the CONFER (Concurrency and Functions: Evaluation and Reduction) working group. Proceedings ~~~~~~~~~~~~ The proceedings will be published by Springer-Verlag in the LNCS series. A special issue of Theoretical Computer Science is planned. Venue and local arrangements ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Nice is ideally located on the French Riviera. September is still very pleasant, while less crowded than the high season. Nice's international airport is well-connected to all major european and non-european cities. The conference will be held at the Hotel Novotel , which is conveniently located in the heart of Nice, between the city center and the old town, and 20 minutes walk to the beach. Steering Committee ~~~~~~~~~~~~~~~~~~ The Steering Committee of CONCUR is composed of Jos Baeten (chair, Eindhoven), Eike Best (Oldenburg), Kim Larsen (Aalborg), Ugo Montanari (Pisa), Scott Smolka (Stony Brook) and Pierre Wolper (Liege). Organizing Committee ~~~~~~~~~~~~~~~~~~~~~ The Organizing Committee of CONCUR 98 is composed of Amar Bouali, Gerard Boudol, Ilaria Castellani, Catherine Juncker, Francoise Martin-Trucas and Dany Sergeant. ============================== For further information, check URL , or mail to concur98@sophia.inria.fr. From cat-dist Fri Dec 5 08:45:25 1997 Received: (from cat-dist@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id IAA09822; Fri, 5 Dec 1997 08:45:24 -0400 (AST) Date: Fri, 5 Dec 1997 08:45:24 -0400 (AST) From: categories To: categories Subject: Re: e-prints Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-Status: Date: Thu, 4 Dec 1997 16:27:02 -0500 (EST) From: James Stasheff you can input your macros directly into your tex file as for the plagarism issue, I will let the experts respond ************************************************************ Until August 10, 1998, I am on leave from UNC and am at the University of Pennsylvania Jim Stasheff jds@math.upenn.edu 146 Woodland Dr Lansdale PA 19446 (215)822-6707 Jim Stasheff jds@math.unc.edu Math-UNC (919)-962-9607 Chapel Hill NC FAX:(919)-962-2568 27599-3250 From cat-dist Fri Dec 5 08:46:03 1997 Received: (from cat-dist@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id IAA09018; Fri, 5 Dec 1997 08:46:01 -0400 (AST) Date: Fri, 5 Dec 1997 08:46:01 -0400 (AST) From: categories To: categories Subject: Re: e-prints Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-Status: Date: Thu, 4 Dec 1997 13:51:23 -0800 (PST) From: john baez Michael Barr writes: > I am all in favor of Jim Stasheff's proposal, but what does one do about > the fact that I, for example, have my own personal macros files and > my TeX files cannot be compiled without them. Preprint servers of the sort Jim is describing have facilities for uploading macro files, postscript files, etc. along with the TeX files. I use them a lot and they work. Best, John Baez From cat-dist Sat Dec 6 16:12:56 1997 Received: (from cat-dist@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id QAA08161; Sat, 6 Dec 1997 16:12:09 -0400 (AST) Date: Sat, 6 Dec 1997 16:12:08 -0400 (AST) From: categories To: categories Subject: Re: Algebraic Theories/Operads Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-Status: Date: Fri, 5 Dec 1997 18:54:36 +0000 (GMT) From: Tom Leinster > > I'm looking for a good reference on the relation between > algebraic theories (a la Lawvere) and operads. > > David Metzler I think the relationship between algebraic theories and (non-symmetric, non-topological) operads is quite simply described. Loosely, algebras for operads are just the same as algebras for strongly regular theories. To be more precise: any operad gives rise to a monad on Set, the algebras for which are the algebras for the operad; a monad on Set arises from an operad iff it arises from a strongly regular theory. So - operadic monads are strongly regular theories. Carboni & Johnstone (1995) call an equation _strongly regular_ if on each side the same variables appear in the same order, without repetition (e.g. (x.y).z=x.(y.z) and x-(y-z)=(x-y)+z, but not x.y=x, x.y=y.x or (x.x).y=x.(x.y)). A theory is called strongly regular if it can be presented by operators and strongly regular equations - for instance, the theory of monoids. They show that a monad (T, eta, mu) on Set is from a s.r. theory ("is s.r.") iff (i) T is finitary (ii) T preserves wide pullbacks & (iii) eta and mu are cartesian. (A wide pullback is a limit over a diagram (X_i --> X) where i ranges over some set I, e.g. if I=2 it's an ordinary pullback.) 1. Operadic => strongly regular If A is an operad, with the function A --> N={natural numbers}, then the functor part of the induced monad T on Set is defined by the pullback square T(X) ----> W(X) | | | | W(!) | | V V A ------> W(1)=N where X is a set and W (for Words) is the free-monoid monad. One can show (e.g. my (1997, sec 4.6)) that the unit and multiplication of T are cartesian. Moreover, one can also show that (a) if W preserves colimits of a given shape then so does T & (b) if W preserves I-ary pullbacks then so does T. Since the theory of monoids is s.r., W preserves all filtered colimits (i.e. is finitary) and all wide pullbacks. So T satisfies (i)-(iii) and is therefore s.r.. 2. Strongly regular => operadic Conversely, take a s.r. theory T. Any s.r. presentation of T gives rise to a natural transformation T --> W which is cartesian and preserves the monad structure. It follows by my (1997, sec 4.6) that the monad T comes from some operad A. References: A Carboni, P T Johnstone (1995), Connected limits, familial representability and Artin glueing. Math Struct in Comp Science, vol 5, pp 441-459. T Leinster (1997, updated 3 Dec), General operads and multicategories. http://www.dpmms.cam.ac.uk/~leinster. I've heard tell that these ideas were explored by Kelly in his work on clubs - can anyone enlighten me? Tom Leinster From cat-dist Sat Dec 6 16:12:57 1997 Received: (from cat-dist@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id QAA24897; Sat, 6 Dec 1997 16:12:56 -0400 (AST) Date: Sat, 6 Dec 1997 16:12:56 -0400 (AST) From: categories To: categories Subject: Re: e-prints Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-Status: Date: Fri, 5 Dec 1997 13:19:58 -0800 (PST) From: john baez Jim Stasheff writes: > you can input your macros directly into your tex file But you don't need to. You can also upload a bunch of separate files using the uufiles program obtainable from the preprint archive. It's painless and easy. Information on this and a million other technical issues is available at the archives themselves. Try: http://eprints.math.duke.edu/ or send email with subject header "help" to q-alg@eprints.math.duke.edu > as for the plagarism issue, I will let the experts respond I'm no expert, but I don't see what the problem is. If you upload your paper to one of these archives, the paper itself and the exact date and time it was first received is publicly accessible, so any attempt by anyone to plagiarize it would be incredibly easy to prove. If you store your papers on your own site, it's much harder to prove you wrote them before someone else. This is one reason why highly competitive physicists rush to put their papers on the archives as quickly as possible: to get a certified time stamp on their paper! Anyway, I've never heard of any problems with plagiarism actually happening. In case it's not been made sufficiently clear, the main advantages of having all papers on a given subject stored electronically at a single institution are: 1) they are easy to find 2) they are easy to refer to 2) they stay there, archived, while the authors move from institution to institution and ultimately perish. Will our institutions keep our websites going after we die, while technology continues to change? Many of my papers (or pointers to them) appear on Ginsparg-style preprint archive, my own website, Hypatia, Mathematical Reviews, the category theory mailing list, and paper journals --- all of which serve different purposes. Presumably some of these systems will fall into disuse in a natural sort of way as time passes. I wouldn't advocate the brutal elimination of existing systems. I think the question now is: would category theory be served by creation of a Ginsparg-style preprint archive for the subject? From cat-dist Sat Dec 6 16:13:28 1997 Received: (from cat-dist@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id QAA08572; Sat, 6 Dec 1997 16:13:27 -0400 (AST) Date: Sat, 6 Dec 1997 16:13:27 -0400 (AST) From: categories To: categories Subject: Free-Forgetful Adjunction for Vect Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: O X-Status: Date: Sun, 7 Dec 1997 03:54:53 +1100 (AEDT) From: Jonathan Burns I've done my best on this, for two weeks. There comes a point at which one calls for help, because one isn't seeing it. A full-rank set of vectors in a vector space defines a basis, obviously. And given an n-dimensional Euclidean manifold, with specified origin, an arbitrary set of n points, "in general position" (i.e. not contained in any proper subspace), defines a basis for it. In other words, a choice of simplex defines a choice of frame. Now, MacLane sets this up as an example of the "free-forgetful" adjoint relationship. Postulate functors V, U between the two categories: V -> Set(s) Vect(or Spaces) <- U and domains I in Set, and V in Vect. The adjunction is: V I -> P U P <- I UV I -> U P VU P <- VI | / | / ^ / v / |u / |n / | / | / I P The interpretation is: V : Set -> Vect takes a set I to V I, the span of I over some field. (Set-to-set arrows go to linear maps.) U : Vect -> Set is the forgetful functor, taking each vector space to "its underlying set"; which as far as one can tell, is the vector space considered as the total set of linear combinations of the basis elements, with all arrows mapped to nowhere-land. The adjoint isomorphism is: [ V I -> P ] ~~ [ I -> U P ] frame simplex That makes sense, as far as it goes. Now consider the unit and counit. u: id(Sets) -> U V => u(I): I -> UV(I) is the natural transformation from any set I to the elements