From cat-dist Tue Jul 1 15:11:34 1997 Received: by mailserv.mta.ca; id AA31042; Tue, 1 Jul 1997 15:11:01 -0300 Date: Tue, 1 Jul 1997 15:11:01 -0300 (ADT) From: categories To: categories Subject: my formula again. Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: O X-Status: Date: Tue, 1 Jul 1997 11:05:19 +0100 (BST) From: Paul Taylor Thanks to Pino Rosolini for pointing out a typo in my formula: for any function f:Sigma x X -> Sigma (not -> X) and predicate a:X -> Sigma f(a) & a = f(true) & a where the parameter x has been suppressed from the equation so in full it reads, less clearly f(a(x),x) & a(x) = f(true,x) & a(x) Paul From cat-dist Tue Jul 1 15:12:20 1997 Received: by mailserv.mta.ca; id AA20147; Tue, 1 Jul 1997 15:12:18 -0300 Date: Tue, 1 Jul 1997 15:12:18 -0300 (ADT) From: categories To: categories Subject: Preprint available Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: O X-Status: Date: Tue, 1 Jul 97 13:38 BST From: Dr. P.T. Johnstone The Pure Mathematics Department of Cambridge University has a new electronic preprint server (accessible via our home page at http://www.pmms.cam.ac.uk). The first preprint available may be of interest to people on the categories mailing list: it is C. Butz and P.T. Johnstone: Classifying toposes for first-order theories Abstract: By a classifying topos for a first-order theory $\Bbb T$, we mean a topos $\cal E$ such that, for any topos $\cal F$, models of $\Bbb T$ in $\cal F$ correspond exactly to open geometric morphisms ${\cal F} \rightarrow{\cal E}$. We show that not every (infinitary) first-order theory has a classifying topos in this sense, but we characterize those which do by an appropriate `smallness condition', and we show that every Grothendieck topos arises as the classifying topos of such a theory. We also show that every first-order theory has a conservative extension to one which possesses a classifying topos, and we obtain a Heyting-valued completeness theorem for infinitary first-order logic. For those who would prefer to receive a hard copy of this paper, I shall be bringing a supply with me to the Vancouver meeting. Peter Johnstone From cat-dist Tue Jul 1 15:13:56 1997 Received: by mailserv.mta.ca; id AA21618; Tue, 1 Jul 1997 15:13:55 -0300 Date: Tue, 1 Jul 1997 15:13:55 -0300 (ADT) From: categories To: categories Subject: Re: comma categories Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: O X-Status: Date: Tue, 1 Jul 1997 11:38:17 -0400 From: Michael Barr You are right. It is called slice categories. Michael Barr >From john@cs.keele.ac.uk Tue Jul 1 04:09:41 1997 Received: from gabriel.cc.keele.ac.uk (gabriel.cc.keele.ac.uk [160.5.20.2]) by triples.math.mcgill.ca (8.6.8/8.6.6) with ESMTP id EAA08244 for ; Tue, 1 Jul 1997 04:09:39 -0400 Received: from nina.cs.keele.ac.uk by gabriel with SMTP (PP); Tue, 1 Jul 1997 09:17:11 +0100 From: "John G. Stell" Date: Tue, 1 Jul 1997 09:14:56 +0100 Message-Id: <6826.199707010814@nina.cs.keele.ac.uk> To: barr@triples.math.mcgill.ca Subject: comma categories Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Content-MD5: P4mFcjNdTLEYzYzmOK7OUw== Status: R > Not that I am blowing my own horn (but why not), you will find something > about comma categories in Barr & Wells, Category Theory for Computing > Science. But no, I know of no other research along those lines. > > Michael Barr Pehaps it would be helpful to the original enquirer to say where it can be found. I am unable to find it in the index of either edition. John Stell From cat-dist Tue Jul 1 15:14:43 1997 Received: by mailserv.mta.ca; id AA17987; Tue, 1 Jul 1997 15:14:43 -0300 Date: Tue, 1 Jul 1997 15:14:42 -0300 (ADT) From: categories To: categories Subject: Re: Query Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: O X-Status: Date: Tue, 1 Jul 1997 09:49:21 -0700 From: Michael J. Healy 206-865-3123 Since there have been some replies to the query about artificial perception, I suppose it's OK to mention my own work in progress. I have been doing research in the formal semantics of neural networks. I am working on a mathematical model in which concepts (formulas) are formed in memory as colimits. The diagrams involve neural structures representing other concepts, going all the way back to simple percepts. A concept is stored in memory as a neuron or neuron pool together with its attendant synaptic connections. Logically closed portions of memory are theories. Functors and natural transformations enter in in the usual fashion of categorical model theory. There is still a lot of work to do on this, and I am still learning the mathematics. I do have a proposed neural implementation of it, and am working on a paper. Previous work along these lines has involved geometric logic, so that I could understand some of the basics of learning, which for me involves working with an observational logic. I have a paper on this, too. Finding reviewers for this kind of material in the neural network community has been difficult. If any of this sounds interesting enough to discuss, I certainly wouldn't mind getting some feedback from category theorists. Sincerely, Mike Healy -- =========================================================================== e Michael J. Healy A FA ----------> GA (425)865-3123 | | FAX(425)865-2964 | | Ff | | Gf c/o The Boeing Company | | PO Box 3707 MS 7L-66 \|/ \|/ Seattle, WA 98124-2207 ' ' USA FB ----------> GB e "I'm a natural man." michael.j.healy@boeing.com B -or- mjhealy@u.washington.edu ============================================================================ From cat-dist Wed Jul 2 13:37:13 1997 Received: by mailserv.mta.ca; id AA23900; Wed, 2 Jul 1997 13:33:45 -0300 Date: Wed, 2 Jul 1997 13:33:45 -0300 (ADT) From: categories To: categories Subject: Re: functions Omega->Omega Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-Status: Date: Tue, 1 Jul 1997 16:22:06 -0400 (EDT) From: Todd Wilson Paul Taylor asks: > f(a) & a = f(true) & a > > I wonder whether anyone has noticed this formula before? There is a section of my thesis devoted to operators on Heyting algebras that satisfy this formula. More generally, I considered "extensional operators" l : A -> A (A is a H.A.), which are characterized by any of the following equivalent conditions: (a) x C y implies l(x) C l(y) (x,y in A, C a Heyting-congruence on A) (b) a & l(x) <= l(a * x) <= a -> l(x) (a,x in A, * in {&,->}) (c) a * l(x) = a * l(a o x) (a,x in A, *,o in {&,->}) (d) a * x = a * y implies a o l(x) = a o l(y) (a,x,y in A, *,o in {&,->}) (e) x <-> y <= l(x) <-> l(y) (x,y in A) The name "extensional operator" comes from (e). If A is complete, extensional operators on A are in 1-1 correspondence with morphisms Omega -> Omega in the topos Sh(A). "Logical operators" are what I called extensional operators satisfying l(true) = true -- or, equivalently, x <= l(x) (x in A). The quasinuclei of Banaschewski are then precisely the monotone logical operators, and nuclei are (therefore) precisely the extensional closure operators. Arbitrary extensional operators can be "built" from "below" or from "above" by specific extensional operators, generalizing the way nuclei can be built from open, closed, and quasiclosed nuclei, and several "structure theorems" of this kind exist. One can also characterize the subsets of A that can appear as the fixedpoint sets of logical operators (equivalently the prefixedpoint sets of extensional operators). My thesis goes on to study "regular operators" -- the regular elements in the lattice of logical operators, or, equivalently, those operators r satisfying r(a->b) = a->r(b) (a,b in A) -- which have an amazing number of properties (e.g., they are idempotent, they preserve "regular" joins and "stable" meets, their fixedpoint sets are the same as the fixedpoint sets of logical operators, any two regular operators commute, and the join of regular operators is function composition, to name several). The set of regular operators on a frame A forms a complete Boolean algebra isomorphic to N^2(A)/--, i.e., the double-negation quotient of the *second assembly* of A (where N(A) = the frame of nuclei on A = the frame of frame congruences on A; see Johnstone, Stone Spaces, pp. 51--57, for more information on the functor N and its iterates). This provides a concrete embedding of any frame into a complete Boolean algebra. I have used the theory regular operators to derive an explicit formula for joins of nuclei, characterize "free meets" in frames, and to answer some questions about fibrewise-Boolean locales. My thesis also characterizes universal monos (and obtains some results about limits and colimits) in the categories of frames and kappa-frames, and generalizes some results of Banaschewki on finitely generated frame extensions. It appeared as CMU tech report CMU-CS-94-186. Todd Wilson Computer Science Department Cornell University From cat-dist Wed Jul 2 13:48:35 1997 Received: by mailserv.mta.ca; id AA24928; Wed, 2 Jul 1997 13:48:14 -0300 Date: Wed, 2 Jul 1997 13:48:14 -0300 (ADT) From: categories To: categories Subject: research position available at Cambridge Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: O X-Status: Date: Wed, 02 Jul 1997 14:15:53 +0100 From: Philippa Gardner [Apologies if you receive multiple copies of this announcement.] ----------------------------------------------------------------- Calculi for Interactive Systems: Theory and Experiment Postdoctoral Research Position University of Cambridge Computer Laboratory A research position is available as part of an on-going project consisting of two interlinked strands: 1. the development of action calculi, a framework for exploring many models of interactive behaviour, such as the pi calculus and its extensions, lambda calculi, calculi for security and object-oriented calculi; 2. the design and study of foundational calculi based upon the pi calculus, and accompanying prototype programming languages, in which to describe and analyse migratory distributed systems. We are looking for someone to focus