July 1999 - Categories - categories.org.au

universal property of tangent bundle
by Nikita Danilov 02 Aug '99

02 Aug '99

Dear category people, Given an object M in the ``normal'' category of finitely dimensional smooth manifolds Man (not in SDG sense), what it the universal property of the tangent bundle TM? So far, I found only the following: For every manifold M there is a functor F:I -> Man0, where Man0 is category of open areas in R^n and smooth mapping, such that M=Colim F, F corresponding to the atlas on M and M is represented as a result of gluing instances of R^n in the atlas. This functor can be trivially modified (by multiplying its values on objects on R^n and modifying morphisms appropriately) to get functor TF:I -> Man0, such that TM=Colim TF. But this doesn't seem satisfactory because: 1. Construction of TF follows one particular construction of TM as a set of triples (x,(U,f),h) where x \in U, (U,f) is in atlas and h \in R^n with appropriate points identified. 2. I hope there should be universal construction with \pi: TM -> M as universal arrow. 3. As tangent bundle is so ubiquitous there should be nice universal property for it. With regards, N. Danilov.

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Paper announcement
by Peter Selinger 31 Jul '99

31 Jul '99

Dear Category Theorists, I am pleased to announce the availability of a new paper, Categorical Structure of Asynchrony, available via http://www.math.lsa.umich.edu/~selinger/papers.html. In this paper, I investigate properties of traced monoidal categories that are satisfied by networks of asynchronously communicating processes. Among these properties are Hasegawa's uniformity principle, as well as a version of Kahn's principle: the subcategory of *deterministic* processes is equivalent to a category of domains. The paper also contains the following observation, which may be of interest to categorists. I do not know whether this was observed before, and would be grateful for references. Suppose T:Set-->Set is a functor which is lax for the symmetric monoidal structure given by products on the category of sets. Then T associates to any category C another category C', which Benabou called the "direct image of C by T". This category is defined as follows: obj(C') = obj(C), and C'(X,Y) = T(C(X,Y)). The observation is that direct images preserve linear structure. More precisely, if the category C possesses some algebraic structure which is given by linear equations, then C' inherits that structure. Non-linear structure is not in general preserved, although one can give conditions on T under which the construction will preserve, for instance, affine structure. One can also loosen the conditions on T, so that it will only preserve non-commutative linear structure. One can use the direct image construction to extract the linear "part" of an arbitrary algebraic structure: for instance, if C has finite products, then C' has a monoidal structure with diagonals, which is precisely the part of a finite product structure which is given by linear equations. Traced monoidal structure with diagonals is the linear part of finite product structure with fixpoints. One direction of this, namely that the latter structure is a special case of the former, was observed by Hasegawa and by Hyland, but I don't know whether it had been noticed that the former is precisely the linear part of the latter. An example of a non-commutative linear structure (given by linear equations where the variables occur in the same left-to-right order on both sides) is the premonoidal structure of Power and Robinson. This is precisely the non-commutative part of monoidal structure. More details and examples are in the paper. Comments are, as usual, welcome. Best wishes, -- Peter Selinger ---------------------------------------------------------------------- ABSTRACT: We investigate a categorical framework for the semantics of asynchronous communication in networks of parallel processes. Abstracting from a category of asynchronous labeled transition systems, we formulate the notion of a categorical model of asynchrony as a uniformly traced monoidal category with diagonals, such that every morphism is total and the focus is equivalent to a category of complete partial orders. We present a simple, non-deterministic, cpo-based model that satisfies these requirements, and we discuss how to refine this model by an observational congruence. We also present a general construction of passing from deterministic to non-deterministic models, and more generally, from non-linear to linear structure on a category.

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New edition of "Category Theory for Computing Science"
by Charles Wells 30 Jul '99

30 Jul '99

Category Theory for Computing Science (Third edition) By Michael Barr and Charles Wells This new edition contains all the material from the first and second editions, including the four chapters excised from the second edition and the solutions to all the exercises, as well as added material on factorization systems, monoidal categories, and other topics. All errors known to the authors have been corrected. The price is only Can$45, approximately US$31, postpaid anywhere on earth. It should be available for ordering from http://crm.umontreal.ca/pub/Ventes/CatalogueEng.html by mid-August. You can also order the book directly by sending an email to sales(a)crm.umontreal.ca. Charles Wells, Department of Mathematics, Case Western Reserve University, 10900 Euclid Ave., Cleveland, OH 44106-7058, USA. EMAIL: charles(a)freude.com. OFFICE PHONE: 216 368 2893. FAX: 216 368 5163. HOME PHONE: 440 774 1926. HOME PAGE: URL http://www.cwru.edu/artsci/math/wells/home.html