of its span; which set is isomorphic to R^|I|, and can be read as the flat space in which I resides. That makes sense if I is a set of points, but is meaningless if I is, say, the set {1,2,3}. n : V U -> id(Vect) => n(P) : VU(P) -> P is the natural transformation from the span of the set of elements of a vector space, to the space itself. But the set of elements is infinite. VU(P) would have to be a vector space with an infinite basis. My perplexities: (1) As above, the unit and counit do meaningless things. (2) The vector spaces defined by V are free on I. It's meaningless to ask whether the elements of I are in general position; they are assumed to be. But in a geometric interpretation, one wants to introduce the arrows to the Boolean domain: C2 : P x P -> B : condition for two points to coincide C3: P x P x P -> B: " " 3 points to be collinear C4: PxPxPxP -> B: " " 4 points to be coplanar .... and so on up to |I|. There has to be a sensible place to plug these into Vect, and I expected the adjoint construction to be it. (3) Otherwise, what is the damn thing good for? By comparison, the Diagonal-Product and Product-Exponential units and counits are the most useful things about those constructions; and the Free-Forgetful adjunction for monoids gives us the Kleene closure. But the Free- Forgetful adjunction for Vect almost seems vacuous. An alternative way to see the problem is, to say that Set is not the right category to be looking for adjoints in. Geometrically, we want Vect to be related not to spaces, but to "linear structures" on spaces, in the sense that a manifold atlas genuinely describes a differentiable structure. Maybe we want something like: V -> Flat Vect <- U where Flat (= linear structure) is equipped with the incidence arrows C2, C3,.., C|I|, and admits only m : Flat -> Flat which are U-images of the exterior products in Vect, and preserve the C's. This is related to the question: is the exterior product (i.e. determinant) the unit of some adjunction? Any help really appreciated. Jonathan Burns From cat-dist Mon Dec 8 13:44:13 1997 Received: (from cat-dist@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id NAA05868; Mon, 8 Dec 1997 13:42:05 -0400 (AST) Date: Mon, 8 Dec 1997 13:42:05 -0400 (AST) From: categories To: categories Subject: Re: Algebraic Theories/Operads Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-Status: Date: Mon, 8 Dec 1997 20:15:23 +1100 (EST) From: Barry Jay Tom, you may care to look at my paper "Languages for monoidal categories" @Article(Jay89b, Author={Jay, C.B.}, Title={Languages for monoidal categories}, Journal=jpaa, Volume=59, Year=1989, Pages={61--85}) and its successors (see my ftp site below). Barry Jay ************************************************************************* | Associate Professor C.Barry Jay, | | Reader in Computing Sciences Phone: (61 2) 9514 1814 | | Head, Algorithms and Languages Group, Fax: (61 2) 9514 1807 | | University of Technology, Sydney, e-mail: cbj@socs.uts.edu.au | | P.O. Box 123 Broadway, 2007, www: linus.socs.uts.edu.au/~cbj | | Australia. ftp: ftp.socs.uts.edu.au/Users/cbj | ************************************************************************* From cat-dist Mon Dec 8 15:41:54 1997 Received: (from cat-dist@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id PAA20619; Mon, 8 Dec 1997 15:41:42 -0400 (AST) Date: Mon, 8 Dec 1997 15:41:42 -0400 (AST) From: categories To: categories Subject: Injectives and choice Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: O X-Status: Date: Mon, 8 Dec 1997 13:11:00 -0500 (EST) From: Colin McLarty Grothendieck's proof that every AB5 category has enough injectives uses the axiom of choice (actually Zorn's lemma--which John Bell points out to me is significantly weaker than choice in toposes). And the proof in Johnstone's TOPOS THEORY that the category of Abelian groups over any Grothendieck topos has enough injectives uses Barr's theorem: Every Grothendieck topos is covered by one that satisfies the axiom of choice. This theorem itself assumes the axiom of choice in the base topos (i.e. the one over which the others are Grothendeick). Are there any good results showing how necessary the axiom of choice, or Zorn's lemma, is to these results? From cat-dist Mon Dec 8 17:25:15 1997 Received: (from cat-dist@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id RAA07508; Mon, 8 Dec 1997 17:25:12 -0400 (AST) Date: Mon, 8 Dec 1997 17:25:12 -0400 (AST) From: categories To: categories Subject: Re: Injectives and choice Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-Status: Date: Mon, 8 Dec 1997 15:01:48 -0500 (EST) From: Andreas Blass Even to prove that there is a non-zero injective abelian group needs a little bit of choice, but only a little. (By contrast, the statement that every divisible abelian group is injective is equivalent to the axiom of choice.) The details are in my paper "Injectivity, projectivity, and the axiom of choice" (Trans. Amer. Math. Soc. 255 (1979) 31--59). Andreas Blass > Date: Mon, 8 Dec 1997 13:11:00 -0500 (EST) > From: Colin McLarty > > > Grothendieck's proof that every AB5 category has enough injectives > uses the axiom of choice (actually Zorn's lemma--which John Bell points out > to me is significantly weaker than choice in toposes). And the proof in > Johnstone's TOPOS THEORY that the category of Abelian groups over any > Grothendieck topos has enough injectives uses Barr's theorem: Every > Grothendieck topos is covered by one that satisfies the axiom of choice. > This theorem itself assumes the axiom of choice in the base topos (i.e. the > one over which the others are Grothendeick). > > Are there any good results showing how necessary the axiom of > choice, or Zorn's lemma, is to these results? > From cat-dist Tue Dec 9 16:36:38 1997 Received: (from cat-dist@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id QAA32565; Tue, 9 Dec 1997 16:35:49 -0400 (AST) Date: Tue, 9 Dec 1997 16:35:49 -0400 (AST) From: categories To: categories Subject: eprint discussion - from moderator Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-Status: Date: Tue, 9 Dec 1997 16:32:02 -0400 (AST) From: Bob Rosebrugh A discussion has been going on by email for several days which, because of its technical nature, has not been forwarded to the categories list though it grew out of Jim Stasheff's posting on the preprint server question. Anyone who wants to join the discussion is welcome to. Simply send an email to me that says `subscribe eprints' in its subject line. If you'd just like to look at the discussion or some of the sites mentioned, I have put a Web page at http://www.mta.ca/~rrosebru/eprint.html which has links to the mail file and various places on the Web. Regards to all, Bob Rosebrugh, moderator, categories list From cat-dist Mon Dec 15 14:17:29 1997 Received: (from cat-dist@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id OAA20264; Mon, 15 Dec 1997 14:16:15 -0400 (AST) Date: Mon, 15 Dec 1997 14:16:15 -0400 (AST) From: categories To: categories Subject: AI&Math'98 Conference Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from QUOTED-PRINTABLE to 8bit by mailserv.mta.ca id OAA20264 Status: RO X-Status: Date: Thu, 11 Dec 1997 23:14:54 +0200 (IST) From: ZIPPIE Gonczarowski A considerable mass of categorical fun is expected in AI&Math'98: CALL FOR PARTICIPATION ------------------------------------------------------------------------- Fifth International Symposium on ARTIFICIAL INTELLIGENCE AND MATHEMATICS ------------------------------------------------------------------------- January 4-6, 1998, Fort Lauderdale, Florida http://rutcor.rutgers.edu/~amai Email: amai@rutcor.rutgers.edu ------------------------------------------------------------------------- APPROACH OF THE SYMPOSIUM The International Symposium on Artificial Intelligence and Mathematics is the fifth of a biennial series. Our goal is to foster interactions among mathematics, theoretical computer science, and artificial intelligence. The meeting includes paper presentation, invited speakers, and special topic sessions. Topic sessions in the past have covered computational learning theory, nonmonotonic reasoning, and computational complexity issues in AI. (Cf., 1996 Symposium.) The editorial board of the Annals of Mathematics and Artificial Intelligence serves as the permanent Advisory Committee for the series. ------------------------------------------------------------------------- INVITED TALKS will be given by * Robert Aumann (Hebrew University, Israel) * Joe Halpern (Cornell University) * Scott Kirkpatrick (IBM, Yorktown Heights) * William McCune (Argonne National Laboratory) ------------------------------------------------------------------------- SPECIAL INVITED SESSIONS The Conference will be hosting the following special invited sessions: * Boolean functions and SAT (organized by Ewald Speckenmeyer) * Category Theory (organized by David Israel and Robert Zimmer) * Constraints (organized by Eugene Freuder) * Neural Networks (organized by Eddy Mayoraz) * Satisfiability (organized by John Franco) * Spatial Reasoning (organized by Boi Faltings) ------------------------------------------------------------------------- IMPORTANT DATES Hotel Reservation: December 8, 1997 Preregistration Deadline: December 19, 1997 AI & Math Symposium: January 4-6, 1998 ------------------------------------------------------------------------- Registration by December 19: $175 after December 20, and at door: $200 Students, by December 19: $90 Students, after December 20, and at door: $100 Payment by check on US bank, made out to FAU Foundation, Account S078, mailed to: Fifth International Symposium on AI and Math Department of Mathematical Sciences Florida Atlantic University 777 Glades Road Boca Raton, FL 33431 Payment by VISA or MasterCard [name of account holder, type, number and expiration date] emailed to: saim5@fau.edu or phoned to: 561-367-3341 [561-297-3341 after November 24] Hotel The Symposium will be held at the Embassy Suites in Fort Lauderdale: Embassy Suites Hotel 1100 S.E. 17th Street Fort Lauderdale, FL 