June 2003 - Categories - categories.org.au

Re: reference : normal categorical subgroup ?
by jpradines 05 Jul '03

05 Jul '03

Though I have no reference for just the definition, I can make some historical remarks which perhaps explain the absence of reference, and which may be of interest for some people, and also give references for some (much less obvious) developments of the subject concerning groupoids in the category of manifolds and much more general ones. About 1964 or 5, I had the opportunity of mentioning to Charles Ehresmann that I had noticed the fact that the theory of factoring a group by a normal (or invariant or distinguished) subgroup extends almost obviously to groupoids. I was very surprised with his answer : "The question of quotients is a very difficult one which I have solved recently and a part of the theory will be proposed as the subject of examination for my students of DEA. I really don't know how you could manage". It is likely that this was a polite way of suggesting that I was certainly wrong in his opinion, but he didn't want to listen more explanation. Sometimes later, reading chapter III of his book on categories (published in 1965), I realized that he was certainly alluding to his very general theory of factoring a category by an equivalence relation or by a subcategory, while satisfying a universal property. Though this theory looks rather exhaustive and contains some rather deep and sophisticated statements, it seems in my opinion strictly impossible to deduce from any of these statements the very simple case of groupoids and normal subgroupoids nor even the very definition of a normal subgroupoid. I just recall here briefly what has certainly been discovered (at least partially) by any people having had the opportunity of meeting the question and thinking ten minutes to it, to know that the case of groups can be exactly mimicked for groupoids with just two precautions : -first, of course, expressions such as xHy have to be understood as denoting all the composites of the form xhy which are defined (where h runs in H) ; as a consequence the condition of normality for H in G (in which y is the inverse of x) bears only on the isotropy groups of H; -secund and more significantly it is no more true in general that the right and left cosets xH and Hx coincide ; however one just has to define the elements of the factor groupoid as consisting of two-sided cosets HxH ; with this slight modification of the theory, everything becomes an obvious exercise. One has also to notice that there is a special case where no modification is required, to know the case when H is actually a subgroup, i.e. just reduced to its isotropy groups. In that case the base of the factor groupoid is not changed. This case is the most obvious and also probably the best known (and possibly for most people the only one known), but in my opinion certainly not the most interesting, since it does not include the quotient of a set by an equivalence relation, whose graph is viewed as a subgroupoid of a coarse groupoid. Now what I really had in mind was not the purely algebraic (rather obvious) setting, but the study of quotients for the differentiable groupoids (nowadays called smooth or Lie) introduced by Ehresmann in 1959, which are groupoids in the category of manifolds. The statement I had obtained (which again certainly cannot by any means be deduced from the general results of Ehresmann concerning topological or structured groupoids) was published in 1966 in my Note (prealably submitted to Ehresmann and transmitted by him) : -Théorie de Lie pour les groupoïdes différentiables. Relations entre propriétés locales et globales, CRAS (Paris), série A, t.263, p.907-910, 19 décembre 1966- in Théorème 5 (in this statement the Bourbaki term "subimmersion" is improperly used and has to be understood in the more restricted acception "submersion onto a submanifold" ; note also that the implication from 2° to 1° is valid only when the fibres of the domain map of H are connected). (Note that in this statement the algebraic theory of the two-sided quotient of a groupoid by an invariant subgroupoid is implicitely considered as "well known" without reference. This was in fact a diplomatic consequence of the above-mentionned conversation ! At least at that period it seems absolutely certain that no reference did exist, and probably very few people, if any, had had the opportunity of thinking to that sort of questions, since the main stream of categoricists were despising groupoids as beig trivial, since equvalent to groups). The unpublished proof of this statement relied on a careful and rather delicate study of the foliation defined by the two-sided cosets. The very elegant proof for the case of Lie groups given in Serre, Lie Algebras and Lie Groups (lecture in Harvard, 1964, p.LG 4.10-11), relying on the so-called Godement's theorem, works only for one-sided cosets and yields only the too special case above-mentioned or more generally the statement of Proposition 2 in the previous Note (which extends to groupoids the classical theory of homogeneous spaces for possibly non invariant subgroups). It is clear that this last proof may be immediately written in a purely diagrammatic way and remains valid in much more general contexts when an abstract Godement's theorem is available. It turns out that this is the case for most of (perhaps almost all) the categories considered by "working mathematicians", notably the abelian categories as well as toposes, the category of topological spaces (with a huge lot of variants), the category of Banach spaces, and many useful categories that are far from being complete.The precise definitions for what is meant by an abstract Godement's theorem were given in my paper : -Building Categories in which a Godement's theorem is available- published in the acts of the Second Colloque sur l'Algèbre des Catégories, Amiens 1975, Cahiers de Topologie....(CTGDC). In this last paper I introduced the term "dyptique de Godement" for a category in which one is given two subcategories of "good mono's" and "good epi's" (playing the roles of embeddings and surmersions in Dif) such that a formal Godement's theorem is valid. These considerations explain why I was strongly motivated for adapting Serre's diagrammatic proof to the case of two-sided cosets (since such a proof would immediately extend the theory of quotients for groupoids in various non complete categories used by "working mathematicians", yielding a lot of theorems completely out of the range of Ehresmann's general theory of structured groupoids). However this was achieved only in 1986 in my Note : -Quotients de groupoïdes différentiables, CRAS (Paris), t.303, Série I, 1986, p.817-820.- The proof requires the use of certain "good cartesian squares" or "good pull back squares", which, though they are not the most general pull back's existing in the category Dif of manifolds, cannot be obtained by the (too restrictive) classical condition of transversality. Though written in the framework of the category Dif (in order not to frighten geometers, but with the risk of frightening categoricists), this paper is clearly thought in order to be easily generalizable in any category where a suitable set of distinguished pull back's is available , assuming only some mild stability properties. In this paper I introduced the seemingly natural term of "extensors" for naming those functors between (structured) groupoids which arise from the canonical projection of a groupoid onto its quotient by a normal subgroupoid. Equivalent characterizations are given.(I am ignoring if another term is being used in the literature).This notion is resumed and used in my paper : -Morphisms between spaces of leaves viewed as fractions- CTGDC, vol.XXX-3 (1989),p. 229-246 which again is written in the smooth context, but using purely diagrammatic descriptions (notably for Morita equivalences and generalized morphisms) allowing immediate extensions for various categories. As a prolongation of this last paper, I intend in future papers to give a description of the category of fractions obtained by inverting those extensors with connected fibres. This gives a weakened form of Morita equivalence which seems basic for understanding the transverse structure of foliations with singularities. Jean PRADINES ---- Original Message ----- From: Marco Mackaay <pmzmm(a)mat.uc.pt> To: categories <categories(a)mta.ca> Sent: Thursday, June 05, 2003 4:49 PM Subject: categories: reference: normal categorical subgroup? > To all category theorists, > , p.> I'm looking for a reference to the definition of a normal categorical