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PSSL 71: First announcement
by gran＠agel.ucl.ac.be 28 Jul '99

28 Jul '99

PERIPATETIC SEMINAR ON SHEAVES AND LOGIC 71st meeting -- First Announcement As announced in Coimbra, the 71st meeting of the PSSL will be held in Louvain-la-Neuve on the weekend of 16-17 October 1999. We welcome contributed talks on category theory and related areas. Further details of the arrangements for the meeting, and a registration form, will be sent out in August. Francis Borceux Marino Gran Mamuka Jibladze Enrico Vitale

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Lectureship in Theoretical Computer Science in Birmingham
by Achim Jung 27 Jul '99

27 Jul '99

The University of Birmingham School of Computer Science LECTURER IN THEORETICAL COMPUTER SCIENCE Applications are invited for a permanent lectureship in Theoretical Computer Science in the School of Computer Science at the University of Birmingham. Applications from all areas of Theoretical Computer Science will be considered but preferential treatment will be given to candidates who show promise to strengthen existing activities. These encompass Mathematical Structures in Computer Science, Lambda Calculus, Type Theory, and Verification of Systems. The School has recently appointed Uday Reddy to a Chair in Programming Languages and close cooperation between the existing Theory group and this new strand of activity is expected. For further information, please see ftp://ftp.cs.bham.ac.uk/pub/dist/info/lect.tcs/particulars.htm Please pass this advert on to any interested individuals in your department. Kind regards, Achim Jung. ------------------------------------------------------------------------- Prof Achim Jung Tel.: (+44) 121 414 4776 School of Computer Science Sec.: (+44) 121 414 3711 The University of Birmingham Fax.: (+44) 121 414 4281 Edgbaston Email: A.Jung(a)cs.bham.ac.uk BIRMINGHAM, B15 2TT Web: http://www.cs.bham.ac.uk England -------------------------------------------------------------------------

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CT 2000
by walters 27 Jul '99

27 Jul '99

Category Theory 2000 CT 2000 will be held from 16th to 22nd July 2000, at Villa Olmo, Como, Italy. RFC Walters

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CTCS`99 Call for Participation
by Samson Abramsky 26 Jul '99