33316 Spacious, newly refurbished two room suites are available at the reduced rate of $129 single or double occupancy - includes separate living room and bedroom, microwave, refrigerator, coffee maker, two TVs, two voice mail telephones with dual lines, data ports, queen size sofa sleeper in living room. You get complimentary full cooked-to-order breakfast with free newspaper, complimentary manager's cocktail reception each evening, complimentary 24 hour transportation to and from Ft. Lauderdale airport, and free parking. For reservations, call 1-800-362-2779 or 954-527-2700, by December 8, 1997. Airline Delta Airlines is our Conference airline - and their discounts have improved. Call them at 1-800-241-6760, and give our FAU's file number: 102789A. Car Rental Avis Rent A Car is our Conference car rental agency, offering us special rates. Call 1-800-331-1600 (in Canada, 1-800-879-2847), and give the AVIS account number for the Symposium: J947092. ------------------------------------------------------------------------- General Chair: Martin Golumbic, Bar-Ilan University, Ramat Gan Conference Chair: Frederick Hoffman, Florida Atlantic University Program Co-Chairs: Endre Boros, Rutgers University Russ Greiner, Siemens Corporate Research / University of Alberta Publicity Chair: Alex Kogan, Rutgers University Program Committee: * Martin Anthony (London School of Economics, England) * Peter Auer (Technical University of Graz, Austria) * Fahiem Bacchus (Univ. Waterloo, Canada) * Peter Bartlett(Australian National University) * Peter van Beek (University of Alberta, Canada) * Jimi Crawford (i2 Technologies) * Adnan Darwiche (American Univ., Lebanon) * Rina Dechter (UC Irvine) * Thomas Eiter (University of Giessen, Germany) * Boi Faltings (EPFL, Switzerland) * Ronen Feldman (Bar-Ilan University, Ramat Gan) * John Franco (University of Cincinnati) * Eugene Freuder (University of New Hampshire) * Giorgio Gallo (University of Pisa, Italy) * Hector Geffner (Universidad Simón Bolívar, Venezuela) * Georg Gottlob (Technical University of Vienna, Austria) * Adam Grove (NEC Research) * Peter L. Hammer (Rutgers University) * David Heckerman (Microsoft Corporation) * Michael Kaminski (Technion, Israel) * Henry Kautz (AT&T) * Helene Kirchner (CNRS-INRIA, Nancy, France) * Richard Korf (UCLA) * Gerhard Lakemeyer (Aachen, Germany) * Jean-Claude Latombe (Stanford) * Maurizio Lenzerini (University of Rome, Italy) * Alon Levy (AT&T) * Fangzhen Lin (Hong Kong University of Science and Technology) * Alan Mackworth (UBC) * Heikki Mannila (University of Helsinki, Finnland) * Eddy Mayoraz (IDIAP, Switzerland) * Anil Nerode (Cornell) * Jeff Rosenschein (Hebrew University, Israel) * Elisha Sacks (Purdue) * Dale Schuurmans (University of Pennsylvania) * Bart Selman (AT&T) * Eduardo D. Sontag (Rutgers University) * Ewald Speckenmeyer (University of Koeln, Germany) * Moshe Vardi (Rice) * Paul Vitanyi (CWI, The Netherlands) ------------------------------------------------------------------------- A non-final LIST of ACCEPTED PAPERS 12/01/97 Papers are listed alphabetically by the speakers' names -- in all capitals: * On the complexity of designing compact perceptrons and some consequences, by EDOARDO AMALDI, (amaldi@cs.cornell.edu), School of Operations Research and Theory Center, Cornell University , Ithaca, NY 14853. * Perceive This as That - Analogical and Metaphorical Cognitive Transitions with Categorical Tools, by ZIPPORA ARZI-GONCZAROWSKI (zippie@actcom.co.il), Typographics, Ltd. Jerusalem, Israel * On the conversion between non-binary and binary constraint satisfaction problems, by PETER VAN BEEK (vanbeek@cs.ualberta.ca), University of Alberta, Canada, and Fahiem Bacchus (fbacchus@logos.math.uwaterloo.ca), University of Waterloo, Canada * Characterization of non-monotone non-constructive systems, by PHILIPPE BESNARD (besnard@irisa.fr), CNRS, IRISA, Campus de Beaulie, F-35042 Rennes Ced, France Torsten Schaub (torsten@cs.uni-potsdam.de), Institut fur Informatik, Universitat Potsdam, Postfach 60 15 53, D-14415 Potsdam, Germany * Monotonocity, decision lists and partially defined discrete functions, by JAN C. BIOCH (bioch@few.eur.nl), * A model theory for Figure Ground Location, by THOMAS BITTNER (bittner@geoinfo.tuwien.ac.at), Department of Geoinformation, Technical University of Vienna and National Center of Geographic Information and Analysis, NCGIA * On the structure of some classes of minimal unsatisfiable formulas in CNF, by HANS KLEINE B"UNING (kbcsl@uni-paderborn.de), University of Paderborn, Department of Mathematics and Computer Science, D-33095 Paderborn, Germany * A Comparison of Linear Logic with Wave Logic, by THOMAS L. CLARKE (tclarke@ist.ucf.edu), University of Central Florida/Institute for Simulation and Training, 3280 Progress Drive, Orlando, FL 32826 * Characterizing consistency based diagnosis, by SYLVIE COSTE-MARQUIS and Pierre Marquis ({coste, marquis}@cril.univ-artois.fr), CRIL/Université d'Artois & IUT de Lens rue de l'Université ­ S.P. 16 ­ F­62307 Lens Cedex, France * Optimizing with constraints: a case study in scheduling maintenance of electric power units, by RINA DECHTER (dechter@ics.uci.edu), and Dan Frost (dfrost@ramat-aviv.ics.uci.edu), Information and Computer Science Dept., University of California, Irvine, Irvine, CA 92717 * Applications of Linear Logic to AI and Natural Language Processing CHRISTOPHE FOUQUERE (Christophe.Fouquere@lipn.univ-paris13.fr), University of Paris, 13, Paris, France * Propositional Search with k-Clause Introduction Can be Polynomially Simulated by Resolution, by ALLEN VAN GELDER, (avg@cs.ucsc.edu), University of California at Santa Cruz. * A Propositional Theorem Prover to Solve Planning and Other Problems, by ALLEN VAN GELDER (avg@cs.ucsc.edu), and Fumiaki Okushi (kamiya@cs.ucsc.edu), University of California, Santa Cruz * Lemma and Cut Strategies for Propositional Model Elimination, by ALLEN VAN GELDER (avg@cs.ucsc.edu), and Fumiaki Okushi (kamiya@cs.ucsc.edu), University of California, Santa Cruz * Exact Classification with 2-Layer Neural Nets: Theoretical Results and Open Problems, by GAVIN GIBSON, (gavin@bioss.sari.ac.uk), Biomathematics and Statistics Scotland, Cathy Z. W. Hassell Sweatman (Catherine.Hassell_Sweatman@ee.ed.ac.uk) and Bernard Mulgrew (bernie@ee.ed.ac.uk), Department of Electrical Engineering, University of Edinburgh * Randomized Local Search with Trap Handling, by JUN GU (gu@cs.ust.hk), University of Science and Technology, Hong Kong * Geometric Foundations for Interval-Based Probabilities, by VU HA (vu@cs.uwm.edu), and Peter Haddawy (haddawy@cs.uwm.edu), Dept of EE & CS, University of Wisconsin-Milwaukee * Set-Theoretic Completeness for Epistemic and Conditional Logic, by JOSEPH Y. HALPERN (halpern@cs.cornell.edu), Dept. Computer Science, Cornell University, Ithaca, NY 14853 * Simulated Annealing and Tabu Search for Constraint Solving, by JIN-KAO HAO (Jin-Kao.Hao@eerie.fr), and Jerome Pannier (pannierg@eerie.fr), LGI2P/EMA­EERIE, Parc Scientifique Georges Besse, F­30000 Nimes, France * A closer look at the pure implicational calculus, by PETER HEUSCH (heusch@informatik.uni-koeln.de), and Ewald Speckenmeyer (esp@informatik.uni-koeln.de), Universit"at zu K"oln, Institut f"ur Informatik, Pohligstr. 1, D-50969 K"oln, Germany * The phase transition in random Horn satisfiability, by GABRIEL ISTRATE (istrate@cs.rochester.edu), and Mitsunori Ogihara, Department of Computer Science, University of Rochester, Rochester, NY 14627 * Continuous And Discrete-Time Nonlinear Gradient Descent Relative Loss Bounds and Convergence, by Manfred Warmuth (manfred@cse.ucsc.edu), and ARUN JAGOTA (jagota@cse.ucsc.edu), Department of Computer Science, University of California at Santa Cruz * Constraints and Universal Algebra, by PETER JEAVONS (p.jeavons@dcs.rhbnc.ac.uk), David Cohen, Department of Computer Science, Royal Holloway, University of London, UK, and Justin Pearson (justin@nts.mh.se), Department of Information Technology, Mid Sweden University, S­851 70 Sundsvall, Sweden * Semantic Dimension: On the Effectiveness of Naive Data Fusion Methods in Certain Learning and Detection Problems, by PAUL KANTOR (kantor@rutcor.rutgers.edu), SCILS, Rutgers University, New Jersey * Functional Dependencies in Horn Theories, by Toshihide Ibaraki, ALEXANDER KOGAN (kogan@rutcor.rutgers.edu), Rutgers University, New Jersey, and Kazuhisa Makino * Gains from Concurrenting of the Constraint Solving, by RICHARD KRAJCOVIECH (krajcovi@elf.stuba.sk), and Margareta Kotocova (kotocova@dcs.elf.stuba.sk), Slovak University of Technology, Ilkovicova 3, 812 19 Bratislava, Slovak Republic * Type Grammar Revisited, by J. LAMBECK (ES@CANTOR.Lan.McGill.CA), McGill University, Montreal, Canada * An Information-Theoretic Approach to Data Mining, by MARK LAST (last@eng.tau.ac.il), and Oded Maimon (maimon@eng.tau.ac.il), Department of Industrial Engineering, Tel-Aviv University, Tel-Aviv 69978, Israel * Nonlinear Regularization, by JOERG C. LEMM (lemm@uni-muenster.de), Institut fuer Theoretische Physik I, Wilhelm-Klemm Str.9, D-48149 Muenster, Germany * Computational Learning by an Optical Thin-Film Model, by XIAODONG LI (xli@csu.edu.au), School of Environmental and Information Science, Charles Sturt University, PO Box 789, Albury NSW 2640, Australia, and Martin Purvis (mpurvis@commerce.otago.ac.nz), * Automating the Finite Element Method: a Test Bed for Soft Computing Methods, by LARRY MANEVITZ (manevitz@mathcs11.haifa.ac.il), Department of Computer Science, University of Haifa, Israel, and Dan Givoli, Faculty of Aerospace Engineering, Technion, Haifa, Israel * Forecasting electricity demand using gated neural networks and statistical pruning, by D. MORGAN MANGEAS, (Morgan.Mangeas@inrets.fr), National Research Institute on Transport and Security, France * On the computational complexity of recognizing regions classifiable by a 2-layer perceptron, by EDDY MAYORAZ, (Eddy.Mayoraz@idiap.ch), IDIAP, Switzerland. * Planning and presenting construction proofs automatically, by ERICA MELIS (melis@cs.uni-sb.de), Universit\"at