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job: Research post in Bangor
by tporter＠informatics.bangor.ac.uk 26 Jun '03

26 Jun '03

Dear All This is an announcement about a forthcoming research position at Bangor. The full announcement will appear on the web at : www.jobs.ac.uk within the next few days. The post is for 10 months only as the funding is for a Pilot project and one of the tasks for the Research Assistant will be to help in the preparation of an extended proposal. Please draw it to the attention of any suitable candidates. Thanks Tim Porter PS. for people outside the U.K. If you don't know North Wales, it is a beautiful area of the U.K. and the School Of Informatics is very near the sea and the mountains!!!! ................... UNIVERSITY OF WALES, BANGOR SCHOOL OF INFORMATICS MATHEMATICS DIVISION Research Officer (Fractafolds, their geometry and topology) Salary: =A318,265 - =A320,311 (on R&A Grade 1A) p.a. Applications are invited for the above Leverhulme funded Pilot Project post available for a period of 10 months. Based in the Mathematics Division of the School of Informatics, you will work on the problem of identifying a class of topological spaces that bear something of the same relationship to certain well structured fractal spaces as manifolds bear to Euclidean spaces. This is a pilot project to evaluate various candidate classes of spaces for =91fractafold=92 status. The candidate spaces are fractal, but also are, in various different ways =91homogeneously fractal=92. The test for success will be indications that a possible fractal analogue of differential geometry can be applied to the study of these spaces. Thus you will study the various classes of candidate spaces to see if the development of such a =91differential geometry=92 on fractals impo= ses extra conditions on them or distinguishes between the different candidate classes. Dependent on the success of this initial testing, it is hoped that a full-scale project lasting a further two years will be awarded. One of your tasks will be to assist the project coordinator in the preparation of full grant applications. You should possess a strong mathematical background (PhD) with research experience in one or more of the following areas: fractals; algebraic, geometric or differential topology; areas of analysis, or differential geometry; category theory; or certain relevant areas of mathematical physics (finite approximation theory, discrete differential manifolds, etc.) or theoretical computer science (digital topology, constructive analysis, etc.). Application forms and further particulars should be obtained by contacting Human Resources, University of Wales, Bangor, Gwynedd LL57 2DG; tel: + 44 (0)1248 382926/388132; e-mail: personnel(a)bangor.ac.uk Please quote reference number 03-2/231 when applying. Closing date for applications: Friday 25th July, 2003. Interviews will be held in early September, 2003. Informal enquiries can be made by contacting Professor T. Porter, e-mail: t.porter(a)bangor.ac.uk tel: +44 (0)1248 382492. Committed To Equal Opportunities Name: advert03-2-231.doc advert03-2-231.doc Type: Winword File (application/msword) Encoding: base64 Download Status: Not downloaded with message ----- End forwarded message ----- -------------------------------------------------- School of Informatics, University of Wales, Bangor This mail sent through IMP: http://horde.org/imp/