on the dynamics of action calculi, in particular on issues such as behavioural congruences, the study of examples, and the analysis of the expressiveness of different calculi. Applications are encouraged from those with a background in some of the following: process algebra, operational semantics, type theory and category theory. Knowledge of action calculi would be helpful but not necessary. The start date is flexible. The position is for between two and three years, depending on the start date and the age of the applicant. For further information regarding action calculi, see the web page http://www.cl.cam.ac.uk/users/pes20/actioncalculi.html If you are interested in the research position, please contact Philippa Gardner at Philippa.Gardner@cl.cam.ac.uk. It would be helpful if you would enclose a CV and brief research summary. Robin Milner Philippa Gardner Peter Sewell From cat-dist Thu Jul 3 18:28:14 1997 Received: by mailserv.mta.ca; id AA10197; Thu, 3 Jul 1997 18:27:19 -0300 Date: Thu, 3 Jul 1997 18:27:19 -0300 (ADT) From: categories To: categories Subject: WoLLIC'97 - Call for Participation Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: O X-Status: Date: Thu, 3 Jul 1997 09:34:23 -0300 From: ruy@di.ufpe.br 4th Workshop on Logic, Language, Information and Computation (WoLLIC'97) August 19-22 Fortaleza (Ceara'), Brazil Re: Selected submissions and Call for Participation Enclosed is the list of papers selected (ordered alphabetically by first author's surname) for presentation at the 4th Workshop on Logic, Language, Information and Computation (WoLLIC'97), to be held between the 19th (Tutorial Day) and the 22nd of August 1997 in Fortaleza (Ceara'), Brazil. The list of selected abstracts is also available from the web page (http://www.di.ufpe.br/~wollic97). There you can also find the registration form, and general information about travel to Fortaleza, as well as the address of places to stay. Please pre-register as soon as you can. You do not need to send any money at this stage. You can pay the registration fee at the reception's desk. With congratulations to the authors of accepted papers, we look forward to welcoming you all in Fortaleza. Best wishes, Yours sincerely, Ruy de Queiroz (On behalf of the 4th WoLLIC'97 Organising Committee) ------------------------------------------------------------------------------- Abstracts Selected (Alphabetical order by first author's surname.) An Analysis for Spanish Comparatives in Categorial Grammar P. Accuosto and D. Wonsever Instituto de Computacion, Universidad de la Republica, URUGUAY Formalization of Knowledge and Belief based on Kleene's Strong Logic M. Alvarado LSI, Technical University of Catalonia, SPAIN and G. Nunez Center of Computational Research, National Technical Institute (IPN), MEXICO Classical Negation can be Expressed by one of its Half J.-Y. Beziau Laboratorio Nacional de Computacao Cientifica (LNCC), BRAZIL A Modal Framework with Dependence for Reasoning About Actions M. A. Castilho, O. Gasquet and A. Herzig Institut de Recherches en Informatique Teorique (IRIT), Universite Paul Sabatier, FRANCE Fuzzy Logic: An Extension Problem J. C. Cifuentes Departamento de Matematica, Universidade Federal do Parana (UFPR), BRAZIL Distributed Semantics via Causal Transition Systems R. J. Coelho da Costa Departamento de Informatica e Estatistica, Univ. Federal de Santa Catarina (UFSC), BRAZIL A Little Note about the Rott Contraction E. L. Ferme and R. Rodriguez Universidad de Buenos Aires, ARGENTINA Modelling Parameterisation in Concurrent Object Systems J. K. Filipe Informatik, Technische Universitaet Braunschweig, GERMANY Complex Combinators and Structural Equations M. Finger Departamento de Ciencia da Computacao, Universidade de Sao Paulo (USP), BRAZIL Modularity and Consequence Relation R. P. de Freitas Laboratorio de Metodos Formais, Pontificia Univ. Catolica do Rio de Janeiro, BRAZIL and S. R. M. Veloso COPPE/ Instituto de Matematica, Universidade Federal do Rio de Janeiro, BRAZIL Proof Search and Proof nets Construction in Linear Logic D. Galmiche CRIN-CNRS & UHP Nancy 1, FRANCE and B. Martin Ecole Nationale Superieure de Lyon, FRANCE Eliminating Commuting Conversions and Constructive Necessity N. Ghani, V. de Paiva and E. Ritter School of Computer Science, University of Birmingham, UNITED KINGDOM On the Expressive Power of the Lambek Calculus Extended with a Structural Modality Ph. de Groote INRIA-Lorraine - CRIN - CNRS, FRANCE Decision Trees, Compression, and Boolean Lattices C. Hammond and R. Levinson Boards of Studies in Computer Engineering & Computer and Information Sciences, University of California at Santa Cruz, USA On the Difference between Arbitration and Majority Merging S. Konieczny and R. Pino Perez Laboratoire d'Informatique Fondamentale de Lille, Universite de Lille 1, FRANCE True Concurrency Model for Read/Write Access Systems M. Korff Nutec Informatica, BRAZIL and L. Ribeiro Instituto de Informatica, Universidade Federal do Rio Grande do Sul (UFRGS), BRAZIL Pure Type Systems with Definitions and Parameters T. Laan, P. Severi and J. Zwanenburg Eindhoven University of Technology, THE NETHERLANDS Distinguished Sets in Theories Without Foundation M. V. Marshall and M. G. Schwarze Departamento de Matematicas, Pontificia Universidad Catolica, CHILE A Nonmonotonic Analytic Consequence Relation C. A. Oller Departamento de Filosofia, Universidad de Buenos Aires, ARGENTINA Rewriting of Types and Diagonalization in the Oyster-Clam System J. Pellegrini and J. Wainer Instituto de Computacao, Universidade Estadual de Campinas (UNICAMP), BRAZIL Labelled Proof Nets for the Syntax and the Semantics of Natural Languages G. Perrier CRIN-CNRS & INRIA Lorraine, FRANCE Jumping to Explanations vs Jumping to Conclusions R. Pino Perez LIFL, Universite de Lille I, FRANCE and C. Uzcategui Departamento de Matematicas, Universidad de Los Andes, VENEZUELA On Program Correctness over Finite Data Types A. Prokhorov FB 17 Mathematik-Informatik, Universitaet-GH Paderborn, GERMANY Recognizing Classes of Logic Programs F. Protti and G. Zaverucha COPPE/Sistemas, Universidade Federal do Rio de Janeiro (UFRJ), BRAZIL An Answer to the Hidden Function Question for Algebraic Specification Methods A. Schoenegge Institut fuer Logik, Komplexitaet und Deduktionssysteme, Universitaet Karlsruhe, GERMANY Schematic Systems J. P. Viana Departamento de Analise, Inst. de Matematica, Univ. Federal Fluminense (UFF), BRAZIL and S. R. M. Veloso and P. A. S. Veloso Instituto de Matematica, Universidade Federal do Rio de Janeiro (UFRJ), BRAZIL Towards Efficient Verification of Time Petri Nets I. B. Virbitskaite and E. Pokozy Institute of Informatics Systems, Siberian Division of the Russian Academy of Sciences, RUSSIA Investigating Equivalence Notions for Time Petri Nets I. B. Virbitskaite and I. V. Tarasyuk Institute of Informatics Systems, Siberian Division of the Russian Academy of Sciences, RUSSIA Temporal Logics for Concurrent Nondeterministic Processes I. B. Virbitskaite and A. Votintseva Institute of Informatics Systems, Siberian Division of the Russian Academy of Sciences, RUSSIA Generalized Lambda-Calculi H. Xi Department of Mathematical Sciences, Carnegie Mellon University, USA ------------------------------------------------------------------------------- From cat-dist Thu Jul 3 22:13:20 1997 Received: by mailserv.mta.ca; id AA16333; Thu, 3 Jul 1997 22:12:50 -0300 Date: Thu, 3 Jul 1997 22:12:50 -0300 (ADT) From: categories To: categories Subject: announcement Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: O X-Status: Date: Thu, 3 Jul 1997 20:52:47 -0400 (EDT) From: Michael Makkai The following paper is announced: On weak higher dimensional categories by Claudio Hermida, Michael Makkai and John Power Abstract: Inspired by the concept of opetopic set introduced in a recent paper by John C. Baez and James Dolan, we give a modified notion called multitopic set. The name reflects the fact that, whereas the Baez/Dolan concept is based on operads, the one in this paper is based on multicategories. The concept of multicategory used here is a mild generalization of the same-named notion introduced by Joachim Lambek in 1969. Opetopic sets and multitopic sets are both intended as vehicles for concepts of weak higher dimensional category. Baez and Dolan define weak n-categories as (n+1)-dimensional opetopic sets satisfying certain properties. The version intended here, multitopic n-category, is similarly related to multitopic sets. Multitopic n-categories are not described in the present paper; they are to follow in a sequel. The present paper gives complete details of the definitions and basic properties of the concepts involved in multitopic sets. The category of multitopes, analogs of opetopes of Baez and Dolan, is presented in full, and it is shown that the category of multitopic sets is equivalent to the category of set-valued functors on the category of multitopes. The paper is available by anonymous ftp from triples.math.mcgill.ca in directory pub/makkai, or via the CRTC home page ftp://triples.math.mcgill.ca/crtc.html and click on "Makkai". The paper is in nine files, each with a name starting with `mult`; they are PostScript files. I will send a limited number of hard copies upon request. Michael Makkai From cat-dist Tue Jul 8 14:18:38 1997 Received: by mailserv.mta.ca; id AA31953; Tue, 8 Jul 1997 14:17:44 -0300 Date: Tue, 8 Jul 1997 14:17:44 -0300 (ADT) From: categories To: categories Subject: addendum to announcement Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: O X-Status: Date: Mon, 7 Jul 1997 18:03:49 -0400 (EDT) From: Michael Makkai A couple of days ago I announced the paper "On weak higher dimensional categories" by C. Hermida, M. Makkai and J. Power. Now, I am announcing some small changes of the arrangements concerning the electronic access to the paper. The paper is available by anonymous ftp from triples.math.mcgill.ca in the directory pub/makkai/multitopicsets [so, the change is that