des Saarlandes, Fachbereich Informatik, D-66041 Saarbr\"ucken, Germany * Combining a logical and an analogical framework for route generation and description, by BERNARD MOULIN (bernard.moulin@ift.ulaval.ca), and Driss Kettani (driss.kettani@ift.ulaval.ca), Computer Science Department, Pouliot Building, Research Center of Geomatics, Casault Building, Laval University, Ste Foy (QC) G1K 7P4, Canada * Parallel Cooperative Propositional Theorem Proving, by FUMIAKI KAMIYA OKUSHI (kamiya@cs.ucsc.edu), University of California at Santa Cruz. * Pattern Recognition using Artificial Neural Networks with White Noise, by J. M. Blackledge, and A. OSANLOU (aosan@vesta.cms.dmu.ac.uk), Department of Mathematical Sciences, De Montfort University, Leicester, UK * Multilayer neural nerworks and polyhedral dichotomies, by Claire Kenyon (kenyon@lri.lri.fr), LRI, Universite de Paris-Sud, France, and H\'EL\`ENE PAUGAM-MOISY (Helene.Paugam-Moisy@ens-lyon.fr), LIP, Ecole Normale Superieure de Lyon, France * Generation and comparison of decision strategies for solving satisfiability problems, by ROBERT RODOSEK (r.rodosek@doc.ic.ac.uk), IC-Park, Imperial College, London SW7 2AZ, England * About arc-consistency in semiring-based constraint problems, by Stefano Bistarelli (bista@di.unipi.it) and FRANCESCA ROSSI, (rossi@di.unipi.it), Dipartimento di Informatica, Corso Italia 40, 56125 Pisa, Italy. * An Algorithm for the Class of Pure Implicational Formulas, by John Franco (franco@gauss.ececs.uc.edu), University of Cincinnati, Judy Goldsmith, University of Kentucky, JOHN SCHLIPF, University of Cincinnati, Ewald Speckenmeyer, Universit\"at zu K\"oln, and R.~P.~Swaminathan, University of Cincinnati * On the Complexity of Computing and Learning with Networks of Spiking Neurons, by Wolfgang Maass (maass@igi.tu-graz.ac.at) and MICHAEL SCHMITT (mschmitt@igi.tu-graz.ac.at), Institute for Theoretical Computer Science, Technische Universit\"at Graz, Klosterwiesgasse 32/2, A--8010 Graz, Austria * An Overview of Backtrack Search Satisfiability Algorithms, by JOAO MARQUES SILVA (jpms@inesc.pt), Cadence European Laboratories, IST/INESC, R. Alves Redol, 9, 1, 1000 Lisboa, Portugal * Switching Portfolios, by YORAM SINGER (singer@research.att.com), AT&T Labs, Florham Park, New Jersey * A Hybrid Concept Language, by Patrick Blackburn (patrick@coli.uni-sb.de), Universitat des Saarlandes, Saarbrucken, Germany, and MIROSLAVA TZAKOVA (tzakova@mpi-sb.mpg.de), Max-Planck Institute fur Informatik, Im Stadtwald, 66123 Saarbrucken, Germany * Sequential diagnosis of double regular systems, by Endre Boros (boros@rutcor.rutgers.edu), and TONGUC UNLUYURT (tonguc@rutcor.rutgers.edu), RUTCOR, Rutgers University, New Jersey * Efficient Graph Search by a Smell-Oriented Vertex Process, by ISRAEL A. WAGNER (israelw@vnet.ibm.com), IBM Haifa Research Lab, Matam, Advanced Technology Center, Haifa 31905, Israel Michael Lindenbaum (mic@cs.technion.ac.il), and Alfred M. Bruckstein (freddy@cs.technion.ac.il). * An automated conversion of documents containing math to SGML, by JANUSZ WNEK (JWNEK@SAIC1.SAIC.cpmspc.mail.saic.com), and Robert Price, Science Applications International Corporation, 1953 Gallows Road, Vienna, VA 22182 * Categories and Problem Solving, by ROBERT ZIMMER (robert.zimmer@brunel.ac.uk), Brunel University, London, England ------------------------------------------------------------------------- SPONSORS The Symposium is partially supported by the Annals of Math and AI, Florida Atlantic University, and the Florida- Israel Institute. Other support is pending. If additional funding is secured, partial travel subsidies may be available to junior researchers. ------------------------------------------------------------------------- Further information and future announcements can be obtained from the Conference Web Site at http://rutcor.rutgers.edu/~amai or by (e)mail to Professor Frederick Hoffman Florida Atlantic University, Department of Mathematics PO Box 3091, Boca Raton, FL 33431, USA hoffman@acc.fau.edu From cat-dist Mon Dec 15 14:17:48 1997 Received: (from cat-dist@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id OAA24744; Mon, 15 Dec 1997 14:17:11 -0400 (AST) Date: Mon, 15 Dec 1997 14:17:11 -0400 (AST) From: categories To: categories Subject: unified electronic preprint archive for mathematics Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-Status: Date: Fri, 12 Dec 1997 18:56:40 GMT From: Paul Taylor An open letter to Jim Stasheff, re the proposed unified electronic preprint archive for mathematics Dear Jim, Last week you published a proposal for a unified electronic preprint archive in mathematics, at http://xxx.lanl.gov/list/math/info making use of the software at Los Alamos National Laboratory which was written by Paul Ginsparg, originally for a certain branch of Physics. Following our extensive semi-private correspondence on this subject, I think it is time for me to write something to the "categories" list. First, I want to commend the efforts of yourself and your committee in taking the initiative to call for a unified archive. Mathematics is a notoriously parochial subject, and the existence of such a central resource may in the long term help us to form The Big Picture. Having said this about the mathematical issues, I am unhappy about the way in which this proposal has been made in terms of management and technical issues. Such a unified archive will immediately acquire considerable de facto authority, and it creates a monopoly over the means of publication in mathematics which is potentially far more significant than the contraints of the existing journal system from which we are trying to free ourselves. You have also accepted wholesale Paul Ginsparg's design decisions, some of which may be accidents of implementation. In several respects there are or could be other paradigms of electronic publishing, which ought to be encouraged to co-exist with his ways of doing things, so that the community at large can decide over a period of years which method is to be preferred. I am worried that you may be making assumptions that things have to be done in one way when in fact alternatives are possible. In short, the proposal should have been "put out to tender" for other software designs and implementations to compete on fair terms on the basis of the facilities that they provide to authors and readers. In these respects this issue is analogous to the debate about TeX macros for commutative diagrams, on which a certain amount of blood was spilt some years ago. In that case someone who had used package X proposed that there be an electronic journal in category theory in TeX source, standarding on package X for commutative diagrams, without being aware of the existence of packages Y, Z, ... Actually this is quite different: in using TeX, or whatever technology they use for their papers, authors are making a considerable commitment, and some of us have made a far greater commitment by writing and maintaining macro packages. In the case of electronic dissemination (of existing files), papers can easily be copied to and linked from many different places without any further effort by the author. Nevertheless, bad decisions at this stage about the database which says where everything (and everybody) is could be significant handicaps in the development of the technology at a later date. I therefore beg you at least to stay the widespread advertising of the new archive until its potential competitors have had a chance to discuss the way in which they should co-operate and compete. I intend to contact Paul Ginsparg myself to discuss some technical issues. In particular I have a number of suggestions to make about the process of registering authors and submitting papers. His collected bibliographical data should be provided in BibTeX format for processing by other services. It would also be possible to integrate his author registration with Hypatia's, which would greatly enhance the usefulness of both systems. In fact it is remarkable how closely the strengths of one system coincide with the shortcomings of the other. Yours, Paul Taylor PS The technical discussion which I have been having with Jim Stasheff, Bob Rosebrugh, Mike Barr and others has now moved to a new email list run from Queen Mary and Westfield College. Details of how to join this, together with the archive of the discussion and other information, can be found at http://hypatia.dcs.qmw.ac.uk/html/eprint.html This message is followed by a separate one on the issue of submission in TeX source form. From cat-dist Mon Dec 15 14:17:48 1997 Received: (from cat-dist@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id OAA29716; Mon, 15 Dec 1997 14:17:48 -0400 (AST) Date: Mon, 15 Dec 1997 14:17:47 -0400 (AST) From: categories To: categories Subject: submission of papers in TeX source code Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-Status: Date: Fri, 12 Dec 1997 19:10:27 GMT From: Paul Taylor Following Jim Stasheff's announcement of a unified maths eprint archive on the "categories" list, one issue which provoked a strong reaction was the requirement that papers be submitted in TeX source form. Mike Barr and others pointed out that they use versions of macro packages which cannot reasonably be expected to work under automatic control or in the hands of anyone apart from themselves. I agree very strongly with their views. I claimed in a previous email that the main site at Los Alamos accepts submissions in numerous formats but that the implementation at Duke University, where several existing maths servers exist, restricts this to TeX. I have spent most of today reading the documentation at xxx.lanl.gov and it has given me a headache: electronic methods have a very long way to go to compete with paper when it comes to reading the whole of a lengthy technical document. So, my claim was wrong. Paul Ginsparg has very strong views in favour of TeX (source): http://xxx.lanl.gov/help/faq/whytex.html and against alternative formats such as PostScript. I agree with a lot of what he says, and would even stick