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Open positions: Research (Bunched ML); Lectureships.
by David Pym 24 Jun '03

24 Jun '03

[Apologies for cross-postings.] Readers of this list may be interested in the following open positions in the (recently established) Department of Computer at the University of Bath, England: 1. One Research Officer position (post-doc) --- UK EPSRC-funded project, "Bunched ML" (roughly, operational and denotational models of ML-like languages with bunched typed systems, based on bunched logic. This project is jointly run by Prof. David Pym at Bath and Profs. Peter O'Hearn and Edmund Robinson at Queen Mary, London. Details below; 2. Two permanent lectureships (roughly, Associate Prof.) --- any area of computer science, though see the reserach areas listed below; 3. One 3-year lectureship (roughly, Assistant Prof.) --- any area of computer science, though see the reserach areas listed below. The University of Bath was placed 5th overall in this year's Times UK University Rankings (6th for CS), see http://www.timesonline.co.uk/section/0,,716,00.html, and is located in a very beautiful city. Official advert follows. UNIVERSITY OF BATH Department of Computer Science: Lectureships (3 posts); Research Officer. Lectureships (Ref: 03/157) The Department of Computer Science seeks to appoint, from as soon as possible, to two lectureships and one fixed-term lectureship (3 years - as a direct result of a Royal Society Industry Fellowship awarded to Professor Pym) The Department is multi-disciplinary and has internationally renowned research. Three main research areas are: Human Computer Interaction, Mathematical Foundations and Applications, Media Technology. We are seeking to appoint in each of the existing main research areas but by exception will also consider well qualified applications in other areas of Computer Science. For teaching purposes we need expertise in mainstream computer science topics. Applicants should normally hold a PhD or have equivalent research experience in Computer Science and show evidence of or the ability to publish in international journals or conferences and to obtain research funding. Salary in the range =A326,270 to =A333,679 (Lecturer Grade B). Informal enquiries to Professor Peter Johnson, Head of Department (P.Johnson(a)bath.ac.uk; Tel +44(0)1225 383214, Fax +44(0)1225 383493). Research Officer Post (Ref: 03/160) Applications are also invited for the post of Research Officer on the EPSRC-funded project "Bunched ML" under the direction of Prof. David Pym, d.j.pym(a)bath.ac.uk, http://www.bath.ac.uk/~cssdjp who may be contacted for an informal discussion of the post. This project is funded jointly with Prof. Peter O'Hearn's group at Queen Mary, University of London, and is concerned with the operational and denotational semantics of ML-like programming languages which use bunched typed systems, based on bunched logic. Applicants should have a doctorate in a relevant area of computer science or mathematics and an interest in programming languages with polymorphism, program logics, and their semantics. Programming skills would be advantageous. The post is available for three years from 1 November, 2003 or as soon as possible thereafter. The starting salary is =A321, 125 pa. Applicants should complete an application form and may attach a CV. More information about the Department can be found at: http://www.bath.ac.uk/comp-sci/ Application forms and further particulars for both posts are available from Juliet Hills, Personnel Officer, University of Bath, Claverton Down, Bath, BA2 7AY, (tel. 01225 386873; fax 01225 386559; e-mail adsjf(a)bath.ac.uk) or e-mail jobs(a)bath.ac.uk or phone the 24 hour answer-phone service on Bath (01225) 386924, or textphone (01225) 386039 quoting the appropriate reference number. Closing date for applications: Friday 25th July 2003. An equal opportunities employer. --=20 Prof. David J. Pym Telephone: +44 (0)1 225 38 3246 Professor of Logic & Computation Facsimile: +44 (0)1 225 38 3493 University of Bath Email: d.j.pym(a)bath.ac.uk Bath BA2 7AY, England, U.K. Web: http://www.bath.ac.uk/~cssdjp

