May 2002 - Categories - categories.org.au

Only two SMC structures on Cat?
by Jason C Reed 27 Jul '02

27 Jul '02

Power, A.J. and Robinson, E.P. Premonoidal categories and notions of computation (ftp://ftp.dcs.qmw.ac.uk/pub/lfp/edmundr/premoncat.ps.gz) in section 2 asserts that there is excatly one symmetric monoidal closed structure on Cat besides the cartesian one. Does anyone know [the location of] a proof? ---Jason

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Open position in CS at Bath, England.
by David J. Pym 31 May '02

31 May '02

Dear Colleagues, We have an open position in the newly-established Department of Computer Science at the University of Bath. Bath was placed 4th in The Times' 2002 ranking of UK (England, Scotland, Wales, Northern Ireland) Universities, and is located in England's most beautiful city. Some details are attached below. All best wishes, David --=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 University of Bath (http://www.bath.ac.uk) Lectureship in Computer Science Department of Computer Science (http://www.bath.ac.uk/comp-sci, website under construction) Applications are invited for a Lectureship in the newly established Department of Computer Science, within the Faculty of Science. The Department, formed in August 2001 from the existing Computing Group in Mathematical Sciences, is multi-disciplinary and has internationally renowned research. Three main research areas are: Human Computer Interaction, Mathematical Foundations and Applications, Media Technology. Within these areas of research interests include: user interaction technologies, collaborative systems, cognitive modelling, accident and error analysis, algorithms and complexity, security and networks, logic and semantics of programming languages=18=13, visualization, computer graphics, image processing. We are seeking to appoint in one of the existing areas but 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. Salary will be in the Lecturer B range of =A325,455 to =A332,537 per annum, according to qualifications and experience. Informal contact may be made through the Head of Department, Professor Peter Johnson, (P.Johnson(a)bath.ac.uk; Tel +44(0)1 225 323214; Fax +44(0)1225 323493). Application forms and further particulars are available from Juliet Hills, Personnel Officer, University of Bath, Claverton Down, Bath, BA2 7AY, (Tel +44 (0)1 225 38 6873; Fax +44 (0)1 225 38 6559; e-mail A.S.Barnard(a)bath.ac.uk) or e-mail jobs(a)bath.ac.uk or phone the 24 hour answer-phone service on Bath +44 (0)1 225 38 6924, or textphone +44 (0)1 225 38 6039, quoting reference 02/157. Closing date for applications: Friday 21 June 2002. An equal opportunities employer.

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lecture notes available
by Thomas Streicher 28 May '02

28 May '02

In June 2000 Jean Benabou gave a course on Distributors at Work of which I prepared lecture notes that were proof read by him and finally accepted in the form as you can find them at http://www.mathematik.tu-darmstadt.de/~streicher/FIBR/DiWo.ps.gz The aim of this course was not to give the latest results but rather to give a most understandable introduction. Nevertheless, one can find there quite a few elementary facts which are probably not so well-known (as e.g. the correspondence to comma and cocomma categories). In the final section of these notes one can also find an outline of Benabou's work on generalised fibrations, i.e. normalised lax functors from B^op to the bicategory of distributors. ----------------------------------------------------------------------------- I use this opportunity also for pointing your attention to my lecture notes for a course on Fibred Categories `a la J. B'enabou which are based on a series of lectures I gave in Spring 1999 on the occasion of a Spring School organised by the PhD Programme "Logic in Computer Science" (for further information about that event look at http://www.pst.informatik.uni-muenchen.de/spring-school99) These lecture notes can be obtained from http://www.mathematik.tu-darmstadt.de/~streicher/FIBR/fib.ps.gz Since the time of the course I have been working occasionally on extending the course notes so that they cover a lot of the topics presented in B'enabou's course on Fibred Categories in Louvain-la-Neuve in 1980. However, in contrast to J.-R. Roisin's hand-written lecture notes of the Louvain-la-Neuve course my lecture notes do not follow any particular course given by Benabou though I am certain that all of the material is due to him. I just have tried to collect in one place most of the facts about fibred categories that I met over the years. I deliberately have excluded the connections with categorical logic and semantics of type theory as can be found in Bart Jacob's encyclopedic book from 1999 published by North Holland. Instead I have devoted some part of the notes to a fibrational understanding of geometric morphism as can be found in the unpublished These of J.-L.Moens from 1982 (clearly influenced by and strongly using the results of Benabou's 1980 course in Louvain-la-Neuve). This aspect is also explained in detail and developed further in Part B of PTJ's "Sketches of an Elephant" (as far as I know). My lecture notes are not too polished, I fear, and haven't been proof read by other people. Nevetheless, they might be useful in providing information which is difficult to access otherwise. Thomas Streicher