my neck out to suggest that Mike Barr probably does too. However, Mike and I feel very strongly that being forced to submit TeX source is a straitjacket, and you can expect us to continue arguing this vigorously (and informedly). Curiously, Paul Ginsparg doesn't discuss DVI (the output of (La)TeX) as an archive format, this being the one for which I would argue. TeX and PostScript are programming languages, but DVI is a very simple and robust "byte code". For anyone worried about the "doomsday scenario" that TeX will no longer exist in 100 years time, the structure of DVI is simple enough that it could be decyphered from existing binary files and a viewer recreated. After all, this was done for hieroglyphs in the 19th century, without the aid of the very sophisicated hardware and artificial intelligence techniques which we can expect to exist in the future. Ginsparg's archives have been running since 1991 and (according to his statistics) take a considerable volume of traffic. From TeX source he generates several other formats, configurably by the reader, apparently on the fly. To promise to do this and still keep your head above water requires an extremely robust system, as I know from having run a major TeX implementation for many years. There is also a lot of documentation about configuring your web browser to accept files in formats for which Netscape was never designed. In other words, he seems to have a very professional way of delivering files to readers. I take my hat off to him, because this is a conspicuous weakness of Hypatia. Whatever the arguments and counterarguments about this particular issue, I suggest that a more liberal attitude to archive submission formats be taken by this and other archives. Paul Taylor PS There was also some discussion of plagiarism, on which subject http://www.cs.cmu.edu/afs/cs/user/nch/www/koala-info.html is interesting. From cat-dist Wed Dec 17 13:52:11 1997 Received: (from cat-dist@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id NAA00394; Wed, 17 Dec 1997 13:51:27 -0400 (AST) Date: Wed, 17 Dec 1997 13:51:27 -0400 (AST) From: categories To: categories Subject: Congratulations! Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: O X-Status: Date: Sun, 14 Dec 1997 17:46:49 -0500 (EST) From: Peter Freyd Ottawa has granted tenure to Rick Blute. Congratulations to Phil and everyone else there. From cat-dist Wed Dec 17 13:53:04 1997 Received: (from cat-dist@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id NAA24498; Wed, 17 Dec 1997 13:53:04 -0400 (AST) Date: Wed, 17 Dec 1997 13:53:04 -0400 (AST) From: categories To: categories Subject: Triples down etc Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: O X-Status: Date: Mon, 15 Dec 1997 10:48:12 -0500 (EST) From: Robert Seely Bob - we have had more troubles with triples, and it is down and out for the time being. Can you please make appropriate adjustments to the categories list, and perhaps post this message to the list as well? All email addresses with "triples" in them ought to just have the "triples" dropped, so, eg, barr@triples.math.mcgill.ca would become barr@math.mcgill.ca, and similarly (for example) for bunge, fox, hermida, lambek, makkai, rags, ruet. The aliasing system we had on triples for the category community is of course not functioning. If there are any problems with email, get in touch with me (rags) or barr (@math.mcgill.ca) and we'll see what can be done. FTP and HTTP url's with "triples" in them will also not work, of course. Some of us have home pages on other machines in the maths dept - those will still function. Our papers are mirrored by Hypatia, so one should check out that site for most purposes. (There is a link on my www page, listed below, if you don't know how to get there.) We hope this problem will be short-lived, bear with us in the meantime. best regards, Robert =========================== RAG Seely =========================== From cat-dist Sat Dec 20 09:50:49 1997 Received: (from cat-dist@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id JAA05700; Sat, 20 Dec 1997 09:50:17 -0400 (AST) Date: Sat, 20 Dec 1997 09:50:17 -0400 (AST) From: categories To: categories Subject: CfP: Workshop & Tutorial on Categorical Rewriting at RTA'98. Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-Status: Date: Wed, 17 Dec 1997 16:16:29 +0100 From: Christoph.Lueth [Apologies if you receive multiple copies. --cxl] Categorical Rewriting --------------------------------------------------- RTA'98 Workshop & Tutorial - Call for Participation The fact that category theory can provide a semantics for rewriting at a level of abstraction between concrete syntax and the relational models given by abstract reduction systems is beginning to be used with increasing success in rewriting. The aim of this workshop and tutorial is to provide an opportunity for the participants of RTA'98 to learn more about categorical term rewriting, and to provide a meeting place for researchers within the field to present and discuss new ideas where category theory can be fruitfully applied to rewriting. The workshop and tutorial will occupy one afternoon of RTA'98. The tutorial will comprise introductory talks about the categorical concepts relevant to term rewriting, such as the theory of monads. For the workshop, talks are invited about work applying categorical or algebraic concepts to term rewriting or related areas, such as graph rewriting, string rewriting or unification. Important dates are as follows: 31 January 1998 Submission deadline 15 February 1998 Notification of acceptance and final programme 1 March 1998 Final versions are due for the informal proceedings 31 March 1998 RTA 98 Workshop & Tutorial on Categorical Rewriting For more information and instructions on submitting a talk see one of http://www.etl.go.jp/~ferjan/CatTRS.html http://www.informatik.uni-bremen.de/~cxl/rta98/workshop.html Registration for the workshop (with or without submitting a talk) should be done via the RTA registration form at http://www.score.is.tsukuba.ac.jp/rta98/ Late on-site registration will be possible. Organisers Neil Ghani Christoph Lueth Fer-Jan de Vries University of Birmingham Universitaet Bremen ETL Birmingham, England Bremen, Germany Tsukuba, Japan nxg@cs.bham.ac.uk cxl@informatik.uni-bremen.de ferjan@etl.go.jp From cat-dist Sat Dec 20 09:50:52 1997 Received: (from cat-dist@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id JAA15711; Sat, 20 Dec 1997 09:50:50 -0400 (AST) Date: Sat, 20 Dec 1997 09:50:50 -0400 (AST) From: categories To: categories Subject: ICALP '98: Call for Papers (reminder) Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-Status: Date: Fri, 19 Dec 1997 09:40:30 +0100 (MET) From: Uffe Henrik Engberg =============== I C A L P '98 =============== 25th International Colloquium on Automata, Languages, and Programming July 13 - 17, 1998 BRICS, Aalborg, Denmark --------------- CALL FOR PAPERS --------------- ICALP '98 important dates: --------------------------------------------- Paper submissions due: January 14, 1998 Notification: March 16, 1998 Final Copies due: April 17, 1998 --------------------------------------------- The 25th annual meeting of the European Association for Theoretical Computer Science (EATCS) will be hosted by the Center for Basic Research in Computer Science (BRICS) at Aalborg University. Aalborg is the fourth largest city in Denmark. The ICALP '98 Programme Committee represents both tracks of the journal Theoretical Computer Science, covering algorithms and formal methods. If enough good papers are submitted, there will be parallel sessions. Papers presenting original contributions in any area of theoretical computer science are being sought. Topics include (but are not limited to): computability, automata, formal languages, new computing paradigms, term rewriting, analysis and design of algorithms, computational geometry, computational complexity, symbolic and algebraic computation, cryptography and security, data types and data structures, theory of data bases and knowledge bases, semantics of programming languages, program specification and verification, foundations of functional and logic programming, parallel and distributed computation, theory of concurrency, theory of robotics, theory of logical design and layout. Authors are invited to submit seven copies of an extended abstract not exceeding 12 pages by January 14, 1998. Electronic submission of papers is solicited. Instructions can be found at http://www.cs.auc.dk/icalp98/submit.html. All correspondence to Prof. Kim G. Larsen -- ICALP'98 Department of Computer Science Aalborg University Fredrik Bajers Vej 7E DK - 9220 Aalborg Denmark e-mail: icalp98-subm@cs.auc.dk Authors from countries where access to copying machines is difficult may submit a single copy of their abstract. Simultaneous submission of papers to any journal or to another conference with published proceedings is not allowed. Invited speakers ---------------- Gilles Brassard, University of Montreal Mark Overmars, Utrecht University Leslie G. Valiant, Harvard University Avi Wigderson, Hebrew University Martin Abadi, DEC Andrew Pitts, Cambridge University Thomas A. Henzinger, University of California at Berkeley Amir Pnueli, Weizmann Institute Programme committee: -------------------- Kim G. Larsen, Aalborg (chair) Sven Skyum, Aarhus (vice-chair) Susanne Albers, Saarbrucken Mark de Berg, Utrecht Ronald Cramer, Zurich Faith Fich, Toronto Burkhard Monien, Paderborn Mike Paterson, Warwick Arto Salomaa, Turku Mikkel Thorup, Copenhagen Ugo Vaccaro, Salerno Shmuel Zaks, Haifa Glynn Winskel, Aarhus (vice-chair) Gerard Boudol, INRIA Sophia-Antipolis Julian Bradfield, Edinburgh Pierre-Louis Curien, Paris Pierpaolo Degano, Pisa Jean-Pierre Jouannaud, Paris Edmund Robinson, QMW, London Bernhard Steffen, Passau Andrzej Tarlecki, Warsaw Frits Vaandrager, Nijmegen Organising Committee -------------------- Kim G. Larsen (chair) Helle Andersen Hans Huttel Ole Hoegh Jensen Lene Mogensen Arne Skou WWW-page -------- For further information, or a postscript version of this document, see http://www.cs.auc.dk/icalp98 From cat-dist Sat Dec 20 09:52:00 1997 Received: (from cat-dist@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id JAA20702; Sat, 20 Dec 1997 09:51:59 -0400 (AST) Date: Sat, 20 Dec 1997 09:51:59 -0400 (AST) From: categories To: categories Subject: ICALP '98: Announcement of Sattellite Events Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from QUOTED-PRINTABLE to 8bit by mailserv.mta.ca id JAA20702 Status: RO X-Status: Date: Fri, 19 Dec 1997 09:57:43 +0100 (MET) From: Uffe Henrik Engberg =============== I C A L P '98 =============== 25th International Colloquium on Automata, Languages, and Programming BRICS, Aalborg, Denmark http://www.cs.auc.dk/icalp98/ --------------------------------- ANNOUNCEMENT OF SATTELLITE EVENTS --------------------------------- The 25th annual meeting of the European Association for Theoretical Computer Science (EATCS) will be hosted by the Center for Basic Research in Computer Science (BRICS) at Aalborg University. The meeting takes place on July 13 - 17, 1998. We are pleased to announce the following sattellite events in connection with ICALP '98. ---------------------------------------------------------------------- Software Tools for Technology Transfer July 12 -14, 1998 Contact person: Bernhard Steffen Lehrstuhl Informatik V Universitaet Dortmund Baroperstr. 