now the paper is put into a subdirectory of pub/makkai]. There are ten files [there were nine before; I have cut the largest into two]. M. Makkai From cat-dist Tue Jul 8 14:19:09 1997 Received: by mailserv.mta.ca; id AA00283; Tue, 8 Jul 1997 14:19:04 -0300 Date: Tue, 8 Jul 1997 14:19:04 -0300 (ADT) From: categories To: categories Subject: Re: actions of groupes on categories Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: O X-Status: Date: Tue, 8 Jul 1997 15:18:11 +1100 From: Ross Street Dear Jim I don't see the big deal about not having a unit in the monoid when looking at (pseudo-)actions; throw one in - we know how it should act. If you agree to this then what you are looking at is a pseudofunctor (or homomorphism of bicategories) R : M --> Cat where M is the monoid regarded as a one-object category. Indeed, M can be any category. There is an equivalence between the 2-category Hom(M,Cat) of homomorphisms from M to Cat and the 2-category Fib/M of opfibrations over M. The study of fibrations has gone off in many directions: for example, it provides the appropriate way of dealing with categories of all sizes (not just small) when working in a topos. As to higher homotopies, Cat doesn't really have enough dimensions for them. But there are trihomomorphisms M --> Bicat. More generally, there will be higher homomorphisms M --> WOC where WOC is the weak omega-category of weak omega-categories - someday - for now we have several fairly good definitions of the objects and arrows of WOC but that's as far as it goes. Higher fibrations is another interesting topic: Claudio Hermida knows about the 2-category case which is relevant to braids since 2-opfibrations over a 2-category M correspond to homomorphisms M --> 2-Cat where 2-Cat is self-enriched via the internal hom for the Gray tensor product of 2-categories (and it is in proving the coherence for this tensor product where braid groups first seriously entered category theory). Also, consider any braided monoidal bicategory B and let t be the n-th tensor power of some object of B. Then there is an action of the kind you describe of the n-string braid group on the hom-category B(t,t). But this is part of a longer story. Some References: John Gray, "Fibred and cofibred categories" Proc Conf Cat Alg, La Jolla 1965 (Springer 1966) [See references to Grothendieck's work in the Gray paper] John Gray, Formal Category Theory SLNM 391 (1974) John Gray, Coherence for the tensor product of 2-categories, and braid groups "Algebra, Topology, and Category Theory" (Academic Press 1976) 63-76 Jean Benabou, Introduction to bicategories SLNM 47 (1967) Jean Benabou, Fibrations petites et localement petites CR Acad Sci Paris A 281 (1975) 897-900 Benabou-Roubaud, Monades et descente CR Acad Sc Paris 270 (1970) 96-98 Gordon-Power-Street, Coherence for tricategories, Memoirs AMS #558 (Sept 1995) Day-Street, Monoidal bicategories and Hopf algebroids, Advances in Math (to appear; galley proofs returned) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Ross Street email: street@mpce.mq.edu.au Mathematics Department phone: +612 9850 8921 Macquarie University fax: +612 9850 8114 Sydney, NSW 2109 Australia Internet: http://www.mpce.mq.edu.au/~street/ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ From cat-dist Tue Jul 8 14:19:25 1997 Received: by mailserv.mta.ca; id AA25102; Tue, 8 Jul 1997 14:19:24 -0300 Date: Tue, 8 Jul 1997 14:19:24 -0300 (ADT) From: categories To: categories Subject: announcement of preprint Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: O X-Status: Date: Tue, 8 Jul 1997 16:32:22 +0200 From: I. Moerdijk Dear colleagues, A ps-file of the following short preprint can be picked up from my homepage (http://www.math.ruu.nl/people/moerdijk) I Moerdijk, J. Vermeulen, Proof of a conjecture of A. Pitts. Abstract: Using only elementary properties of inverse limits and localization, we prove the Beck-Chevalley condition for lax pullbacks of coherent toposes. In this way, we obtain a simple and constructive proof of the descent theorem for coherent (pre)toposes. With best regards, Ieke Moerdijk. From cat-dist Tue Jul 8 14:21:01 1997 Received: by mailserv.mta.ca; id AA29688; Tue, 8 Jul 1997 14:21:00 -0300 Date: Tue, 8 Jul 1997 14:21:00 -0300 (ADT) From: categories To: categories Subject: Signed associahedra Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: O X-Status: Date: Tue, 8 Jul 1997 12:47:46 -0400 (EDT) From: James Stasheff Reiner and Burgiel's recent paper provoked the questions at the beginning and end of the following: ************************************************************ 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 ---------- Forwarded message ---------- Date: Tue, 8 Jul 1997 11:33:31 -0500 (CDT) From: Victor Reiner To: jds@math.upenn.edu Cc: burgiel@math.uic.edu Subject: Signed associahedra Dear Jim, > Only thing more I could ask is to have the tree descrition > in addition to the triangulation description of the cells. I think we can oblige. A signed dissection of the (n+2)-gon corresponds to a plane tree T having n+1 leaves in which one assigns +,-, or 0 to every "nook" between two branches of the tree (think of the +,-,0's as being like lint trapped between ones toes!). For example, a vertex having 5 children in the tree will have 4 nooks between its branches, and hence require 4 choices of +,-,0. Furthermore, whenever any of the nooks below some vertex are assigned 0, all of the nooks below that vertex must be assigned 0. Then a signed dissection of the first kind (which indexes the cells in the simple signed associahedron) requires that only the root vertex can have its nooks assigned 0. And a signed dissection of the second kind (which indexes the cells in the non-simple signed associahedron) requires that only the vertices whose children are all leaves can have their nooks assigned 0. The partial order, roughly speaking, translates into contracting non-leaf edges in the tree and comparing the +,-,0 assignments in the nooks. Do you know of any category/homotopy theoretic applications for either of these signed associahedra? Best wishes, Vic Reiner From cat-dist Tue Jul 8 20:15:33 1997 Received: by mailserv.mta.ca; id AA07627; Tue, 8 Jul 1997 20:15:10 -0300 Date: Tue, 8 Jul 1997 20:15:10 -0300 (ADT) From: categories To: categories Subject: 2nd CFP - Computing: The Australiasian Theory Symposium (CATS98) Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: O X-Status: Date: Fri, 27 Jun 1997 16:20:09 +0800 From: lxue@cs.uwa.edu.au CALL FOR PAPERS CATS'98 - Computing: The Australasian Theory Symposium University of Western Australia Perth, Western Australia 2-3 February, 1998 CATS'98 will be held at the University of Western Australia as part of the Australasian Computer Science Week (ACSW98) which also includes: . the Australasian Computer Science Conference (ACSC'98) . the Australasian Database Conference (ADC'98) . the Australasian Computer Architecture Conference (ACAC'98) Following on from CATS'94 in Sydney, CATS'96 in Melbourne, and CATS'97 in Sydney, CATS'98 aims at providing a forum for researchers in theoretical computer science. Typical, but not exclusive, topics of interest include: - Algorithms and data structure - Category theory - Complexity - Computational algebra, biology, geometry, logic, and number theory - Concurrency - Distributed and parallel computing - Formal semantics, specification, synthesis, and verification Original research papers are solicited. Submissions to CATS'98 this year will be again conducted electronically, and should be sent in standard Postscript format to cats98@cs.uwa.edu.au by the submission deadline. Authors unable to access e-mail may send 4 hard copies of their papers to the program committee chair: Xuemin Lin -- CATS'98 Department of Computer Science University of Western Australia Crawley, Western Australia 6907 Australia E-mail: cats98@cs.uwa.edu.au http://www.cs.uwa.edu.au:80/~lxue/CATS98/index.html In both cases, confirmation of receipt will be given, in the case of a postscript submission, once the file has been successfully printed. Submissions should include an abstract, 3-6 key words, and the fax number and e-mail address of the corresponding author. The contribution of the paper should be clearly explained in both general and technical terms, and authors should make every effort to ensure the technical content of their papers is understandable by a broad audience. The paper (an extended abstract or full paper) should not exceed 15 A4 pages using 11 point or larger font. Submission of a paper should be regarded as an undertaking that, should the paper be accepted, at least one of the authors will attend the conference to present the work. Papers will be judged on originality, significance, correctness, and clarity. Accepted papers will be published in the proceedings of the Symposium, which will appear in the DMTCS series of Springer-Verlag. ========================================= INVITED SPEAKERS: Ming Li (University of Waterloo, Canada) Takeshi Tokuyama (IBM, Japan) ========================================= IMPORTANT DATES: Submission Deadline: Friday 15 August 1997. This is a hard deadline; submissions postmarked after this date will be returned. Author Notification: Friday 24 October 1997. Final Version: Friday 14 November 1997. Acceptance of papers for the conference will be conditional upon the registration of at least one of the authors by 21 November 1997. ========================================= GENERAL CHAIR: James Harland RMIT PROGRAM COMMITTEE CHAIR: Xuemin Lin UWA LOCAL CHAIR: Chi-Ping Tsang UWA STEERING COMMITTEE: John Crossley Monash University Peter Eades University of Newcastle James Harland RMIT Michael Johnson Macquarie University John Staples University of Queensland Harald Sondergaard University of Melbourne PROGRAM COMITTEE: Cristian Calude University of Auckland Hossam Elgindy University of Newcastle Matthew Hennessy University of Sussex Xuemin Lin University of Western Australia