26 Jul '99

CATEGORY THEORY AND COMPUTER SCIENCE (CTCS'99) 10-12 SEPTEMBER 1999, EDINBURGH, SCOTLAND http://www.dcs.ed.ac.uk/home/ctcs99 CALL FOR PARTICIPATION EARLY REGISTRATION DEADLINE: 10th August 1999 CTCS '99 is the 8th 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. While the emphasis is upon applications of category theory, it is recognized that the area is highly interdisciplinary. Previous meetings have been held in Guildford (Surrey), Edinburgh, Manchester, Paris, Amsterdam, Cambridge, and S. Margherita Ligure (Genova). This document contains 1. Invited speakers 2. List of accepted papers 3. Programme committee 4. Registration form A WWW-version containing all this information plus abstract of contributed papers can be found under www.dcs.ed.ac.uk/home/ctcs99 1. Invited speakers ------------------- Ryu Hasegawa Univ. of Tokyo (Japan) Peter Freyd Univ. of Pennylvania (USA) Marcelo Fiore Univ. of Sussex (UK) Doug Smith Kestrel Institute (USA) 2. List of accepted papers (19 out of 39 submissions) -------------------------- Concurrent Realizations of Reactive Systems. Marek Bednarczyk, Andrzej Borzyszkowski Functorial semantics for Petri nets under the individual token philosophy. Roberto Bruni, Jose Meseguer, Ugo Montanari, Vladimiro Sassone Equational Lifting Monads. Anna Bucalo, Alex Simpson, Carsten Fuehrmann Structured Theories and Institutions F Duran, J Meseguer Coalgebra to Algebra Morphisms. A Eppendahl On the Semantics of Message Passing Processes. Lindsay Errington A Fully abstract presheaf semantics for SCCS with finite delay. Thomas Hildebrandt Abstract Games for Linear Logic. Martin Hyland, Andrea Schalk Internal Languages for Autonomous and *-Autonomous Categories. T W Koh and C-H L Ong Dependent Coercions. Zhaohui Luo and Sergei Soloviev Precategories for combining probabilistic automata. Paulo Mateus, Amilcar Sernadas, Cristina Sernadas Monads, shapely functors, and traversals. E Moggi, G Belle, C B Jay Exhausting Strategies, Joker Games and IMLL with Units. A S Murawski and C-H L Ong Hilbert Q-Modules and Nuclear Ideals in the Category of v-Semilattices with a Duality. Jan Paseka A Coalgebraic Foundation for Linear Time Semantics. John Power, Daniele Turi Denotational Completeness Revisited. Thomas Streicher A domain-theoretic semantics of lax generic functions. Hideki Tsuiki A Bi-Categorical Axiomatisation of Concurrent Graph Rewriting. Fabio Gadducci, Reiko Heckel and Merce Llabres. Higher-dimensional syntax. Martin Wehr. 3. Programme committee ---------------------- J. Adamek TU Braunschweig (Germany) N. Benton Microsoft Research, Cambridge (UK) R. Blute U. Ottawa (Canada) T. Coquand Chalmers (Sweden) M. Escardo LFCS Edinburgh (UK) M. Hasegawa Kyoto Univ. (Japan) M. Hofmann (Chair) LFCS Edinburgh (UK) P. O'Hearn Queen Mary West (UK) D. Pavlovic Kestrel Institute (California) H. Reichel TU Dresden (Germany) G. Rosolini U. Genova (Italy) A. Scedrov U. Penn (Pennsylvania) Organising Committee -------------------- S. Abramsky LFCS Edinburgh (UK) P. Dybjer Chalmers U. (Sweden) E. Moggi U. Genova (Italy) A. Pitts U. Cambridge (UK) 4. Registration form -------------------- Please complete this form and email it to ctcs99-reg(a)dcs.ed.ac.uk before 10th August 1999. You can also fax the form to +44 131 667 7209 Attn: CTCS-REG or send it to M Lekuse, CTCS-REG, JCMB, KB, Mayfield Rd, Edinburgh EH9 3JZ, UK. ******************************************************* * REGISTRATION FOR CTCS '99 * ******************************************************* A PERSONAL DETAILS ------------------ LAST NAME: _______________________________ FIRST NAME: ______________________________ AFFILIATION: _____________________________ ADDRESS: _________________________________ _________________________________ _________________________________ PHONE NUMBER: ____________________________ FAX: _____________________________________ E-MAIL: __________________________________ WWW (optional): __________________________ DATE OF ARRIVAL: __/__ 1999 DATE OF DEPARTURE: __/__ 1999 ANY SPECIAL DIETARY REQUIREMENTS (e.g. vegetarian): ______________________ B CONFERENCE FEES ----------------- The conference fee will cover lunches, coffee breaks, and proceedings. (It also includes costs for invited speakers and seminar room bookings.) Regular Student -------------------------------------------- Early registration: GBP115 GBP95 by 19th July Late registration: GBP170 GBP170 after 19th July There will be a conference dinner on Saturday, 11th September. It will cost GBP30 (students GBP15). I will attend the dinner YES ( ) NO ( ) Total fees payable: GBP ____ I have paid the fees by ____________________ on __/__1999. Please pay your fee by - bank draft in GBP - Eurocheque in GBP - any other cheque drawn on a British bank payable to "The University of Edinburgh". Unfortunately, we cannot acccept credit cards and bank transfers. C ACCOMMODATION --------------- We should like to ask you to book your own accommodation directly. The Edinburgh Tourist Board offers a very efficient booking service. You can either book by phone (+44-131-473-3874), fax (+44-131-473-3636) or e-mail (conventions(a)eltb.org) When you contact them they will supply you with a booking form which lists a number of accommodation types from simple guest houses to 5* hotels. Please book early. Although the Edinburgh International Festival will be over, September is still a very busy time. ---------------------------------------------------------------- **Please state clearly on the accommodation booking form that your accommodation should be within easy reach of the King's Buildings, University of Edinburgh.** ---------------------------------------------------------------- You should receive confirmation of your booking within one day. You need to give them your credit card number which will serve as a security. You will actually have to pay your accommodation directly later. If you do not have a credit card, or you encounter any difficulties in booking your accommodation, then please get in touch with us directly. Please contact (ctcs99-reg(a)dcs.ed.ac.uk) and state your requirements. The conference will be held in the James Clerk Maxwell Building (Lecture theatre B), King's Buildings, Edinburgh EH9 3JZ. You will find maps at http://www.visres.ed.ac.uk/internal/maps. Important dates --------------- 9 April 1999 Notification of intention to submit 23 April 1999 Submission deadline 4 June 1999 Notification of authors of accepted papers 30 July 1999 Deadline for final versions of accepted papers Address for paper submissions ----------------------------- Martin Hofmann Laboratory for Foundations of Computer Science Division of Informatics JCMB, King's Buildings Mayfield Road Edinburgh EH9 3JZ Scotland Local organization ------------------ Monika Lekuse Laboratory for Foundations of Computer Science Division of Informatics JCMB, King's Buildings Mayfield Road Edinburgh EH9 3JZ Scotland Conference e-address ctcs99(a)dcs.ed.ac.uk -------------------- Conference homepage http://www.dcs.ed.ac.uk/home/ctcs99 ------------------- Related event 2nd APPSEM workshop, 6-9 September 1999 ------------- http://www.md.chalmers.se/Cs/Research/Semantics/APPSEM/index.html