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Theo Gray
by Peter Freyd 27 May '02

27 May '02

John Gray's son: Copyright 2002 Nationwide News Pty Limited Sunday Herald Sun [Sydney, Australia] May 26, 2002, Sunday SECTION: WIRED WORLD; Pg. U02 LENGTH: 331 words HEADLINE: Elementary table BYLINE: SAMANTHA AMJADALI BODY: SAMANTHA AMJADALI reports on a marriage of carpentry and chemistry Carpenter Theodore Gray could not understand why every periodic table -- the tabular listing of chemical elements according to their atomic numbers and properties -- he ever spied was either hanging on walls or printed on paper. Had no one else noticed the word "table" in the phrase? Surprised by the 133 year-long oversight, and horrified by scientists "generally doing all kinds of things with it that have nothing to do with being a table", Gray, a lover of mathematics and chemistry, resolved to one-day rectify the situation by creating a genuine periodic table table. So, last year, when he was commissioned to create an "unusual" conference table for US-based Jensan Scientifics, Gray grabbed the opportunity and has spent the past year crafting a table based on a traditional Periodic Table. Gray records progress on his work, dubbed the Periodic TABLE, on his website. The gigantic wooden effort, made from teak, birch, cherry and white oak, looks like a typical grid-based periodic table, except that each element is represented by a thick wooden panel that, when opened, reveals a small sample of whatever element it describes. Gray hasn't been able to find samples of all 110 elements. He's still missing about 30 samples, many of which are hard to find or, like mercury and uranium, too dangerous to store in an unstable environment outside a laboratory. Each element is accompanied by a hand-carved explanation of the element's chemical symbol, atomic weight, group and chemical number. The panels sit flush with the table's surface. The finished table will have a panel of glass over the top so that it can be used to write on. Gray's multitude of talents extend to programming. He's one of the chief programmers on Mathematica, high-end mathematical software used by professional mathematicians to plot complex formulas. [Indeed, he's a cofounder of Mathematica and member of the Executive Committee. -pjf] Theo Gray's website: www.mathpuzzle.com/Periodic.htm

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categorified Yang-Mills equations
by baez＠math.ucr.edu 25 May '02

25 May '02

A while ago I gave a talk on "Categorified Gauge Theory" at the 2002 Joint Spring Meeting of the Pacific Northwest Geometry Seminar and Cascade Topology Seminar. I've just put the transparencies for this talk on my website: http://math.ucr.edu/home/baez/gauge/ Here's the abstract: In electromagnetism we can think of the vector potential as a 1-form A which couples to charged point particles in a very natural way - we simply integrate it over the particle's worldline to obtain a term in the action. Similarly, in string theory there naturally arises a 2-form B, the Kalb-Ramond field, which we integrate over the string worldsheet. The resulting theory of "2-form electromagnetism" is formally very similar to Maxwell's equations: in particular, we define a curvature 3-form G = dB and require that *d*G = J where the current J is now a 2-form. Just as the electromagnetic vector potential should really be regarded as a connection on a U(1) bundle, the Kalb-Ramond field should really be thought of as a connection on a "U(1) gerbe". Moreover, just as U(1) bundles are classified by the 1st Cech cohomology with coefficients in the sheaf of smooth U(1)-valued functions, U(1) gerbes are classified by the 2nd Cech cohomology with coefficients in this sheaf. Electromagnetism can be generalized to Yang-Mills theory by replacing the group U(1) by an arbitrary compact Lie group. This raises the question of whether we can similarly generalize 2-form electromagnetism to some sort of "higher-dimensional Yang-Mills theory". We show how to do this by categorifying the concepts of smooth manifold, Lie group and Lie algebra, and setting up a theory of bundles, connections and curvature in this new context. In particular, we define a "Lie 2-group" to be a category C where the set of objects and the set of morphisms are Lie groups, and source, target, identity and composition maps are homomorphisms of Lie groups. This turns out to be the same as a "Lie crossed module": a pair of Lie groups G and H with a homomorphism t: H -> G and an action of G on H satisfying the equations in the usual definition of crossed module. Just as a connection on a trivial G-bundle is the same as a Lie(G)-valued 1-form, a connection on a trivial C-2-bundle turns out to be a Lie(G)-valued 1-form together with a Lie(H)-valued 2-form. Following ideas of Breen and Messing, we give formulas defining the curvature of such a connection, which consists of a Lie(G)-valued 2-form together with a Lie(H)-valued 3-form. We write down the obvious generalization of the Yang-Mills action for a connection on a trivial C-2-bundle, and derive the "categorified Yang-Mills equations" from this action. We also show that in certain cases these equations admit self-dual solutions in five dimensions. We conclude by sketching how nontrivial C-2-bundles can be classified by the 2nd nonabelian Cech cohomology.