Bruce Maggs Carnegie-Mellon University Martin Odersky University of South Australia Hong Shen Griffith University Harald Sondergaard University of Melbourne Antonios Symvonis University of Sydney Tadao Takaoka University of Canterbury Ron van der Meyden University of Technology, Sydney Lusheng Wang City University of Hong Kong Sue Whitesides McGill University David Wolfram Australian National University ===================================== ADDRESS FOR ALL PAPER SUBMISSION CORRESPONDENCE Xuemin Lin -- CATS'98 Department of Computer Science University of Western Australia Crawley, Western Australia 6907 Australia Telephone: +61 9 380 3449 Facsimile: +61 9 380 1089 E-mail: cats98@cs.uwa.edu.au ===================================== ADDRESS FOR CORRESPONDENCE, OTHER THAN PAPER SUBMISSION, RELATED TO ANY CONFERENCE FORMING PART OF THE AUSTRALIAN COMPUTER SCIENCE WEEK ACSW'98 Information Department of Computer Science The University of Western Australia Crawley, Western Australia, 6907 Telephone: +61 9 380 2533 Email: acsw98info@cs.uwa.edu.au ORGANISING COMMITTEE CHAIR Chris McDonald Department of Computer Science The University of Western Australia Crawley, Western Australia, 6907 Email: chris@cs.uwa.edu.au ACSW'98 Hosts: Department of Computer Science, The University of Western Australia Department of Computer Science, Curtin University of Technology Department of Computer Science, Edith Cowan University Computer Science Programme, Murdoch University From cat-dist Tue Jul 8 20:17:01 1997 Received: by mailserv.mta.ca; id AA11437; Tue, 8 Jul 1997 20:17:01 -0300 Date: Tue, 8 Jul 1997 20:17:01 -0300 (ADT) From: categories To: categories Subject: Research positions in formal methods at Kestrel Institute Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: O X-Status: Date: Tue, 8 Jul 1997 11:46:19 -0700 From: careers@kestrel.edu [apologies for multiple copies] ------------------------------------------------- Career Opportunities at Kestrel Institute in Palo Alto, California (http://www.kestrel.edu) ------------------------------------------------- Kestrel has openings and is hiring and interviewing now. We have several openings in R&D for senior researchers as well as recent graduates. About Kestrel Technology ------------------------ Kestrel's focus is on advancing the state-of-the-art in software development. We are interested in highly automated design methods that emphasize correctness, performance, scalability, productivity, ease of use, and security. These capabilities arise from the articulation and incorporation of precise software design knowledge and principles. Areas of Interest ------------------- Toward the goal of advancing the state-of-the-art in software development, Kestrel is interested in formal and mechanized support for: * Specification of software systems * Refinement / transformation of specifications * Design evolution * Code generation We are interested in a variety of technologies as they apply to the development of the next generation of software development environments: * Algebraic specification * Algorithm design, software generators * Analysis techniques and slicing for programs and specifications * Category theory, mathematical logic * Constraint solving * Datatype refinement * Formal methods * Inference - First-order - Higher-order - Rewriting - Decision procedures * Program synthesis and optimization techniques * Program transformation * Refinement to high-performance parallel and sequential architectures * Semantics and type theory * Software architectures * User interface design * Visualization Recent projects --------------- Kestrel's recent projects include (among others): * Development of the theory and tools for the design and automated synthesis of high performance scheduling and planning algorithms for transportation, logistics, power plant maintenance, and manufacturing; * Synthesis of very fast parallel algorithms; * High performance knowledge bases; * Security of network software; * Synthesis of data base integration software; * Methods for evolving software and managing software changes and impact; * Improving software analysis and testing using automated reasoning engines; * On-the-fly software visualization; * Specification, synthesis, verification and simulation of reactive systems; Qualifications -------------- We are now hiring for several positions, and need people with backgrounds ranging from Experienced Researchers to Recent Graduates. We are interested in project staff as well as potential project leaders. We look for some (but not necessarily all) of these capabilities: 1. Researchers - Ph.D. Level * Experience in program synthesis or related fields * Broad knowledge of formal methods and/or Knowledge-based methods * Deep knowledge of one or more formal methods areas * Excellent implementation skills * Excellent verbal communication and writing skills * Ability to perform original research and publish * Interest in developing working applications for end-users * Experience with automated proof systems * Ability to lead and manage projects * Skills in documentation and teaching 2. Researchers and Implementors at the MS Level * MS in Computer Science or equivalent (exceptional BS graduates will be considered) * Strong implementation and software engineering skills * Ability to work with applications of advanced mathematical concepts to software engineering * Documentation, support, training skills 3. Application Developers Our Application Developers may also be researchers and implementors who have interest in developing working applications based on our technologies. Activities include documentation, support, contact with customers, and training. Our current applications include synthesis of very fast scheduling algorithms, parallel algorithms, secure software, very large knowledge bases, and several others. The Best Of The Research And Commercial Worlds From Theory to Practical Applications ---------------------------------------------- Kestrel provides opportunities for involvement in technology transition, including equity interest in startup companies. For example, Kestrel licensed technology to Reasoning Inc, a company active in Reengineering and Year 2000 Solutions. (See http://www.reasoning.com) Kestrel is funded through government grants, as well as contracts with private companies. In order to prove the feasibility of our ideas, and to transfer our theories to the real world, our research often involves implementing working prototype systems and tranferring these prototypes to commercial enterprises for development of products. Kestrel Institute itself is an independent, non-profit research institute, but is also affiliated with Kestrel Development Corporation, a for-profit corporation. Kestrel also licenses software to other commercial enterprises. Inquiries and Job Applications ------------------------------ Please send a resume or curriculum vitae, a statement of research interests, a description of previous work, or questions (in any combination). You may send these in ASCII, MS Word, or Postscript. We are also interested in recent papers. When sending email, we prefer you to send pointers to papers (citations or URLs) rather than the papers themselves. If you do not yet have all of your materials assembled, we would appreciate receiving what you do have (the URL for your web page, for example). We strive to find world-class people and welcome qualified applicants from outside the US. Good English language skills are required. Send email to: careers@kestrel.edu or regular mail to Careers Kestrel Institute 3260 Hillview Ave Palo Alto, CA 94304 U.S.A. or fax to (in USA) 415-424-1807 More information about Kestrel, and recent papers, can be found at http://www.kestrel.edu or by calling (in USA) 415-493-6871 (ask for Carol Lei). From cat-dist Wed Jul 9 10:20:09 1997 Received: by mailserv.mta.ca; id AA29001; Wed, 9 Jul 1997 10:19:34 -0300 Date: Wed, 9 Jul 1997 10:19:34 -0300 (ADT) From: categories To: categories Subject: CT97 PROGRAM Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: O X-Status: Date: Tue, 8 Jul 97 16:59:35 -0700 From: John MacDonald INTERNATIONAL CATEGORY THEORY MEETING (CT97) July 13-19, 1997 University of British Columbia Vancouver, Canada The conference arrival day is Sunday July 13 with a reception 6-9pm in the Fireplace Lounge of Walter Gage Towers on the UBC campus. The scientific program will begin Monday morning July 14 at 9am in Angus 104 and will finish on Saturday July 19 at the end of the morning session (12:30pm). =========================================================================== CT97 Conference Program =========================================================================== SUNDAY, JULY 13 18:00-21:00 Wine and Cheese Reception and Registration Fireplace Lounge, Walter Gage Towers University of British Columbia Campus MONDAY, JULY 14 09:00-09:10 Welcome 09:10-10:00 Saunders Mac Lane The Scope of Category Theory 10:00-10:30 Break 10:30-11:00 Michael Barr Some questions--and some answers--on *-autonomous categories 11:10-11:40 Heinrich Kleisli The chu *-algebra of a group 11:50-12:30 Susan Niefield A Skeletal Topos of Finite Sets: Implementing Finite Structures in Mathematica 12:30-14:00 Lunch 14:00-14:30 Robert Dawson When can a double diagram be composed? 14:40-15:10 John MacDonald Distributivities and Liftings 15:20-16:00 Art Stone Soft adjunctions: stacking cubes, co-existence 16:00-16:30 Break 16:30-16:55 Michel Hebert Syntactic characterization of locally finitely generated categories 17:00-17:25 Ron Ferguson Pullbacks and the unit group of ZCn 17:30-18:00 Fred Linton Cones, convexity, star-shapedness, contractibility and Cone-algebras TUESDAY, JULY 15 09:00-10:00 Ross Street Developments in Higher Category Theory 10:00-10:30 Break 10:30-11:00 Jiri Velebil Categories as domains 11:10-11:40 Marco Grandis Weak subobjects and weak limits in categories and homotopy categories 11:50-12:30 Peter Johnstone Which first-order theories have classifying toposes? 