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Re: co-exponential question
by Paul Levy 23 Jul '99

23 Jul '99

I don't know if this is relevant to your question, but there is an example in programming semantics where the dual of a cartesian closed category has independent significance, due to Lafont, Streicher, Reus and Hofmann. (Some further work was done by Selinger.) It is found in the following paper: @Article{StreicherReus:continuations, title = "Classical logic, continutation semantics and abstract machines", author = "Th. Streicher and B. Reus", pages = "543--572", journal = "Journal of Functional Programming", month = nov, year = "1998", volume = "8", number = "6", } The construction is as follows. Let C be a distributive category, and let Ans (the "answer type") be an object in C, such that the exponential X -> Ans exists for each object X. Define two categories K and N as follows. Both have the same objects as C. In K, a morphism from X to Y is a C-morphism from X x (Y -> Ans) to Ans. In N, a morphism from X to Y is a C-morphism from (X -> Ans) x Y to Ans. Clearly these two categories are dual. Streicher and Reus' paper makes it clear that just as K can be used to interpret a typed call-by-value language with control effects (which was well-known), N can be used to interpret a typed call-by-name language with control effects. Like any call-by-name model, N is cartesian closed: the product of X and Y in N is given by X+Y the exponential from X to Y in N is given by (X -> Ans) x Y K is certainly an important category, but I wouldn't say that the fact that it has coexponentials is significant. Paul =========================================================================== Paul Blain Levy, Department of Computer Science, Queen Mary and Westfield College, LONDON E1 4NS http://www.dcs.qmw.ac.uk/~pbl/ ===========================================================================

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Re: Cartesian Monads and Pullbacks
by N Ghani 23 Jul '99

23 Jul '99

I asked the question >> Do cartesian monads preserve pullbacks. May be with some extra >> conditions such as finitariness? without properly defining what I meant by a cartesian monad. What I mean was that the unit and multiplication of the monad are cartesian natural transformations, ie the associated naturality squares are pullbacks. Soory for the confusion Neil

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Answer to Davilov
by Andree Ehresmann 21 Jul '99

21 Jul '99

Davilov writes: >Given an object M in the ``normal'' category of finitely dimensional >smooth manifolds Man (not in SDG sense), what it the universal property >of the tangent bundle TM? Several authors have been interested in this problem many years ago, that has led to the study of the functors from Man to the category of vector bundles. Such functors are completely characterized in Epstein, "Natural vector bundles", Lecture Notes in Math. 99, Springer 1969, p. 171-195. >>From his theorems, it results in particular that Ehresmann's first order velocity functors Tn which associate to a manifold M the vector bundle of the 1-jets from R^n to M (in particular T for n=1) are the only such product preserving functors. This result is generalized in an abstract setting to characterize connections in: Bowshell, "Abstract velocity functors", Cahiers de Topologie et Geom. Diff. XII-1 (1971), 57-82. Later on, related (or more general) problems are considered in: Palais & Terng, "Natural bundles have finte order", Topology 16 (1977), 271-277, Epstein & Thurston, "Transformation groups and natural bundles", Proc. London Math. Soc. 38 (1979), 219-236. Eck, "Product preserving functors on smooth manifolds, J. Pure & App. Algebra 42 (1986), 133-140. Kolar, An abstract characterization of the jet spaces, Cahiers de Topologie et Geom. Diff. XXXIV-2 (1993), 121-125. Dupovec & Kolar, On the jets of fibered manifold morphisms, Cahiers de Topologie et Geom. Diff. XXXIV-2 (1993), 121-125. Hoping these old references can be of some interest Best regards Andree C. Ehresmann

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