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Papers available
by Thorsten Palm 24 Jun '03

24 Jun '03

Dear categorists, My Ph.D. dissertation, entitled `Dendrotopic Sets for Weak Infinity-Categories', and a preliminary version of my paper `Dendrotopic Sets' can now be downloaded from the web-page www.math.yorku.ca/Who/Grads/palm . The content of the two works is summarized below, where they are referred to as [A] and [B] respectively. Best regards Thorsten Palm ---------------- In his unpublished paper [1], Makkai defined a notion of _weak infinity-category_ (under the name `multitopic omega-category'). The underlying geometric structures, called _multitopic sets_, are described in the three-part paper [2]. Makkai takes a weak infinity-category to be a multitopic set with the mere property that _compositions_ exist, which are defined as equivalences of certain _coslice_ objects. [A] gives a definition of weak infinity-categories equivalent to Makkai's. While this definition falls into the same two stages, it is considerably shorter and more elementary in each of them. The description of the underlying geometric structures, called _dendrotopic sets_ here, is done purely combinatorially (whereas [2] uses the algebraic machinery of multicategories). A coslice object comes in two guises, in both of which it is a dendrotopic set with mild extra structure in the form of a dendrotopic map (whereas in [1] it is a model for a new signature for Makkai's first-order logic with dependent sorts). [A] also presents an alternative method of introducing composition to a dendrotopic set. Here one has to impose the extra structure of a _universality system_: a subset that behaves in such a way that each member can be thought of as a universal arrow. The main theorem of [A] states that a dendrotopic set containing a universality system is a Makkai weak infinity-category. The concept of a dendrotopic set is defined at a more leisurely pace in [B], where the equivalence to the concept of a multitopic set is, indirectly, established. References: [1] M. Makkai: `The multitopic omega-category of all multitopic omega-categories'; mystic.biomed.mcgill.ca/Makkai [2] C. Hermida, M. Makkai, A. J. Power: `On weak higher dimensional categories'; Journal of Pure and Applied Algebra. Part 1: 154 (2000), pp. 221-246; part 2: 157 (2001), pp. 247-277; part 3: 166 (2002), pp. 83-104

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first isomorphism theorem
by Andrei.Prokopiw＠Dartmouth.EDU 24 Jun '03

24 Jun '03

Is there a suitable first isomorphism theorem in category theoretic language? One barrier for me seems to be the correct notion of an image. What seems best right now would be that given f:X->Y, ker(coker f) = coker ( ker f). Here the left hand side would represent im f, and the right hand side X/kerf. If this is the right notion, what are the necessary conditions on the category for it to hold? -Andrei Prokopiw

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Halchin's question re Curry-Howard
by F W Lawvere 24 Jun '03