12:30-14:00 Lunch 14:00-14:30 Claudio Hermida Spans, multicategories and operads 14:40-15:10 Renato Betti Cauchy generators of functor categories 15:20-16:00 Michael Johnson Higher homotopies and higher category theory 16:00-16:30 Break 16:30-16:55 Anneliese Schauerte Separation properties in the category of biframes 17:00-17:25 David Benson Martin L"of Type Theories with Family Structure have Diers categories as Duals 17:30-18:00 Steve Lack On the monadicity of finite monads WEDNESDAY, JULY 16 09:00-10:00 F.W. Lawvere "Geneology and Kinship" an application of topos theory 10:00-10:30 Break 10:30-11:00 G. Rosolini Some general constructions of models of the lambda-calculus 11:10-11:40 R.A.G. Seely Linearly distributive functors and nuclearity for linearly distributive categories 11:50-12:30 Vaughan Pratt Is linear logic complete for dinaturality in Chu? 14:30 City Tour of Vancouver followed by Dinner Cruise on Harbour Ferries Meet outside Gage Towers just before 2:30PM for bus pickup THURSDAY, JULY 17 09:00-10:00 Peter Freyd Paracategories 10:00-10:30 Break 10:30-11:00 Dominique Bourn n-groupoids from n-truncated simplicial objects 11:10-11:40 Jim Otto Unifying lambda-terms using bicategories of resolutions 11:45-12:45 Max Kelly On the monadicity over graphs of categories with limits 12:45-14:00 Lunch 14:00-14:30 J"urgen Koslowski Beyond the Chu-Construction 14:40-15:10 Paul Taylor An Abstract Stone Duality 15:20-16:00 Jiri Rosicky Enriched accessible categories 16:00-16:30 Break 16:30-16:55 Ali Madanshekaf On the category of Heyting hyperalgebras 17:00-17:25 Hiroyuki Miyoshi A combinatorial definition of Baez-Dolan omega category 17:30-18:00 Till Plewe Weakly connected maps of locales FRIDAY, JULY 18 09:00-09:25 Sandro Fusco Stable Functors and the Grothendieck Construction 09:30-10:00 Jorge Picado A theorem of Eframovi in pointfree context 10:00-10:30 Break 10:30-11:00 Jonathon Funk Bifibrations and KZ-doctrines 11:10-11:40 C. Leopoldo Roman On quantic nuclei and conuclei for orthomodular lattices 11:50-12:30 Cristina Pedicchio Exactness and regularity for locally presentable categories 12:30-14:00 Lunch 14:00-14:30 Walter Tholen Separated and dissonant morphisms 14:40-15:10 Anders Kock A deRham chain complex in Synthetic Differential Geometry 15:20-16:00 Hongde Hu Coherence completions and free bicompletions of categories 16:00-16:30 Break 16:30-16:55 Lourdes Sousa On the existence and construction of solid hulls 17:00-17:25 Dorette Pronk The fundamental group of a triangulated orbifold 17:30-18:00 Joanne Walters-Wayland Regular Lindelof frames - Rings of continuous functions 19:30 Banquet in Ruth Blair Lounge, Gage Towers SATURDAY, JULY 19 09:00-10:00 Bob Pare' Further developments on double limits 10:00-10:30 Break 10:30-11:00 Bob Rosebrugh Entity-relationship models and sketches 11:10-11:40 Robin Cockett Feedback in (=traced) linearly distributive categories 11:50-12:30 R. J. Wood Groupoidal completely distributive lattices From cat-dist Wed Jul 9 10:20:38 1997 Received: by mailserv.mta.ca; id AA25983; Wed, 9 Jul 1997 10:20:37 -0300 Date: Wed, 9 Jul 1997 10:20:37 -0300 (ADT) From: categories To: categories Subject: Re: actions of groupes on categories Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: O X-Status: Date: Wed, 9 Jul 1997 12:11:32 +1000 From: Michael Batanin An addition to Ross Street's answer. Wilst the notion of weak \omega-functor is not yet worked out adequately the corresponding topological theory of A_{\infty} and E_{\infty} maps between A_{\infty} and E_{\infty}-spaces has been constructed by Boardman,Vogt, May, Segal and others. The theory of natural transformations up to ALL higher homotopies between simplicial functors has been developed by Dawer,Kan, Cordier, Porter, Bourn, Batanin, Heller and others. Simplicial A_{\infty}-categories and A_{\infty}-functors were defined and studied by Batanin and topological version of it by Schwanzl and Vogt (they call them \Delta-categories and use the idea related to the Segal delooping mashine.) Some (not all) references: 1. Batanin M.A., Coherent categories with respect to monads and coherent prohomotopy theory, Cahiers Topologie et Geom. Diff., vol.XXXIV-4, pp.279-304, 1993. 2. Batanin M.A., Homotopy coherent category theory and A_{\infty}-structures in monoidal categories, to appear, dvi file available at http://www-math.mpce.mq.edu.au/~mbatanin/papers.html 3. Boardman J.M., R.M.Vogt, Homotopy Invariant Algebraic Structures on Topological Spaces, Lecture Notes in Math., vol. 347, Springer-Verlag, Berlin, Heidelberg, New York, 1973. 4. Cordier J.-M., Porter T., Vogt's Theorem on categories of homotopy coherent diagrams, Math. Proc. Cambridge Phil. Soc., vol. 100, pp 65-90, 1986. 5. Cordier J.-M., Porter T., Maps between homotopy coherent diagrams, Topology and its Appl., 28, pp.255-275, 1988. 6. Cordier J.-M., Porter T., Homotopy coherent category theory, to appear in Transactions of the AMS, 7. Dwyer W.G., Kan D.M., Realizing diagrams in the homotopy category by means of diagrams of simplicial sets, Proc. Amer. Math. Soc., 91, pp.456-460, 1984. 8.Heller A., Homotopy in Functor Categories, Transactions AMS., v.272, pp.185-202, 1982. 10. Schw\"{a}nzl R., Vogt R., Homotopy homomorphisms and the Hammock localization, Boletin de la Soc. Mat. Mexicana, 37, 1-2, pp.431-449, 1992. From cat-dist Wed Jul 9 10:22:20 1997 Received: by mailserv.mta.ca; id AA22245; Wed, 9 Jul 1997 10:22:19 -0300 Date: Wed, 9 Jul 1997 10:22:18 -0300 (ADT) From: categories To: categories Subject: Re: actions of groupes on categories Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-Status: Date: Wed, 9 Jul 1997 08:14:31 -0400 (EDT) From: James Stasheff the Deligne paper Action du groupe des tresses... Inv math 128 (1997)159-175 ************************************************************ 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 Jul 10 10:21:18 1997 Received: by mailserv.mta.ca; id AA03037; Thu, 10 Jul 1997 10:21:08 -0300 Date: Thu, 10 Jul 1997 10:21:08 -0300 (ADT) From: categories To: categories Subject: Re: CT97 PROGRAM Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-Status: Date: Wed, 9 Jul 1997 11:10:28 -0400 (EDT) From: James Stasheff hopefully many of these talks will lead to papers not only announced here but also posted to q-alg ************************************************************ 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 Jul 10 10:21:20 1997 Received: by mailserv.mta.ca; id AA01921; Thu, 10 Jul 1997 10:20:03 -0300 Date: Thu, 10 Jul 1997 10:20:03 -0300 (ADT) From: categories To: categories Subject: Re: actions of groupes on categories Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-Status: Date: Wed, 9 Jul 1997 11:05:02 -0400 (EDT) From: James Stasheff for A_\infty cats and/or fucntors see also Fukawa where the applicaitons are to Floer cohomology if I recall and thence to physics! ************************************************************ 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 Jul 10 10:23:54 1997 Received: by mailserv.mta.ca; id AA04641; Thu, 10 Jul 1997 10:23:53 -0300 Date: Thu, 10 Jul 1997 10:23:53 -0300 (ADT) From: categories To: categories Subject: un peu de r'eclame Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: O X-Status: Date: Wed, 9 Jul 1997 18:01:19 +0200 From: Pierre Ageron Let me advertise for some more or less recent work of mine about sketches/accessible categories (not available electronically, but I'll be happy to send reprints or preprints on request). ------- (1) Cat'egories accessibles `a limites projectives non vides et cat'egories accessibles `a limites projectives finies Diagrammes 34 (1995) 1-10 For fixed b, b-accessible categories with non-empty limits are characterized as the categories of models of specific sketches. As a corollary, the category of these categories is Cartesian closed. (Proved independantly by Ad'amek.) Accessible categories with finite limits are also characterized. ------- (2) Effective taxonomies and crossed taxonomies Cahiers de Top. et de G'eom. Diff. Cat. XXXVII (1996) 82-90 A taxonomy is a "category without identities". This bare structure is somewhat dull, but "crossed modules of taxonomies" seem more interesting. In the latter structure, "Dedekind-finite" objects play a role similar to that of finitely presentable objects in a category. A notion similar to that of accessibility can thus be defined. ------- (3) La tour holomorphe d'une esquisse Cahiers de Top. et de G'eom. Diff. Cat. XXXVII (1996) 295-314 A construction of Lair's in the category of sketches is revisited and noticed to specialize to the construction of the holomorph when restricted to groups. The iteration of this construction reveals two invariants of a sketch: an ordinal and a group. Some explicit computations are provided. ------- (4) Cat'egories accessibles `a produits fibr'es (preprint) Continuation of (1). Accessible categories with (finite) pullbacks are characterized in terms of sketches. This is achieved by introducing "free" colimits in Set: such colimits are proved to be exactly those that commute with pullbacks. ------- (5) Limites projectives conditionnelles dans les cat'egories accessibles (preprint) For fixed b, those b-accessible categories s.t. every diagram with a cone has a limit are characterized in terms of sketches. As a corollary, the category of these categories is Cartesian closed. Similarly for those b-accessible categories s.t. every non-empty diagram with a cone has a limit, or for those with "consistent wide pullbacks". ------- PIERRE AGERON 1) coordonnees bureau adresse : mathematiques, Universite de Caen, 14032 Caen Cedex telephone : 02 31 56 57 37 telecopie : 02 31 93 02 53 adresse electronique : ageron@math.unicaen.fr 2) coordonnees domicile adresse : 28 rue de Formigny 14000 Caen telephone : 02 31 84 39 67 From cat-dist Fri Jul 11 15:34:21 1997 Received: by mailserv.mta.ca; id AA03947; Fri, 11 Jul 1997 15:33:15 -0300 Date: Fri, 11 Jul 1997 15:33:15 -0300 (ADT) From: categories To: categories Subject: Re: What is q-alg ???????????????????? Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: O X-Status: Date: Fri, 11 Jul 1997 07:59:27 -0400 (EDT) From: James Stasheff Some of you have asked: what is q-alg? q-alg@eprints.math.duke.edu is a fully automated electronic archive and distribution server for papers on QUANTUM ALGEBRA AND TOPOLOGY (INCLUDING KNOT THEORY) (starting from Dec, 1994) This is an eprint archive for mathematics papers on ``quantum algebraic'' topics such as quantum groups (also known as noncommutative Hopf algebras) and related constructions, representations of affine Lie algebras, vertex operator algebras and operads, algebraic aspects of the KP and Toda lattice hierarchies, etc. (JDS: although not listed explicitly, category theroy, especially higher dim cats, is certainly appropriately posted to this server) For the time being, the archive also welcomes submissions of mathematics papers on modern knot theory (Jones and HOMFLY polynomials, Reshetikin-Turaev invariants, etc.). A separate archive will be formed for knot theory when the traffic becomes sufficient to warrant it. Papers submitted to this archive should be intended for an audience of mathematicians; we also welcome cross-listings of appropriate papers from physics or other fields which are archived elsewhere. Other mathematics archives running the same software: o alg-geom@eprints.math.duke.edu Algebraic Geometry o auto-fms@msri.org Automorphic Forms o cd-hg@msri.org Complex Dynamics and Hyperbolic Geometry o dg-ga@msri.org Differential Geometry and Global Analysis o q-alg@eprints.math.duke.edu Quantum Algebra (including Knot Theory) For information about archives in other fields, consult http://xxx.lanl.gov/help/ ------------------------------------------------------------------------- ------------------------------------------------------------------------- In the generic xxx help text, substitute q-alg@eprints.math.duke.edu for the generic e-mail address arch-ive@xxx.lanl.gov ------------------------------------------------------------------------- ------------------------------------------------------------------------- Outgoing mail from the e-print archive has the username no-reply (to avoid problems due to occasional mail that bounces back). Commands to the system should always be sent to arch-ive@xxx.lanl.gov with the command in the subject field (e.g. Subject: help). Only one command at a time is accepted. Subscribers automatically receive a listing of new titles/abstracts on days papers are received. You will have a more pleasurable time using the archives if you read this file carefully, read ALL responses you get to your interactions with the archives, and follow the instructions therein. This help file summarizes the email interface commands. This information can be more easily accessed via the WorldWideWeb at http://xxx.lanl.gov/help/ . ************************************************************ 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 Jul 11 15:34:49 1997 Received: by mailserv.mta.ca; id AA19291; Fri, 11 Jul 1997 15:34:48 -0300 Date: Fri, 11 Jul 1997 15:34:48 -0300 (ADT) From: categories To: categories Subject: European School on Graph Transformation Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: O X-Status: Date: Fri, 11 Jul 1997 18:18:58 +0200 From: Frank Drewes ************************************************* * First Call for Participation * * European School on Graph Transformation * * * * Bremen (Germany) * * March 2-7, 1998 * ************************************************* [for a PostScript version of this call see http://www.informatik.uni-bremen.de/grp/ag-ti/getgrats] Aims and Scope Graph grammars originated in the late 60s, motivated by considerations about pattern recognition and compiler construction. Since then the list of areas which have interacted with the development of graph grammars has grown quite impressively. Besides the aforementioned areas it includes software specification and development, VLSI layout schemes, massively parallel computer architectures, database design, modeling of concurrent systems, logic programming, computer animation, developmental biology, music composition, visual languages, and many others. The area of graph grammars and graph transformation generalizes formal language theory based on strings and the theory of term rewriting based on trees. As a matter of fact within the area of graph grammars, graph transformation is considered a fundamental programming paradigm where computation includes specification, programming, and implementation. The main goal of the School is to disseminate ``the basic knowledge'' about the area of graph grammars and graph transformation and to present in a systematic way the state of the art and the recent advances in the theory and applications of graph transformation systems. The aim is to bring together students, young researchers and senior scientists interested in the area. The expected audience for the School consists of two groups: (i) participants from outside the area: these are the students and researchers who want to learn (for various reasons) about graph grammars and graph transformation, (ii) participants from inside the area: these are students and researchers that already have some knowledge of graph grammars, but they are interested to get a more systematic insight into the area. The objective of the School (especially as the first group is concerned) is to make the participants ``literate'' in the area of graph grammars and graph transformation. This means that, after the School, the participants will find it easier to follow basic literature, and to consider applications of graph grammars and graph transformations in their areas of interest. The program of the School covers main developments in both theory and applications of graph transformation. Certificates The School will issue certificates to acknowledge a successful participation. Organization The School is one of the main events organized by the TMR Research Network GETGRATS (General Theory of Graph Transformation Systems). Also, the ESPRIT Working Group APPLIGRAPH (Applications of Graph Transformation) participates in the organization of the school. Program Committee Michel Bauderon, Hartmut Ehrig, Dirk Janssens, Hans-Joerg Kreowski (Cochair), Ugo Montanari, Francesco Parisi-Presicce, Grzegorz Rozenberg (Chair) Organizing Committee Frank Drewes, Hans-Joerg Kreowski (Chair), Grzegorz Rozenberg Grants The organizers hope to be able to offer grants to cover (parts of) the costs for travel and subsistence. Information For more information please contact the organizers by email ({drewes,kreo}@informatik.uni-bremen.de). You can also look up the WWW homepage of the School. Just follow the respective link at http://www.informatik.uni-bremen.de/grp/ag-ti/getgrats. Registration To register for the School please return the form at the end before December 6, 1997. Pre-registrations (without obligation) are welcome at any time. The registration fee will be around DM 1200,- - DM 1300,-. This covers lodging (6-7 nights), full board, and the teaching material including the handbook. Scientific Programme The scientific programme consists of 4 parts: INTRODUCTORY LECTURE provides an informal panoramic sketch of the area. BASIC CORE covers basic approaches to defining graph transformations. Each of the following four approaches is covered by a strand of lectures. (1) node rewriting (2) (hyper)edge rewriting (3) logical descriptions (4) algebraic approaches LAYER 1 consists of lectures on various ways of defining graph transformations not covered in the Basic Core, as well as various specialistic topics from the 4 strands of the Basic Core. (1) term graph rewriting (2) foundations of the PROGRES approach (3) concurrency (4) coordination (5) 2-structures (6) pullback-approach (7) high-level approaches LAYER 2 consists of lectures covering various applications of graph transformation and topics strongly rooted in applications. (1) term graph rewriting in functional programming (2) the use of PROGRES in a software engineering environment (3) modularization (4) distributed algorithms (5) visual design of distributed systems (6) image generation (7) graph drawing The lectures will be given by leading experts in the field of graph grammars and graph transformation. Presentation of Tools In addition to the scientific programme various systems and tools (PROGRES, AGG, GRAPHED, CLEAN, COLLAGE-VR, etc.) will be presented. Teaching Material - copies of transparencies, relevant papers, and lecture notes - the Handbook on Graph Grammars and Computing by Graph Transformations, Volume 1: Foundations, World Scientific 1997 -------------------------- Registration form --------------------------- I would like to [ ] pre-register / [ ] register for the European School on Graph Transformation. Name: ____________________________________ Position: ____________________________________ Address: ____________________________________ ____________________________________ ____________________________________ ____________________________________ email and fax: ____________________________________ I need financial support: [ ] yes [ ] no (Please return this form to Prof. Dr. Hans-Joerg Kreowski, Universitaet Bremen Fachbereich 3 Postfach 330440 D-28334 Bremen (Germany) email: kreo@informatik.uni-bremen.de Fax: +49-421-218-4322) From cat-dist Fri Jul 11 15:42:51 1997 Received: by mailserv.mta.ca; id AA25150; Fri, 11 Jul 1997 15:42:51 -0300 Date: Fri, 11 Jul 1997 15:42:51 -0300 (ADT) From: categories To: categories Subject: Tuesday evening at CT97, future of publication Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: O X-Status: Date: Fri, 11 Jul 97 11:22:43 -0700 From: Art Stone The Tuesday evening of CT97, 15 July, we contemplate having an open discussion on the future of publication in category theory. Questions that are likely to come up: Are the paper publications really