301 44221 Dortmund Germany steffen@andorfer.informatik.uni-dortmund.de ---------------------------------------------------------------------- INFINITY '98 3rd International Workshop on Verification of Infinite State Systems July 17 - 18, 1998 Contact person: Javier Esparza Technical University of Munich esparza@informatik.tu-muenchen.de http://wwwbrauer.informatik.tu-muenchen.de/INFINITY98/ ---------------------------------------------------------------------- SOAP Semantics of Objects As Processes July 18, 1998 Contact person: Uwe Nestmann BRICS, Aalborg University Fredrik Bajersvej 7E 9220 Aalborg Denmark uwe@cs.auc.dk http://www.cs.auc.dk/~hans/soap.html ---------------------------------------------------------------------- APPROX '98 1st International Workshop on Approximation Algorithms for Combinatorial Optimization Problems July 18 - 19, 1998 Contact person: Klaus Jansen, APPROX '98 Max-Planck Institute for Computer Science Im Stadtwald 66 123 Saarbrücken Germany approx98@mpi-sb.mpg.de http://www.mpi-sb.mpg.de/~approx98/ ---------------------------------------------------------------------- Summer School in Cryptology and Data Security University of Aarhus July 20 - 24, 1998 Organised by: BRICS (Denmark) - TUCS (Finland) - IPA (Holland) Contact person: Ivan Damgaard BRICS, University of Aarhus Ny Munkegade, building 540 DK-8000 Aarhus C, Denmark ivan@daimi.aau.dk http://www.brics.dk/Activities/98/CryptDatSecSchool/ ---------------------------------------------------------------------- From cat-dist Sat Dec 20 09:52:53 1997 Received: (from cat-dist@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id JAA20596; Sat, 20 Dec 1997 09:52:52 -0400 (AST) Date: Sat, 20 Dec 1997 09:52:52 -0400 (AST) From: categories To: categories Subject: non-Abelian categories Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-Status: Date: Fri, 19 Dec 1997 13:43:23 -0500 (EST) From: Colin McLarty Are there known axioms that stand to all groups the way the Abelian category axioms stand to Abelian groups? From cat-dist Sat Dec 20 09:53:50 1997 Received: (from cat-dist@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id JAA32685; Sat, 20 Dec 1997 09:53:49 -0400 (AST) Date: Sat, 20 Dec 1997 09:53:49 -0400 (AST) From: categories To: categories Subject: abstract algebraic geometry Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-Status: Date: Fri, 19 Dec 1997 12:22:05 -0800 From: Zhaohua Luo The following is the third part of "The language of analytic categories", which is a report on my paper CATEGORICAL GEOMETRY. Again comments and suggestions are welcome. Z. Luo _____________________________________________ THE LANGUAGE OF ANALYTIC CATEGORIES By Zhaohua Luo (1997) ------------------------------------------------------------ Content 1. Analytic Categories 2. Distributive Properties 3. Coflat Maps 4. Analytic Monos 5. Reduced Objects 6. Integral Objects 7. Simple objects 8. Local Objects 9. Analytic Geometries 10. Zariski Geometries References Analytic Dictionary ------------------------------------------------------------- 9. Analytic Geometries An "analytic geometry" is an analytic category satisfying the following axioms: (Axiom 4) Any intersection of strong subobjects exists. (Axiom 5) Any non-initial object has a non-initial reduced strong subobject. (Axiom 6) Any strong subobject is an intersection of disjunctable strong subobjects. Thus an analytic geometry is a perfect, reducible, and locally disjunctable analytic category. Suppose C is an analytic geometry. (9.1) Any object has a radical; the full subcategory of reduced subobjects is a reduced analytic geometry. (9.2) If X is the join of two strong subobjects U and V in R(X), then {U, V} is a unipotent cover on X. (9.3) If U and V are two strong subobjects of an object X, then rad(U \vee V) = rad(U) \vee rad(V). (9.4) Denote by D(X) the set of reduced strong subobjects of X. The radical mapping rad: R(X) --> D(X) is the right adjoint of the inclusion D(X) --> R(X), which preserves finite joins. (9.5) The dual D(X)^{op} of the lattice D(X) is a locale; a reduced strong subobject is integral if and only if it is a prime element of D(X)^{op}. (9.6) The spectrum Spec(X) of an object X is homeomorphic to the space of points of the locale D(X)^{op} (therefore is a sober space); an analytic geometry is spatial iff D(X)^{op} is a spatial locale for each object X. (9.7) The functor sending each object X to D(X)^{op} and each map f: Y --> X to rad(f)^{-1} is equivalent to the analytic topology on C (cf. [L4]). (9.8) If V is a strong subobject of a non-initial object X in a spatial analytic geometry then the join of all the primes contained in V is the radical of V. (9.9) A non-initial reduced object X in a spatial analytic geometry is integral iff its spectrum is irreducible. (9.10) Suppose f: Y --> X is a mono in a spatial analytic geometry. If f is coflat then Spec(f) is a topological embedding; if f is analytic then Spec(f) is an open embedding; if f is strong then Spec(f) is a closed embedding. (9.11) (Chinese remainder theorem) Let X be an object in a strict analytic geometry. Suppose U_1, U_2, ..., U_n are strong subobjects of X such that U_i, U_j are disjoint for all i \neq j, then the induced map \sum U_i --> \vee U_i is an isomorphism. -------------------------------------------------------------- 10. Zariski Geometries Most of the results stated in this section are due to Diers (in the dual situation). Our purpose is to present a geometric approach using the language of analytic categories developed above. A category is "coherent" if the following three axioms are satisfied: (Axiom 7) It is locally finitely copresentable. (Axiom 8) Finite sums are disjoint and stable. (Axiom 9) The sum of its terminal object with itself is finitely copresentable. It is easy to see that a coherent category is an analytic category. A "Zariski geometry" (resp. "Stone geometry") is a locally disjunctable (resp. locally decidable) coherent category. Diers proved in [D1] that a locally finitely copresentable category is a coherent category (resp. Stone geometry) iff its full subcategory of finitely copresentable objects is lextensive (resp. lextensive and decidable). Note that a category is a coherent category (resp. Stone geometry) iff its opposite is a "locally indecomposable category" (resp. "locally simple category") in the sense of [D1]. Let C be a coherent category. A map f: Y --> X is called "indirect" if it does not factor through any proper direct mono to X. A non-initial object is "indecomposable" if it has exactly two direct subobjects. A maximal indecomposable subobject is called an "indecomposable component". (10.1) Any non-initial object has a simple prime and an extremal simple subobject; a coherent category is a spatial reducible perfect analytic category. (10.2) Cofiltered limits and products of coflat maps are coflat; intersections of coflat monos are coflat monos; intersections of fractions are fractions; any map can be factored uniquely as a quasi-local map followed by a fraction. (10.3) Any composite of locally direct mono is locally direct; any map can be factored uniquely as an indirect map followed by a locally direct mono. (10.4) Any non-initial object has an indecomposable component; an indecomposable subobject is an indecomposable component iff it is a locally direct subobject. (10.5) The extensive topology is naturally a strict metric topology, which is determined by the canonical functor to the category of Stone spaces (preserving cofiltered limits and colimits whose right adjoint preserving sums). (10.6) A Stone geometry is a strict reduced Zariski geometry whose opposite is a regular category, and its analytic topology coincides with the extensive topology. Let C be a Zariski geometry. A "locality" is a fraction with a local object as domain. A "local isomorphism" is a map f: Y -- > X such that, for any locality v: V --> Y, the composite f.v: V --> X is a locality. A complement of a set of strong monos is called a "semisingular mono". Note that (10.13) below implies that our definitions of reduced and integral objects coincide with those of Diers's in a Zariski geometry. (10.8) A Zariski geometry is a spatial analytic geometry; The spectrum Spec(X) of any object is a coherent space for any object X; if f: Y --> X is a unipotent map then Spec(f) is surjective. (10.9) If f: Y --> X is a finitely copresentable (i.e. f is a finitely copresentable object in C/X) local isomorphism, then Spec(f): Spec(Y) --> Spec(X) is an open map. (10.10) A simple subobject on an object is a residue iff it is maximal (i.e. it is not contained in any larger simple subobject); any integral object X has a unique generic residue. (10.11) (Going Up