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job: Post in Liverpool
by Peter McBurney 24 May '02

24 May '02

[ Please would you forward to anyone you think may be interested. Thanks ] -------------------------------------------------------------------------- Chair in Computer Science (Logic and Computation) Department of Computer Science University of Liverpool Liverpool, UK [ Closing date for applications: 14-JUN-02. Salary negotiable ] Applications are invited for a Chair in the Department of Computer Science at the University of Liverpool, to be attached to the Logic and Computation research group. The group carries out research in formal methods, including algebraic methods, contextual reasoning, modal and temporal theorem-proving and verification, databases, and programming languages. The successful candidate will have an excellent track record of research leadership, and will be expected to contribute to research and research leadership in both the Logic and Computation group and Department generally. For further details of the Group, Department and University, see http://www.csc.liv.ac.uk/research/logics/ http://www.csc.liv.ac.uk/ http://www.liv.ac.uk/ Informal enquiries are welcome, and should be directed to Professor Michael Fisher, Head of Logic and Computation Group, email: M.Fisher(a)csc.liv.ac.uk Further particulars and details of the application procedure should be requested from The Director of Personnel, The University of Liverpool, Liverpool L69 3BX 0151 794 2210 (24 hr answerphone) or via email:jobs@liv.ac.uk Job reference number: B/844 --------------------------------------------------------------------- | Michael Fisher M.Fisher(a)csc.liv.ac.uk | | Department of Computer Science tel: (+44) 151 794 6701 | | University of Liverpool fax: (+44) 151 794 3715 | | Liverpool L69 7ZF, U.K. http://www.csc.liv.ac.uk/~michael | --------------------------------------------------------------------- **************************************************************** Peter McBurney Department of Computer Science University of Liverpool Liverpool L69 7ZF U.K. Tel: + 44 151 794 6760 Email: P.J.McBurney(a)csc.liv.ac.uk Web page: www.csc.liv.ac.uk/~peter/ ****************************************************************

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html presentation
by Philippe Gaucher 23 May '02

23 May '02

Title : Concurrent Process Up to Homotopy : Presentation of the Globular Approach Comment : html presentation Remark : Do not try to reach the url directly from my home page : it is not yet modified. Url : http://www-irma.u-strasbg.fr/~gaucher/presentation_glob/ Abstract: A concurrent machine is a computer where several tasks can be performed at the same time. This can be a true parallelism like in the case of several processors running concurrently, or also the particular case of a mono-processor UNIX machine where a unique CPU is sharing its calculation time between several different tasks. I present here the geometric model of concurrent processes I am working with. This geometric model allows to formalize very precisely the notion of dihomotopy. Two concurrent processes (i.e. the corresponding geometric models) are said dihomotopic when they can be geometrically deformed to each other without changing their computer-scientific properties. The purpose of this text is not to be technical, but only to explain how some algebraic constraints have led me to introducing the constructions I am working with. 24-May-2002 09:16:32 -0300,3129;000000000000-00000000

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Preprint : Whitehead's Theorem in Homotopy Theory of Concurrency
by Philippe Gaucher 23 May '02