dying? (With diminishing library budgets, one Vancouver area university has been forced to cancel both Cahiers and JPAA, and with limited library space, no longer has available on its shelves journals more than 10 or 15 years old.) How do we provide for archiving in such a situation? What are the opinions of the current editors of our journals? We're fortunate to have TAC. Is there need for a wider range of styles of publication? What are the alternatives? Is CD-ROM a possibility? (Might it give us again the freedom we had in the early volumes of Springer's LNM -- or would that be a good thing?) Would it be better to have an e-archive, like q-alg? How? Where? Would it be secure, a lasting archive? What is to be learned from existing or past examples: Imperial College, Hypatia, triples.math.mcgill, the Sydney category seminar? Frequently papers appear which the authors subsequently wish they could change. And terminology changes over time -- as we begin to understand what it was we were trying to say. Might we want to have "papers" or "books" that can be modified over time (with ongoing version numbers as we have now for software)? For the most basic and important works, might we prefer something that approaches what Bourbaki intended to give us: works that would evolve over time and never to go out of date? (Bourbaki's vision preceded the development of media that would make it possible.) And how do we want to treat the proceedings of CT97? At first, papers should be available by ftp on math.ubc.ca, but what do we want in the long run? Art Stone From cat-dist Sat Jul 12 14:55:22 1997 Received: by mailserv.mta.ca; id AA23356; Sat, 12 Jul 1997 14:55:00 -0300 Date: Sat, 12 Jul 1997 14:55:00 -0300 (ADT) From: categories To: categories Subject: Re: functions Omega->Omega Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: O X-Status: Date: Fri, 11 Jul 1997 16:56:25 -0400 (EDT) From: Andre Scedrov > f(a) & a = f(true) & a > > I wonder whether anyone has noticed this formula before? Similar formulas and their analogs in intuitionistic second-order propositional calculus are discussed in my paper in the Annals Pure Appl. Logic 27 (1984) 155-164. That paper was motivated by Higgs's observation that every monic Omega -> Omega in a topos is an involution, see Peter Johnstone's paper "Automorphisms of Omega" in Alg. Universalis 9 (1979) 1-7. Andre Scedrov From cat-dist Sat Jul 12 14:56:54 1997 Received: by mailserv.mta.ca; id AA11141; Sat, 12 Jul 1997 14:56:54 -0300 Date: Sat, 12 Jul 1997 14:56:54 -0300 (ADT) From: categories To: categories Subject: Interesting item for categories Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: O X-Status: Date: Fri, 11 Jul 1997 18:41:36 -0400 From: Michael Barr I just got this from Adam. I think it might be interesting to post. Mike >From adamba@microsoft.com Fri Jul 11 14:09:13 1997 Received: from mail5.microsoft.com (mail5.microsoft.com [131.107.3.31]) by triples.math.mcgill.ca (8.6.8/8.6.6) with ESMTP id OAA04707 for ; Fri, 11 Jul 1997 14:09:12 -0400 Received: by mail5.microsoft.com with Internet Mail Service (5.0.1458.49) id <3W9L4D7D>; Fri, 11 Jul 1997 11:16:22 -0700 Message-ID: <9D311811F5DFD011A37800805FD4BA8803A91B@RED-66-MSG.dns.microsoft.com> From: "Adam Barr (Win NT)" To: "'barr@triples.math.mcgill.ca'" Subject: lecture abstract Date: Fri, 11 Jul 1997 11:14:29 -0700 X-Priority: 3 X-Mailer: Internet Mail Service (5.0.1458.49) Status: R This is a talk at Microsoft -- the abstract mentions category theory!! - adam ************************************************************************ ******** WHO: Erik Meijer AFFILIATION: Utrecht University, The Netherlands TITLE: The Next 700 Scripting Languages, or COM meets Functional Programming WHEN: Wednesday July 16, 1997 WHERE: 9s/1007 TIME: 3:00-4:30 HOST: Conal Elliott VIDEO Not Available ************************************************************************ ******* Please pass on this information to any other interested internal employees. The Next 700 Scripting Languages, or COM meets Functional Programming More than 30 years ago, Peter Landin proposed to define domain specific languages by embedding them into the purely functional host language ISWIM. The host language captures how things are described in terms of other things, and is specialized for a certain problem domain by an appropriate choice of primitive operations. In 1997-speak, we would say that Landin proposed to have a single scripting language to glue together application specific software components. This is very similar to using Visual Basic for scripting COM/ActiveX components. For a purely functional language however, it is easier said than done; especially if we want to introduce impure, side-effecting, primitives. Surprisingly, it turns out that the concept of monads from category theory provides an elegant solution to the problem of integrating interaction in a purely functional language. Finally, after 30 years, Landin's idea can be put into practice, and Fran, Haskell/CGI, Haskore, Tk/Gofer, AgentScript, and the Haskell-COM integration are collectively becoming a nice proof of concept. In this talk we will argue why we think lazy functional language (such as Haskell) are especially suited as scripting languages as they allow users to define their own control structures, or as we say, combinators. During the talk, the Microsoft Agent genie will navigate the Microsoft internet Explorer through a tour of dynamically generated HTML pages, everything scripted in Haskell. Biography ======= Erik Meijer is currently a visiting research professor at the Oregon Graduate Institute, on leave from Utrecht University in The Netherlands. He is known from his theoretical work on functional programming (Squiggol) and compiler construction, but now spends his time on practical applications of functional programming, especially promoting them as scripting languages. He is recently working on making COM components available from Haskell and encapsulating Haskell programs as COM components, and is a member of the Standard Haskell Committee. Home Page : http://tibet.cse.ogi.edu/Personal/Default.html" . msrlecture From cat-dist Mon Jul 14 20:26:17 1997 Received: by mailserv.mta.ca; id AA14261; Mon, 14 Jul 1997 20:25:22 -0300 Date: Mon, 14 Jul 1997 20:25:22 -0300 (ADT) From: categories To: categories Subject: Re: functions Omega->Omega Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: O X-Status: Date: Mon, 14 Jul 1997 14:24:43 -0400 From: Philip J. Scott >Date: Fri, 11 Jul 1997 16:56:25 -0400 (EDT) >From: Andre Scedrov > > > > f(a) & a = f(true) & a > > > > I wonder whether anyone has noticed this formula before? > >Similar formulas and their analogs in intuitionistic second-order >propositional calculus are discussed in my paper in the Annals Pure >Appl. Logic 27 (1984) 155-164. That paper was motivated by Higgs's >observation that every monic Omega -> Omega in a topos is an involution, >see Peter Johnstone's paper "Automorphisms of Omega" in Alg. Universalis >9 (1979) 1-7. > > Andre Scedrov For a logical proof of Higgs' theorem, based on the above observations of Scedrov, see Lambek-Scott (Introd. to Higher Order Cat. Logic), p.160, Exercise 4. A further result along these lines is in Lemma 12.3, p. 190 of our book. Phil Scott From cat-dist Tue Jul 29 15:25:59 1997 Received: by mailserv.mta.ca; id AA00293; Tue, 29 Jul 1997 15:24:38 -0300 Date: Tue, 29 Jul 1997 15:24:37 -0300 (ADT) From: categories To: categories Subject: final CFP - Computing: The 4th Australiasian Theory Symposium (CATS98) Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: O X-Status: Date: Tue, 29 Jul 1997 17:38:57 +0800 From: lxue@cs.uwa.edu.au CALL FOR PAPERS CATS'98 - Computing: The Australasian Theory Symposium University of Western Australia Perth, Western Australia 2-3 February, 1998 CATS'98 will be held at the University of Western Australia as part of the Australasian Computer Science Week (ACSW98) which also includes: . the Australasian Computer Science Conference (ACSC'98) . the Australasian Database Conference (ADC'98) . the Australasian Computer Architecture Conference (ACAC'98) Following on from CATS'94 in Sydney, CATS'96 in Melbourne, and CATS'97 in Sydney, CATS'98 aims at providing a forum for researchers in theoretical computer science. Typical, but not exclusive, topics of interest include: - Algorithms and data structure - Category theory - Complexity - Computational algebra, biology, geometry, logic, and number theory - Concurrency - Distributed and parallel computing - Formal semantics, specification, synthesis, and verification Original research papers are solicited. Submissions to CATS'98 this year will be again conducted electronically, and should be sent in standard Postscript format to cats98@cs.uwa.edu.au by the submission deadline. Authors unable to access e-mail may send 4 hard copies of their papers to the program committee chair: Xuemin Lin -- CATS'98 Department of Computer Science University of Western Australia Crawley, Western Australia 6907 Australia E-mail: cats98@cs.uwa.edu.au http://www.cs.uwa.edu.au:80/~lxue/CATS98/index.html In both cases, confirmation of receipt will be given, in the case of a postscript submission, once the file has been successfully printed. Submissions should include an abstract, 3-6 key words, and the fax number and e-mail address of the corresponding author. The contribution of the paper should be clearly explained in both general and technical terms, and authors should make every effort to ensure the technical content of their papers is understandable by a broad audience. The paper (an extended abstract or full paper) should not exceed 15 A4 pages using 11 point or larger font. Submission of a paper should be regarded as an undertaking that, should the paper be accepted, at least one of the authors will attend the conference to present the work. Papers will be judged on originality, significance, correctness, and clarity. Accepted papers will be published in the