Theorem) If f: Y --> X is a coflat map and V is in the image of Spec(f), any prime of X containing V is also in the image of Spec(f) (i.e. the image of Spec(f) is closed under generalizations). (10.12) Any colimits and cofiltered limits of reduced objects is reduced; the full subcategory of reduced objects is a reduced Zariski geometry. (10.13) An object is integral (resp. reduced) iff it is a quotient of a simple object (resp. a coproduct of simple objects). (10.14) A Zariski geometry is strict iff any finite analytic cover is not contained in any proper subobject. Suppose C is strict. A mono is analytic iff it is singular (resp. a finitely copresentable fraction); a mono is a fraction iff it is semisingular (resp. a local isomorphism); a mono is direct iff it is strong and analytic. References [D1] Diers, Y. Categories of Boolean Sheaves of Simple Algebras, Lecture Notes in Mathematics Vol. 1187, Springer Verlag, Berlin, 1986. [D2] Diers, Y. Categories of Commutative Algebras, Oxford University Press, 1992. [L1] Luo, Z. On the geometry of metric sites, Journal of Algebra 176, 210-229, 1995. [L2] Luo, Z. On the geometry of framed sites, preprint, 1995. [L3] Luo, Z. Categorical Geometry, preprint, 1997. [L4] Luo, Z. Abstract Algebraic Geometry, preprint, 1997. ---------------------------------------------------------- END OF THIRD PART From cat-dist Sun Dec 21 16:08:46 1997 Received: (from cat-dist@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id QAA09730; Sun, 21 Dec 1997 16:08:15 -0400 (AST) Date: Sun, 21 Dec 1997 16:08:15 -0400 (AST) From: categories To: categories Subject: Re: non-Abelian categories Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: O X-Status: Date: Sat, 20 Dec 1997 14:21:35 GMT From: Michael Barr Colin's question, which essentially asks for a solution to the proportion abelian groups:groups :: abelian category:x does not of course have a unique answer. One solution was exact category and that was definitely one of the things I had in mind. In fact, I think I even said so. From my current vantage, I would add the following two properties: pointed and Mal'cev. For an equational category, that is almost enough to force a group structure (associativity is missing). I don't know how to force associativity by categorical properties, but pointed, exact and Mal'cev has to come awfully close to answering the question. Michael From cat-dist Sun Dec 21 16:08:55 1997 Received: (from cat-dist@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id QAA14618; Sun, 21 Dec 1997 16:08:53 -0400 (AST) Date: Sun, 21 Dec 1997 16:08:53 -0400 (AST) From: categories To: categories Subject: Re: non-Abelian categories Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: O X-Status: Date: Sat, 20 Dec 1997 13:41:28 -0500 (EST) From: Colin Mclarty Paul Taylor wrote to me Sat, 20 Dec > >> Are there known axioms that stand to all groups the way >> the Abelian category axioms stand to Abelian groups? > >This is a very cryptic question, Colin, why don't you say >in a bit more detail what you have in mind? I guess it was cryptic. And maybe it is trivial once spelled out. The thing is that I am writing a note on the Abelian category axioms as a foundation for the general theory of linear transformations, or of transformations linear over a given ring, etc. It is a reply to several of Sol Feferman's old complaints about categorical foundations which he recently affirmed unchanged on another e-mail list. In preparation I noticed that Emmy Noether used to look for "set theoretic foundations of group theory" by which she meant foundations that would NOT refer to elements or operations but would take the notion of quotient group as basic--and rely on her homomorphism and isomorphism theorems. By "group theory" she meant the study of varous categories. At least: the category of all groups, the category of groups with a fixed set of operators on them and homomorphisms prserving the operators, and the same for Abelian groups in place of all groups. Her Abelian groups with a fixed set of operators are in effect modules over a fixed ring. She was hugely attached to non-commutative algebras and to the generality of her proto-category-theoretic methods. She tends to present "all groups" and "commutative groups" as very similar things. I believe that most logicians today and philosophers of math also see these as quite similar, and that's who I'm writing for. So far as I see, they are not very similar categorically. The Abelian category axioms nicely suit Noether's goals for the Abelian cases--her homomorphism and isomorphism theorems become definitions and axioms on kernels and cokernels. I don't know anything comparable for all groups (or all groups with operators). You could axiomatize the category of all groups by, in effect, axioms for the category of sets (to be construed as free groups) plus the quotients given by the triple for groups over sets. And the same for groups with any set of operators. You could do the same for Abelian groups (or modules over fixed ring) but this is far less elegant than the Abelian category axioms with a projective generator--which you can then relate to set theory if you like by assuming completeness and that the generator is small. The triples approach axiomatizes completeness first, and the group structure as an add-on to it. Are there known axioms for the category of groups that do not in effect axiomatize the category of sets at the same time? Anything as elegant as the Abelian category axioms--though of course elegance is often in the eye of the beholder. Thanks, Colin From cat-dist Sun Dec 21 16:09:58 1997 Received: (from cat-dist@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id QAA13363; Sun, 21 Dec 1997 16:09:57 -0400 (AST) Date: Sun, 21 Dec 1997 16:09:57 -0400 (AST) From: categories To: categories Subject: correction on category of groups Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: O X-Status: Date: Sat, 20 Dec 1997 20:09:34 -0500 (EST) From: Colin Mclarty In an earlier post today I misdescribed a way of axiomatizing the category of groups by the triple for groups over sets. The point is that you can axiomatize the category of sets and the Eilenberg-Moore category for the triple for groups over it, and then identify the category of sets with the non-full subcategory of free groups and homomorphisms taking generators to generators; so that in a very narrow sense you would "only be talking about groups and homomorphisms". But really this amounts to defining groups as structured sets. What I want to know is, are there known axioms approaching the category of groups directly. From cat-dist Mon Dec 22 10:50:17 1997 Received: (from cat-dist@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id KAA23971; Mon, 22 Dec 1997 10:49:51 -0400 (AST) Date: Mon, 22 Dec 1997 10:49:51 -0400 (AST) From: categories To: categories Subject: non-Abelian groups Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-Status: Date: Mon, 22 Dec 1997 10:33:36 +0100 (MET) From: Anders Kock Concerning Colin McLarty's questions: The category of groups should really be seen as a 2-category, in fact as part of the 2-category of groupoids. From cat-dist Tue Dec 23 10:24:46 1997 Received: (from cat-dist@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id KAA21550; Tue, 23 Dec 1997 10:23:47 -0400 (AST) Date: Tue, 23 Dec 1997 10:23:47 -0400 (AST) From: categories To: categories Subject: Re: non-Abelian groups Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-Status: Date: Mon, 22 Dec 1997 11:34:35 -0500 (EST) From: Colin McLarty >Date: Mon, 22 Dec 1997 10:33:36 +0100 (MET) >From: Anders Kock > >Concerning Colin McLarty's questions: The category of groups should really >be seen as a 2-category, in fact as part of the 2-category of groupoids. > This gives an approach I had not thought of, and should have: take axioms for the category of categories, and change the description of the generator 2 to make it a groupoid. For the category of categories, 2 has no non-constant, non-identity endofunctors. For the category of groupoids it has exactly one, and that is an involution. (By a constant functor I mean one factoring through the terminal category 1.) A few other changes might be needed, depending on details of the axioms for the category of categories. But the key seems to be that the category of groupoids is cartesian closed and its insertion into the category of categories preserves exponentials--the prominent fact that a natural transformation with all components iso is a natural iso. So the center of the strength of the cat-of-cats axioms can be kept unchanged for the cat of groupoids. This is somehow orthogonal to the approach Mike Barr suggested, in that cartesian closedness of the category of categories is very close to associativity of composition. Mike lost associativity, but kept groups as opposed to groupoids. Anders's strategy gets associativity/cc-ness by foregoing uniqueness of objects. I have no idea how far this shows something objective, and how far it is an accident of the approaches we've thought of. From cat-dist Tue Dec 23 21:43:56 1997 Received: (from cat-dist@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id VAA00012; Tue, 23 Dec 1997 21:43:48 -0400 (AST) Date: Tue, 23 Dec 1997 21:43:48 -0400 (AST) From: categories To: categories Subject: job in Sydney Univ. School of Maths about to be advertised. Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: O X-Status: Date: Tue, 23 Dec 1997 14:41:37 +1100 (EST) From: Max Kelly The following is an extract from our "School News", and refers only to a post in Pure Mathematics, suppressing the others which are in Applied Maths or in Mathematical Statistics. It contains some junk I didn't get around to removing, in the way of printing instructiond, but seems to be legible. I'm sure the Registrar can supply the position-code that is not yet announced, if anyone applies without it to the given address. _______ The following positions will be advertised in the Australian newspaper on January 7, 1998. The closing date will be January 29, 1998.