23 May '02

Hello, The following preprint is available. Comments are welcome. Title : Whitehead's Theorem in Homotopy Theory of Concurrency Comments : 1) 100 pages, LaTeX2e 2) this is a totally new version, not an update, of the old "Unifying The Globular and The Topological Approach of Dihomotopy" with a lot of new results. Abstract : We introduce the category of flows and an equivalence relation on it called weak dihomotopy. The category of globular CW-complexes introduced in a previous paper can be embedded in a canonical way into the category of flows. This embedding induces a category equivalence from the category of globular CW-complexes up to dihomotopy to the one of flows up to weak dihomotopy. This statement is proved thanks to a directed version of Whitehead's theorem (the one concerning the equivalence between weak homotopy and homotopy for CW-complex). So studying HDA up to dihomotopy is equivalent to working within the category of flows. This setting is better than the one of globular CW-complexes because the category of flows is complete and cocomplete. However it is not cartesian closed. But it does have a closed monoidal structure called tensor product which turns out to correspond to the interleaving of all possible asynchronous executions. In particular, the tensor product of the flow associated to the m-cube by the flow associated to the n-cube is the flow associated to the (m+n)-cube. Url : http://www-irma.u-strasbg.fr/~gaucher/flow.ps http://www-irma.u-strasbg.fr/~gaucher/flow.pdf http://www-irma.u-strasbg.fr/~gaucher/flow.ps.gz http://www-irma.u-strasbg.fr/~gaucher/flow.pdf.gz 23-May-2002 10:28:45 -0300,1864;000000000000-00000000

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CTCS '02, Aug. 15-17, Ottawa
by P. Scott 22 May '02

22 May '02

CATEGORY THEORY AND COMPUTER SCIENCE (CTCS'02) AUGUST 15-17, 2002 GRADUATE STUDENT PRECONFERENCE AUGUST 12-14, 2002 University of Ottawa Ottawa, Ontario, Canada First Call for Participation ***************************************************************************** CTCS '02 is the 9th 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. The emphasis is upon applications of category theory, but it is recognized that the area is highly interdisciplinary. Typical topics of interest include, but are not limited to, category-theoretic aspects of the following: coalgebras and computing concurrent and distributed systems constructive mathematics declarative programming and term rewriting domain theory and topology foundations of computer security linear logic modal and temporal logics models of computation program logics, data refinement, and specification programming language semantics type theory Previous meetings have been held in Guildford (Surrey), Edinburgh (twice), Manchester, Paris, Amsterdam, Cambridge, and S. Margherita Ligure (Genova). This is the first time CTCS will be held in North America. The proceedings of the conference will be published as a special issue of ENTCS (Electronic Notes in Theoretical Computer Science). Paper copies of the proceedings will be available to participants at the conference. The conference will have 4 invited speakers, and they are: Eric Goubault (CEA/Saclay) Guy McCusker (Sussex) Peter Selinger (Ottawa) Paul Syverson (Naval Research Laboratory) GRADUATE STUDENT PRECONFERENCE One new feature that CTCS will have this year is a "preconference" from August 12-14. This is supported in part by a grant from CRM, the Centre de Recherches Mathematiques (Univ. of Montreal). The goal is to prepare students for CTCS, through mini-courses in the basic areas underlying the fields of the conference. We anticipate offering courses in the following areas: Introduction to Category Theory Introduction to Categorical Logic Coalgebras Communication and Concurrency Game Semantics Linear Logic PROGRAMME COMMITTEE Rick Blute, Chair (Ottawa) Robin Cockett (Calgary) Thierry Coquand (Chalmers) Andrea Corradini (Pisa) Thomas Ehrhard (Luminy) Ryu Hasegawa (Tokyo) Martin Hofmann (Munich) Bart Jacobs (Nijmegen) Michael Johnson (Macquarie) Dusko Pavlovic (Kestrel Institute) Alex Simpson (Edinburgh) ORGANIZING COMMITTEE E. Moggi, Chair, (Genova) S. Abramsky (Oxford) P. Dybjer (Chalmers) B. Jay (Sydney) A. Pitts (Cambridge) LOCAL ORGANIZING COMMITTEE R. Blute (Ottawa) rblute(a)mathstat.uottawa.ca P. Scott (Ottawa) phil(a)site.uottawa.ca, scpsg(a)matrix.cc.uottawa.ca HOTEL INFORMATION We have arranged several special hotel rates. Both hotels are within walking distance of the conference. We request that you make hotel reservations yourself. If there are any problems, please contact one of the local organizers. (Note that all prices are in Canadian dollars.) 1) Ramada Hotel & Suites Ottawa (Use Group Code 2451 to get special rates.) 111 Cooper Street Ottawa, ONTARIO K2P 2E3 CANADA Tel: 1-613-238-1331 FAX: 1-613-230-2179 email: ramada(a)ramada-ottawa.com website: www.ramada.ca/ottsuit.html This is avalable from Wednesday, August 14, 2002 to Sunday, August 18, 2002 (departure on Monday). Rate: $109.00 single or double occupancy Deadline: July 14th, 2002 2) Novotel Ottawa Hotel (Use Contract #0002166 and Reference #3878 to get special rates.) 33 Nicholas Street Ottawa, ONTARIO K1N 9M7 CANADA Phone:1-613-230-3033 or 1-800-668-6835 (Reservations worldwide-no charge dial) website: www.bestlodging.com/sites1/17534/index.shtml This is available from Wednesday, August 14, 2002 to Sunday, August 18, 2002 (departure on Monday). Rate: $129 single or double, $144 triple, $159 Quad Deadline: June 30th, 2002 We may also have a VERY limited number of university dorm rooms available at much cheaper rates. We will give them away on a first come, first served basis. Contact local organizers for this. CONFERENCE HOMEPAGE Updated information is available at http://www.mathstat.uottawa.ca/lfc/ctcs2002 . Registration forms will appear there within the next few days, as well as dormitory registration forms. Please register as soon as possible. (NOTE: CTCS is being held at U. Ottawa, but the conference registrar and coordinator is Ms. Gillian S. Murray, at Carleton University, as shown on the Registration Forms). A complete list of accepted papers will appear in the second call for participation. 23-May-2002 05:23:59 -0300,2437;000000000000-00000000