proceedings of the Symposium, which will appear in the DMTCS series of Springer-Verlag. ========================================= INVITED SPEAKERS: Ming Li (University of Waterloo, Canada) Takeshi Tokuyama (IBM, Japan) ========================================= IMPORTANT DATES: Submission Deadline: Friday 15 August 1997. This is a hard deadline; submissions postmarked after this date will be returned. Author Notification: Friday 24 October 1997. Final Version: Friday 14 November 1997. Acceptance of papers for the conference will be conditional upon the registration of at least one of the authors by 21 November 1997. ========================================= GENERAL CHAIR: James Harland RMIT PROGRAM COMMITTEE CHAIR: Xuemin Lin UWA LOCAL CHAIR: Chi-Ping Tsang UWA STEERING COMMITTEE: John Crossley Monash University Peter Eades University of Newcastle James Harland RMIT Michael Johnson Macquarie University John Staples University of Queensland Harald Sondergaard University of Melbourne PROGRAM COMMITTEE: Cristian Calude University of Auckland Hossam Elgindy University of Newcastle Matthew Hennessy University of Sussex Xuemin Lin University of Western Australia Bruce Maggs Carnegie-Mellon University Martin Odersky University of South Australia Hong Shen Griffith University Harald Sondergaard University of Melbourne Antonios Symvonis University of Sydney Tadao Takaoka University of Canterbury Ron van der Meyden University of Technology, Sydney Lusheng Wang City University of Hong Kong Sue Whitesides McGill University David Wolfram Australian National University ===================================== ADDRESS FOR ALL PAPER SUBMISSION CORRESPONDENCE Xuemin Lin -- CATS'98 Department of Computer Science University of Western Australia Crawley, Western Australia 6907 Australia Telephone: +61 9 380 3449 Facsimile: +61 9 380 1089 E-mail: cats98@cs.uwa.edu.au ===================================== ADDRESS FOR CORRESPONDENCE, OTHER THAN PAPER SUBMISSION, RELATED TO ANY CONFERENCE FORMING PART OF THE AUSTRALIAN COMPUTER SCIENCE WEEK ACSW'98 Information Department of Computer Science The University of Western Australia Crawley, Western Australia, 6907 Telephone: +61 9 380 2533 Email: acsw98info@cs.uwa.edu.au ORGANISING COMMITTEE CHAIR Chris McDonald Department of Computer Science The University of Western Australia Crawley, Western Australia, 6907 Email: chris@cs.uwa.edu.au ACSW'98 Hosts: Department of Computer Science, The University of Western Australia Department of Computer Science, Curtin University of Technology Department of Computer Science, Edith Cowan University Computer Science Programme, Murdoch University From cat-dist Wed Jul 30 13:39:52 1997 Received: by mailserv.mta.ca; id AA04801; Wed, 30 Jul 1997 13:39:18 -0300 Date: Wed, 30 Jul 1997 13:39:18 -0300 (ADT) From: categories To: categories Subject: Preprint available Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: O X-Status: Date: Wed, 30 Jul 1997 15:51:32 +0200 (MET DST) From: Carsten Butz Dear Colleagues, the ps-file of the following preprint is available at the homepage http://www.brics.dk/~butz : Topological Completeness for Higher-Order Logic by Steve Awodey (awodey@cmu.edu), Carsten Butz (butz@brics.dk). Abstract: Using recent results in topos theory, two systems of higher-order logic are shown to be complete with respect to sheaf models over topological spaces---so-called ``topological semantics''. The first is classical higher-order logic, with relational quantification of finitely high type; the second system is a predicative fragment thereof with quantification over functions between types, but not over arbitrary relations. The second theorem applies to intuitionistic as well as classical logic. Best regards, Steve Awodey and Carsten Butz From cat-dist Thu Jul 31 16:31:30 1997 Received: by mailserv.mta.ca; id AA20440; Thu, 31 Jul 1997 16:31:30 -0300 Date: Thu, 31 Jul 1997 16:31:30 -0300 (ADT) From: categories To: categories Subject: CTCS'97 final CFP Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: O X-Status: Date: Wed, 30 Jul 1997 19:48:54 +0200 From: Eugenio Moggi [Please look at the conference URL for more detailed information] CATEGORY THEORY AND COMPUTER SCIENCE (CTCS'97) 4-6 SEPTEMBER 1997, S. MARGHERITA LIGURE (GENOA), ITALY CONFERENCE URL: "http://www.disi.unige.it/conferences/ctcs97/" FINAL CALL FOR PARTICIPATION CTCS'97 is the 7th conference on Category Theory and Computer Science. The purpose of the conference series is the advancement of the foundations of computing using the tools of category theory, algebra, geometry and logic. While the emphasis is upon applications of category theory, it is recognized that the area is highly interdisciplinary. The proceedings will be published by Springer in the LNCS series. LOCATION. The conference will take place at Hotel Regina Elena, a 4 stars hotel with private beach, located in S. Margherita Ligure. S. Margherita is a beautiful sea resort in Liguria very close to Portofino promontory and about 30 km east of Genova. INVITED SPEAKERS - J. Baez, Univ. of California at Riverside (USA) - R. Bird, Oxford Univ. (UK) - B. Jay, Univ. of Technology Sydney (Australia) - G. Plotkin, Univ. of Edinburgh (UK) LATE REGISTRATION AND HOTEL RESERVATION. The late registration fee is 400000 It.Lire, and includes the welcome reception, coffee breaks, lunches, a copy of the proceedings. See the CONFERENCE URL for details on hotels and how to register. CONTACT INFORMATION: ctcs97@disi.unige.it (email), +39-10-3536699 (fax) ----------------------------------------------------------------------------- CONFERENCE PROGRAMME HOTEL REGINA ELENA Lungomare Milite Ignoto 44, 16038 S. Margherita Ligure, Italy phone: +39 (185) 287003, fax: +39 (185) 284473 WEDNESDAY, 3 September 18.00 Welcome Reception and Registration THURSDAY, 4 September 09.00 Invited Talk: Richard Bird 10.15 Coffee Break 10.40 Proof Principles for Datatypes with Iterated Recursion by Ulrich Hensel, Bart Jacobs 11.20 A Calculus for Collections and Aggregates by Kazem Lellahi, Val Tannen 12.00 When do datatypes commute? by Paul Hoogendijk, Roland Backhouse 12.40 Lunch 14.45 Invited Talk: John Baez 16.00 Coffee Break 16.30 A factorisation theorem for external derivations by Paul-Andre Mellies 17.10 Monads and Modular Term Rewriting by Christoph Lueth, Neil Ghani 17.50 A 2-Categorical Presentation of Term Graph Rewriting by Andrea Corradini, Fabio Gadducci FRIDAY, 5 September 09.00 Invited Talk: Barry Jay 10.15 Coffee Break 10.40 Presheaf Models for the pi-Calculus by Gian Luca Cattani, Ian Stark, Glynn Winskel 11.20 Categorical Modelling of Structural Operational Rules: case studies by Daniele Turi 12.00 Specifying Interaction Categories by Dusko Pavlovic, Samson Abramsky 12.40 Lunch 14.45 Invited Talk: Gordon Plotkin 16.00 Coffee Break 16.30 Lifting by A. Bucalo, G. Rosolini 17.10 General Synthetic Domain Theory -- A Logical Approach by Bernhard Reus, Thomas Streicher 17.50 Discussion on CTCS 20.00 Conference Dinner SATURDAY, 6 September 09.00 Shedding New Light in the World of Logical Systems by Uwe Wolter, Alfio Martini 09.40 Combining and Representing Logical Systems by Till Mossakowski, Andrzej Tarlecki, Wieslaw Pawlowski 10.20 Coffee Break 10.50 A decision algorithm for linear isomorphism of types O(nlog^2n) by Alexander Andreev, Sergei Soloviev 11.30 Effectiveness of the Global Modulus of Continuity on Metric Spaces by Klaus Weihrauch, Xizhong Zheng 12.30 Lunch Free Afternoon ----------------------------------------------------------------------------- From cat-dist Thu Jul 31 16:32:51 1997 Received: by mailserv.mta.ca; id AA21600; Thu, 31 Jul 1997 16:32:38 -0300 Date: Thu, 31 Jul 1997 16:32:38 -0300 (ADT) From: categories To: categories Subject: Pratt's construction Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-Status: Date: Wed, 30 Jul 1997 16:30:49 -0400 From: Michael Barr Since Vaughan insists on doing these things in terms of matrices and we benighted mathematicians insist on thinking in terms of pairings, I thought it might be helpful to describe what he did in those terms. First off, he erred in writing Chu instead of chu. So it is the separated extensional part. I will describe it for chu(Set,2), since nothing much changes for other values of K except you get more dinats. I will describe three types of objects. If A = (A_1,A_2) is an object, I will say that A_1 is the set of points and A_2 the set of states and treat A_2 as a set of subsets of A_1. I will say that A is type I if there is a point in no state AND if the empty set is a state. I will say that A is of type II if there is a point in every state and if the whole of A_1 is a state. These would appear to be quite different, but they are exchanged by the non-trivial automorphism of 2, which means they have the same properties. All remaining objects will be of type III. The first observation is that the type is invariant under formation of A -o A. That is, A -o A has the same type as A. Second, if A and B are of different types, then at least one of Hom(A,B) and Hom(B,A) is empty. This implies that if there is a map A --> B, then B -o A can only be (0,1) or (0,0) (0 is the empty set). That is is either initial or a quotient of the initial object. In either case, it has at most one arrow to any other object and any diagram starting with it commutes. The result of this is that any naturality condition that involves objects of different types is automatic. Either there is no map A --> B to test or there is one and the diagram is automatically commutative. For an object of type I, there is a zero map that takes every point to the (unique!) point not in any state and takes every state to the empty state. This is natural restricted to the type I objects and there is a similar 0 map for type II's. Now there are at least four dinatural endomorphisms of the functor that takes A and B to A -o B. They are all the identity on type III objects and can be either the identity or the 0 map on type I and the same on type II. Michael