April 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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Homology question
by Michael Barr 07 May '02

07 May '02

Suppose you have an exact sequence of chain complexes 0 --> C' --> C' + C --> C -->0 in which the middle term has boundary operator given by the matrix [ d -f ] [ 0 d ] for some f: C --> C'. This is more or less the mapping cone of f. Suppose in addition that f(Z(C)) is included in B(C'). It then follows immediately that 0 --> H(C') --> H(C' + C) --> H(C) --> 0 is exact. Is it split? The answer is yes if this is a sequence of abelian groups (or modules over a hereditary ring) and C is projective. Anyone know of a counter-example? Michael 29-Apr-2002 16:12:19 -0300,2233;000000000000-00000000

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preprint: Entropic Hopf algebras and models...
by Paul RUET 30 Apr '02

30 Apr '02

The following paper: "Entropic Hopf algebras and models of non-commutative logic", by Rick Blute, Fran=E7ois Lamarche and Paul Ruet, is available at the address http://iml.univ-mrs.fr/~ruet/. Abstract: We give a definition of categorical model for the multiplicative fragment of non-commutative logic. We call such structures entropic categories. We demonstrate the soundness and completeness of our axiomatization with respect to cut-elimination. We then focus on several methods of building entropic categories. Our first models are constructed via the notion of a partial bimonoid acting on a cocomplete category. We also explore an entropic version of the Chu construction, and apply it in this setting. It has recently been demonstrated that Hopf algebras provide an excellent framework for modeling a number of variants of multiplicative linear logic, such as commutative, braided and cyclic. We extend these ideas to the entropic setting by developing a new type of Hopf algebra, which we call entropic Hopf algebras. We show that the category of modules over an entropic Hopf algebra is an entropic category (possibly after application of the Chu construction). Several examples are discussed, based first on the notion of a bigroup. Finally the Tannaka-Krein reconstruction theorem is extended to the entropic setting. 30-Apr-2002 18:47:58 -0300,3462;000000000001-00000000

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Thesis - Symmetric Operads for Globular Sets
by Mark Weber 30 Apr '02

30 Apr '02

Greetings categorists! A PDF version of my thesis entitled "Symmetric Operads for Globular Sets" is now available at http://www.maths.mq.edu.au/~mweber/ -------------------------------------------------------------------------------------------------- ABSTRACT This thesis considers various issues related to the adaptation of Batanin's higher operads to the problem of describing $k$-fold monoidal weak $n$-categories and related structures. These higher operads have been found to be successful in providing descriptions of the monads on $\Glob$, the category of globular sets, whose algebras are structures like strict and weak $\omega$-categories. One of the features of the endofunctors and monads on $\Glob$ that arise in this theory, is that they bear a formal resemblance to power series. The first contribution of this thesis is to view this phenomenon as an instance of a general notion of power series. This notion is based on a presheaf category together with a chosen full subcategory, whose objects turn out to be the exponents of the resulting power series. Other examples of this notion include the usual notions of power series which correspond to certain endofunctors of $\Set$. By definition, $k$-fold monoidal weak $n$-categories are weak $(n+k)$-categories which have exactly one $r$-cell for $r < k$. The second contribution of this thesis is the description and analysis of a simple construction called \emph{suspension}, which takes a finitary monad $T$ on $\Glob$, and produces another finitary monad whose algebras are one-$0$-cell $T$-algebras. Applying this construction $k$ times to $T$ produces the monad whose algebras are ``$k$-fold monoidal $T$-algebras''. Batanin's higher operads are describable as cartesian monad morphisms into the monad $\TREE$, whose algebras are strict $\omega$-categories. Such a description is possible since $\TREE$ satisfies a certain property: it is a club in the sense of Kelly. However, applying suspension at least twice to Batanin operads gives rise naturally to a monad morphism into a monad which is not a club. This situation has more in common with \emph{symmetric} operads in $\Set$. The third contribution of this thesis is to provide a common generalisation of symmetric operads in $\Set$ and Batanin's operads. This new operad notion also includes the clubs originally considered by Kelly in the early 1970's for the study of categories with structure and their coherence. -------------------------------------------------------------------------------------------------- Regards, Mark Weber