24 Jun '03

>> I have been reading up on the Curry-Howard isomorphism. >> In the last chapter of Conceptual Mathematics, Lawvere >> and Schanuel say that the logical connectives are >> completely analogous to the categorical operations x, >> map object and +. Is this an oblique reference to the >> Curry-Howard isomorphism? At the 1963 Model Theory conference in Berkeley, I pointed out that an interlocking system of adjoints occurring in set theory and type theory has also as a very special example the one arising in the logic of parts. In Eilenberg and Kelly's 1965 pioneering paper on closed categories, part of my result was cited and it came to be known as the statement that Heyting algebras are cartesian closed categories. In my papers "Adjointness in Foundations"(submitted December 15th 1967), "Equality in Hyperdoctrines...", and "Diagonal Arguments...", I tried to clarify these and related matters. I became aware at some point that Haskell Curry in one of his books had informally pointed out earlier the possible importance of this as an analogy. In the late 1960s, Bill Howard, a student of Mac Lane, began circulating his results which were finally published in 1980; Howard's paper could be described as containing an oblique reference to the closed category theorems. The term "isomorphism" which has emerged in the literature is rather misleading since the map in question is bijective at best at the level of subjective presentations, rather than at the level of objective algebras. That is to say, a symbolic presentation of a particular Heyting algebra can always be construed in many ways as an image of a presentation of a cartesian closed category, but there is the additional draconian rule of inference which says that any two maps with a given domain and codomain are equal. I tried to give a more accurate description of this situation by referring to "an adjunction" rather than to an isomorphism in my paper "Adjointness in and Among Bi-categories" Logic and Algebra, Lecture Notes in Pure and Applied Mathematics, vol. 180, pp 181-189, edited by A. Ursini and P. Agliano', Marcel Dekker, 1996. Bill Lawvere ************************************************************ F. William Lawvere Mathematics Department, State University of New York 244 Mathematics Building, Buffalo, N.Y. 14260-2900 USA Tel. 716-645-6284 HOMEPAGE: http://www.acsu.buffalo.edu/~wlawvere ************************************************************

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Union College Conference
by Susan Niefield 21 Jun '03

21 Jun '03

UNION COLLEGE MATHEMATICS CONFERENCE Saturday and Sunday Schenectady November 8-9, 2003 New York This is a preliminary announcement for the eleventh Union College Mathematics Conference. This year the conference topics are algebraic topology, category theory, and differential geometry. In addition to plenary lectures of interest to the entire Conference audience, there will also be shorter contributed talks in parallel sessions. Anyone interested in giving such a talk should contact one of the organizers. The meeting will begin with an evening reception on Friday, November 7, and end on Sunday afternoon. A more detailed notice will be mailed later this summer. Information will also be available at the Union College Mathematics Department website (www.math.union.edu) in August. Union College is centrally located in New York's capital district about 10 miles from the Albany International Airport, easily accessible by train from NYC, and just 3 to 4 hours by car from NYC, Boston, and Montreal. We hope to see you in November! ORGANIZERS Category Theory Susan Niefield niefiels(a)union.edu Kimmo Rosenthal rosenthk(a)union.edu Algebraic Topology Brenda Johnson johnsonb(a)union.edu Kathryn Lesh leshk(a)union.edu Differential Geometry Christina Tonnesen-Friedman tonnesec(a)union.edu

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CFP: WRLA 2004
by alberto＠sip.ucm.es 21 Jun '03