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cfp: GT-VMT'02
by Mark Minas 18 May '02

18 May '02

Sorry if some of you receive multiple copies of this message. Paolo Bottoni and Mark Minas (GT-VMT'02 Co-Chairs) ------------------------------------------------------------------------ Call for Papers ************************************************************************ * * * International Workshop on * * Graph Transformation and Visual Modeling Techniques (GT-VMT '02) * * * * http://www2.cs.fau.de/GTVMT02/ * * * * Barcelona, Spain * * October 11-12, 2002 * * * ************************************************************************ A satellite event of the First International Conference on Graph Transformation (ICGT 2002) As diagrammatic notations, such as UML, become widespread in software engineering and visual end user environments, there is an increasing need for formal methods to precisely define the syntax and semantics of such diagrams. In particular, when visual models of systems or processes constitute executable specifications of systems, not only is a non-ambiguous specifications of their static syntax and semantics needed, but also an adequate notion of diagram dynamics. Such a notion must establish links (e.g., morphisms) which relate diagram transformations and transformations of the objects of the underlying domain. The field of Graph Grammars and Graph Transformation Systems has contributed much insight into the solution of these problems, but also other approaches (e.g., meta modelling, constraint-based and other rule-based systems), have been developed to tackle specific issues. The workshop follows in the line of successful workshops on Graph Transformations and Visual Modelling Techniques, which were before held as satellite events of ICALP'00 and ICALP'01. It aims at gathering researchers working with different methodologies to discuss the relative merits and weaknesses of the different approaches to problems such as diagram parsing, diagram transformation, integrated management of syntactic and semantic aspects, tool support for working with visual models. The focus will be on methodological aspects rather than on particular technical aspects. Program Committee ----------------- Paolo Bottoni (Co-Chair), Italy Andrea Corradini, Italy Gregor Engels, Germany Reiko Heckel, Germany Stuart Kent, UK Bernd Meyer, Australia Mark Minas (Co-Chair), Germany Francesco Parisi Presicce, Italy Mauro Pezze', Italy Grzegorz Rozenberg, The Netherlands Gabriele Taentzer, Germany Submission ---------- Authors are invited to submit extended abstracts of 5 to 10 pages in ENTCS format (http://math.tulane.edu/~entcs/) until June 15, 2002 electronically via our submission web form (http://www2.cs.fau.de/GTVMT02/submission.html) The contributions should report about ongoing research in the area of graph transformation and visual modeling techniques, especially on the syntax and semantics of visual languages according to the scope and objectives of the workshop. Contributions exploring the use of Graph Grammars and Graph Transformation Systems are particularly welcome, as well as papers which cover several aspects or integrate different formalisms for the definition of visual modeling techniques. Position papers and contributions making methodological statements are strongly encouraged. Publication ----------- Accepted contributions will appear in an issue of Elsevier's Electronic Notes in Theoretical Computer Science (ENTCS). A preliminary version of the issue will be available at the workshop. Important Dates --------------- June 15, 2002: Submission Deadline July 15, 2002: Notification of Acceptance Sept. 6, 2002: Camera Ready Version Further Information ------------------- GT-VMT'02 web site: http://www2.cs.fau.de/GTVMT02/ ICGT 2002 web site: http://www.lsi.upc.es/icgt2002/ 22-May-2002 05:48:41 -0300,5484;000000000001-00000000

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