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FME 2002: call for participation
by mailinglist-admin＠fmeurope.org 29 Apr '02

29 Apr '02

Dear collegue, FME 2002 is the eleventh in a series of symposia organised by Formal Methods Europe (www.fmeurope.org) an independent association whose aim is to stimulate the use of, and research on, formal methods for software development. These symposia have been notably successful in bringing together a community of users, researchers, and developers of precise mathematical methods for software development. Registration for FME 2002 is now open! Please visit http://floc02.diku.dk/FME/ and http://floc02.diku.dk/floc/register.html for more information and and on-line registration. Don't miss out on this event! _______________________________________________ Mailinglist mailing list Mailinglist(a)fmeurope.org http://www.fmeurope.org/mailman/listinfo/mailinglist 29-Apr-2002 16:12:19 -0300,2530;000000000000-00000000

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PDF version of "Transition & Cancellation"
by Vaughan Pratt 28 Apr '02

28 Apr '02

I recently announced the availability of "Transition and Cancellation in Concurrency and Branching Time" in gzipped Postscript as http://boole.stanford.edu/pub/seqconc.ps.gz While I don't know about the members of this list, in general people nowadays seem better set up to handle Adobe's PDF than Postscript. I've therefore converted the paper to PDF using dvipdfm (a lot less hassle than the extensive preparation required for good results from Acrobat Distiller). To read it directly from your browser, visit http://chu.stanford.edu/ and click on the first item, SEQCONC. The way I've set it up (in http://chu.stanford.edu/seqconc.html) probably could do with some tuning, so I'd appreciate hearing about any problems you run into or suggestions for changes to seqconc.html. Vaughan Pratt 30-Apr-2002 18:47:57 -0300,2883;000000000001-00000000

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2nd CfP: Categorical Methods for Concurrency, Interaction, and Mobility
by Alexander Kurz 26 Apr '02

26 Apr '02

[ Apologies for multiple copies ] Workshop on CATEGORICAL METHODS FOR CONCURRENCY, INTERACTION, AND MOBILITY Brno, Czech Republic, 24 August 2002 affiliated with CONCUR 2002 Second Call for Papers Aims and Scope: The aim of the workshop is to bring together researchers applying category theory to concurrency, interaction, or mobility. Topics of interest include, but are not limited to: categorical algebras of processes categorical methods in game semantics and geometry of interaction categorical models of term/graph rewriting or rewriting logic Chu spaces coalgebras, bialgebras, coinduction comparing models of concurrency enriched categories of processes interaction categories presheaf models Programme Committee: Samson Abramsky (Oxford) Thomas Hildebrandt (Copenhagen) Alexander Kurz (Amsterdam) Ugo Montanari (Pisa) Prakash Panangaden (Montreal) Horst Reichel (Dresden) Jiri Rosicky (Brno) Bob Walters (Como) Important dates: Deadline for submission: May 24, 2002 Notification of acceptance: July 5, 2002 Final version due: July 25, 2002 Workshop: August 24, 2002 Location: The workshop will be held in Brno in August 2002. It is a satellite workshop of CONCUR 2002. For venue and registration see the CONCUR web page at http://www.fi.muni.cz/concur2002/ Submissions: It is planned to publish the proceedings of the meeting as a volume in Elsevier's ENTCS series. Papers must contain original contributions, be clearly written, and include appropriate reference to and comparison with related work. Papers should be submitted as PostScript files by email to kurz(a)cwi.nl, containing `CMCIM-submission' in the subject. A separate message should also be sent (subject: CMCIM-abstract), containing authors, title, a text-only abstract, as well as mailing addresses (both postal and electronic) of the corresponding author. Workshop organizer: Alexander Kurz CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands email: kurz(a)cwi.nl Further information at http://www.cwi.nl/cmcim or from kurz(a)cwi.nl -- http://www.cwi.nl/~kurz 27-Apr-2002 18:50:22 -0300,1320;000000000000-00000000

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Enriched 2categories
by Toby Bartels 25 Apr '02