21 Jun '03

[[ -- Apologies for multiple copies of this message -- ]] + + + + + WRLA'04 + + + + + CALL FOR PAPERS + + + + + WRLA'04 + + + + + +----------------------------------------------------------+ | | | 5th International Workshop on | | Rewriting Logic and its Applications | | | | W R L A 2004 | | | | Barcelona, Spain, March 27-28, 2004 | | | | http://www.fdi.ucm.es/wrla2004 | +----------------------------------------------------------+ The workshop will be held in conjunction with ETAPS 2004 7th European Joint Conferences on Theory and Practice of Software March 27 - April 4, 2004 http://www.lsi.upc.es/etaps04 IMPORTANT DATES November 24, 2003 Deadline for submission January 15, 2004 Notification of acceptance February 18, 2004 Final version in electronic form March 27-28, 2004 Workshop in Barcelona AIMS AND SCOPE Rewriting logic (RL) is a natural model of computation and an expressive semantic framework for concurrency, parallelism, communication and interaction. It can be used for specifying a wide range of systems and languages in various application fields. It also has good properties as a metalogical framework for representing logics. In recent years, several languages based on RL (ASF+SDF, CafeOBJ, ELAN, Maude) have been designed and implemented. The aim of the workshop is to bring together researchers with a common interest in RL and its applications, and to give them the opportunity to present their recent works, discuss future research directions, and exchange ideas. The topics of the workshop comprise, but are not limited to, * foundations and models of RL; * languages based on RL, including implementation issues; * RL as a logical framework; * RL as a semantic framework, including applications of RL to - object-oriented systems, - concurrent and/or parallel systems, - interactive, distributed, open ended and mobile systems, - specification of languages and systems; * extensions of RL, including - real-time and probabilistic extensions, - tile logic, - rewriting approaches to behavioral specifications; * verification techniques for RL specifications, including - equational and coherence methods, and - verification of properties expressed in modal and temporal logics; * comparisons of RL with existing formalisms having analogous aims, including - rho-calculus, - structural operational semantics, - concurrency calculi, - dynamic algebras. PAST EVENTS Previous WRLA workshops have been organized in - Asilomar, California, September 3-6, 1996, - Pont-a-Mousson, France, September 1-4, 1998, - Kanazawa, Japan, September 18-20, 2000, - Pisa, Italy, September 19-21, 2002. The proceedings of the WRLA workshops have been published as volumes 4, 15, 36, and 71 in the Elsevier ENTCS series, available at http://www.elsevier.nl/locate/entcs Selected papers from WRLA'96 have been published in a special issue of Theoretical Computer Science, Volume 285(2), 2002. LOCATION WRLA 2004 will be held in Barcelona, Spain in March 27-28, 2004. It is a satellite workshop of ETAPS 2004, the European Joint Conferences on Theory and Practice of Software. For venue, registration and suggested accommodation see the ETAPS 2004 web page http://www.lsi.upc.es/etaps04 For information about Barcelona, see among others the city web page http://www.bcn.es/english/ihome.htm PROGRAM COMMITTEE David Basin ETH Zurich Manuel Clavel Universidad Complutense de Madrid Steven Eker SRI International, Menlo Park Kokichi Futatsugi JAIST, Tatsunokuchi Fabio Gadducci Universita di Pisa Alexander Knapp LMU, Muenchen Claude Kirchner INRIA Lorraine & LORIA, Nancy Salvador Lucas Universidad Politecnica de Valencia Narciso Marti-Oliet Universidad Complutense de Madrid (Chair) Jose Meseguer University of Illinois at Urbana-Champaign Ugo Montanari Universita di Pisa Pierre-Etienne Moreau INRIA Lorraine & LORIA, Nancy Grigore Rosu University of Illinois at Urbana-Champaign Carolyn Talcott SRI International, Menlo Park SUBMISSIONS Submissions will be evaluated by the Program Committee for inclusion in the proceedings, which will be available at the time of the workshop and are expected to be published in the Elsevier ENTCS series. Papers must contain original contributions, be clearly written, and include appropriate reference to and comparison with related work. They must be unpublished and not submitted simultaneously for publication elsewhere. Papers (of at most 15 pages) should be submitted electronically, preferably as PDF files, to the workshop email address wrla2004(a)sip.ucm.es providing also a text-only abstract, and detailed contact information of the corresponding author. The final program of the workshop will also include system demonstrations and two invited presentations by Gilles Dowek Ecole Polytechnique & INRIA, Palaiseau Mario Rodriguez-Artalejo Universidad Complutense de Madrid Based on the quality and interest of the accepted papers, the program committee will study the possibility of preparing a special issue of a scientific journal in the field. ORGANIZING COMMITTEE Narciso Marti-Oliet, Manuel Clavel, and Alberto Verdejo Departamento de Sistemas Informaticos y Programacion Universidad Complutense de Madrid, Spain CONTACT INFORMATION For more information, please contact the organizers wrla2004(a)sip.ucm.es or visit the workshop web page http://www.fdi.ucm.es/wrla2004 IMPORTANT DATES November 24, 2003 Deadline for submission January 15, 2004 Notification of acceptance February 18, 2004 Final version in electronic form March 27-28, 2004 Workshop in Barcelona + + + + + WRLA'04 + + + + + CALL FOR PAPERS + + + + + WRLA'04 + + + + +

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My email address
by Charles Wells 20 Jun '03

20 Jun '03

My correct email address is cwells(a)oberlin.net My freude.com address was canceled in January and I just found out that my cwru.edu address hasn't been working for a couple of weeks. If anyone has recently sent me messages to those address, please resend them. Thanks Charles Wells Charles Wells professional website: http://www.cwru.edu/artsci/math/wells/home.html personal website: http://www.oberlin.net/~cwells/index.html genealogical website: http://familytreemaker.genealogy.com/users/w/e/l/Charles-Wells/ NE Ohio Sacred Harp website: http://www.oberlin.net/~cwells/sh.htm

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Categories in Economics
by Tony Bryant 18 Jun '03

18 Jun '03

Dear Categorists, Can anyone supply me with references to uses of category theory and related concepts/arguments in economic theory? Thanks, Tony Bryant Head of Economics MACQUARIE UNIVERSITY

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