Applications: Four copies are required and should include a curriculum vitae, list of publications and the names, addresses and fax numbers of three confidential referees.

Applications must quote the position reference number which is still to be advised and be sent to 

   The Personnel Officer
   College of Sciences and Technology
   Carslaw Building (F07)
   The University of Sydney
   NSW 2006 
   Australia


Associate Lecturer/Lecturer


Applications are invited for an associate lectureship/lectureship in Pure
Mathematics as part of the 'new-blood' program in the School of Mathematics
and Statistics. The School is one of the largest in Australia in terms of
staff, undergraduate and postgraduate students and has active research groups
spanning a wide range of pure mathematics including algebra, analysis,
categories, geometry and topology and nonlinear analysis.



Applications are encouraged from those with a demonstrated record of research
excellence in any of the above areas, but preference may be given to those
whose research interests would support the research strengths of the School in
algebra (especially computational algebra and representation theory) or
nonlinear analysis. Candidates must have a PhD, a strong research record, a
demonstrated ability to teach Pure Mathematics at undergraduate levels,
possess good written and verbal communication skills and present evidence of a
commitment to excellence in teaching and an ability to work cooper atively
with others.



The position will be offered on a tenurable basis to an exceptional candidate
or fixed term for a period of five years. In the latter case, there is the
possibility of further offers of employment up to three years, subject to need
and funding. Membership of a University approved superannuation scheme is a
condition of employment for all new employees. Further information may be
obtained from Associate Professor C. J. Durrant, tel. 9351 3373, fax 9351
4534, email
C.Durrant@maths.usyd.edu.au .



(Level of appointment and responsibility will be commensurate with
qualifications and experience.)




________
Good luck - Max Kelly.


From cat-dist Tue Dec 30 21:30:43 1997
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Date: Tue, 30 Dec 1997 21:29:42 -0400 (AST)
From: categories 
To: categories 
Subject: 2nd cfp: Workshop on Generic Programming 98 
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Date: Mon, 29 Dec 1997 14:24:48 +0100 (MET)
From: Johan Jeuring 


                         Call for Papers

                  Workshop on Generic Programming

                 June 18th 1998, Marstrand, Sweden

    (In Conjunction with Mathematics of Program Construction Conference)

              http://www.cse.ogi.edu/PacSoft/conf/wgp/


Generic programming is about making programs more adaptable by making them more
general.  A generic program embodies some sort of polymorphism; ordinary 
programs are obtained from it by suitably instantiating its parameters. The
parameters may be other programs, types or type constructors, or even 
programming paradigms.

Generic programming techniques have always been of interest, both to 
practitioners and theoreticians, but to date have rarely been a specific 
focus of research.  Recent developments in functional and 
object-oriented programming lead the organizers of this workshop to believe 
that there is sufficient interest to warrant the organisation of a one-day
workshop on the theme of generic programming.  The workshop will be on 
June 18th, 1998, following on from the Mathematics of Program Construction 
conference.  

The goal of the workshop is to inventorise the full diversity of research 
activities in the area of generic programming, both theoretical and applied, 
by attracting as wide a spectrum of participants as possible to the workshop. 
The results of the workshop will be published in the form of a detailed summary
of all presentations, prepared by the organizers and made available on 
internet.

We cordially invite all those with an active interest in this important new 
area to submit a short position paper on their work to Roland Backhouse
(rolandb@win.tue.nl).  The position paper should outline your current research
activities in this area and include references to published papers and/or 
web links to technical reports where more information can be found.  
The recommended length is approximately three pages.  The
deadline for submission is 16th February, 1998.   Notification of acceptance 
will be on or before 15th March, 1998.



The organizers are as follows:

Roland Backhouse (Cochair), Netherlands   Tim Sheard (Cochair), USA
Robin Cockett, Canada                     Barry Jay, Australia
Johan Jeuring, Sweden                     Karl Lieberherr, USA                
Oege de Moor, UK                          Bernhard Moeller, Germany
Jose Oliveira, Portugal                   Fritz Ruehr, USA


For further details on the Mathematics of Program Construction and this 
workshop please consult:

             http://www.md.chalmers.se/Conf/MPC98/