25 Apr '02

¿Has a theory been developed of bicategories enriched in an appropriately weak sense over monoidal bicategories? -- one level higher than categories enriched over monoidal categories. I'd especially like to know if things have been developed to the point of weighted enriched weak 2limits. Ideally, somebody will cite a book by 2Kelly ^_^, but I'm interested in whatever is known. -- Toby Bartels toby(a)math.ucr.edu 27-Apr-2002 18:50:19 -0300,3140;000000000000-00000000

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functors between categories of monads?
by Claus Juergensen 23 Apr '02

23 Apr '02

Please help! I need information on functors between categories of monads. Any links/references are welcome. Thanx! -- Dipl.-Math. Claus Juergensen Inst. f. Theoretische Informatik, Technische Universitaet Dresden, D-01062 Dresden, Germany phone: +49(0)351/463-38253, http://wwwtcs.inf.tu-dresden.de/~claus/ 27-Apr-2002 18:50:16 -0300,1203;000000000000-00000000

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Galois and Hopf 2002 - Registration/Abstracts/Proceedings
by Walter Tholen 20 Apr '02

20 Apr '02

Dear Colleagues: This is an update regarding the "Workshop on Categorical Structures for Descent and Galois Theory, Hopf Algebras and Semiabelian Categories" to be held September 23-28, 2002, at the Fields Institute in Toronto. http://www.fields.utoronto.ca/programs/scientific/02-03/galois_and_hopf/ REGISTRATION is now open, a registration form can be found at the conference website. EVERY conference participant must register. The program of the workshop will commence on Monday September 23, at 9am and run until noon Saturday September 28. In addition to the invited lectures (for a list of speakers, see below) we expect to be able to place up to 30 contributed 20-minute talks in the program. CALL FOR PAPERS (***modified***) We invite you to submit an abstract by 15 May 2002, using the easy-to-use abstract submission service linked to the workshop webpage. Alternatively, you may send your abstract as a plain message directly and simultaneously to all three organizers: George Janelidze (janeli(a)math.ist.utl.pt) Bodo Pareigis (pareigis(a)rz.mathematik.uni-muenchen.de) Walter Tholen (tholen(a)mathstat.yorku.ca) Notification of acceptance will be given by 15 June 2002. There will also be a poster session at the workshop. If you are interested in presenting a poster, please indicate this with your abstract submission. PROCEEDINGS The organizers invite contributions to - the conference proceedings, to appear as a volume of the "Fields Institute Communications" series, published with the American Mathematical Society - a special volume of the journal "Applied Categorical Structures" (Kluwer) on descent theory Further details will be communicated in the Third Announcement, to be sent in late June. HOUSING Participants should arrange for accommodation on their own. Since tourism is still very active in Toronto during late summer/early fall, we advise participants to make reservations early and call the hotel of their choice soon. Mention that you are visiting the Fields Institute at the University of Toronto to obtain the special rate. Normally a credit card number is required to guarantee a reservation. There is a link to a list of conveniently located hotels and guest houses from the website given above. We hope to welcome you at the workshop. George Janelidze, Bodo Pareigis, Walter Tholen. Confirmed speakers (as of 15 April 2002): Michael Barr, McGill University, Canada Francis Borceux, Univ. Catholique de Louvain, Belgium Dominique Bourn, Univ. Littoral, France Ronnie Brown, Univ. of Wales, UK Marta Bunge, McGill University, Canada Stefaan Caenepeel, Vrije Univ. of Brussels, Belgium Aurelio Carboni, Univ. dell'Insubria, Italy Peter Freyd, Univ. of Pennsylvania, USA Johannes Huebschmann, Univ. de Lille, France Andre Joyal, Univ. de Quebec a Montreal, Canada Max Kelly, Univ. of Sydney, Australia F.W. Lawvere, Univ. of New York at Buffalo, USA Andy Magid, Univ. of Oklahoma, USA Michael Makkai, McGill University, Canada Robert Pare', Dalhousie Univ., Canada Peter Schauenburg, Univ. of Munich, Germany Manuela Sobral, Univ. de Coimbra, Portugal Ross Street, Macquarie Univ., Australia Mitsuhiro Takeuchi, Univ. of Tsukuba Sakura-Mura, Japan Myles Tierney, Rutgers Univ., USA Enrico Vitale, Univ. Catholique de Louvain, Belgium 21-Apr-2002 13:26:20 -0300,4358;000000000000-00000000

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