January 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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paperback announcement: Categorical Logic and Type Theory
by Bart Jacobs 16 Mar '02

16 Mar '02

Dear Colleague, I am happy to announce that Elsevier has now published a paperback version of my book B. Jacobs, Categorical Logic and Type Theory Studies in Logic and the Foundations of Mathematics 141, North Holland, Elsevier, 1999. 780 pages. The regular price of the paperback is NLG 150 / Euro 68.07 / US$ 74 Elsevier now offers a discount of 25% for this paperback if you order before 31 july 2001, using the attached form. In that case the price is: NLG 112.50 / Euro 51 / US$ 55.50. If you wish to use this special offer, please fill in the form, and send it in time to Andy Deelen at Elsevier (precise address at bottom of the form). Do not send it to me. The book gives a survey of categorical logic and type theory starting from the unifying concept of a fibration. Its intended audience consists of logicians, type theorists, category theorists and (theoretical) computer scientists. It contains the following chapters. Prospectus Introduction to fibred category theory Simple type theory Equational Logic First order predicate logic Higher order predicate logic The effective topos Internal category theory Polymorphic type theory Advanced fibred category theory First order dependent type theory Higher order dependent type theory References Notation index Subject index More information can be obtained from the authors webpage: http://www.cs.kun.nl/~bart/CLT/bookinfo.html Bart Jacobs, Dep. Comp. Sci., Univ. Nijmegen, P.O. Box 9010, 6500 GL Nijmegen, The Netherlands. Email: bart(a)cs.kun.nl PS. Please pass this information on to your institute's librarian.

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Positions in Paris 7 University
by Pierre-Louis Curien 01 Feb '02

01 Feb '02

Universite Paris 7 - CNRS Laboratoire d'Informatique Algorithmique : Fondements et Applications (LIAFA) Laboratoire Preuves,, Programmes et Systemes (PPS) APPEL A CANDIDATURES / ANNOUNCEMENT Il y aura au concours 2002 / University Paris 7 will hire in 2002 - 2 postes de professeur d'universite / 2 professors - 3 postes de maitres de conferences / 3 assistant professors en informatique / in computer science. La recherche en informatique est repartie sur deux laboratoires / There are two computer science laboratories at Paris 7: - LIAFA (algorithms and combinatorics, automata, modelisation and verification) - PPS (logic and programming) Les deux laboratoires souhaitent renforcer et elargir leurs thematiques / Both laboratories seek to reinforce and enlarge their research themes. Profils recherches / some possible research profiles for applicants - tous les domaines de competence actuels des deux laboratoires / all present themes of LIAFA and PPS - LIAFA: bases de donnees, bio-informatique, cryptographie, ingenierie de la langue, systemes a evenements discrets / data bases, bio-informatics, cryptography, computational linguistics, discrete event systems - PPS: nous recherchons une ouverture sur les objets, ainsi que sur concurrence et mobilite / we seek expertise on objects, and on mobility and concurrency Application information: The positions will be officially open for application in early 2002. Only candidates who have gone through the national Qualification procedure (application during the autumn of year n for applying to a position in year n+1) are eligible. Rather fluent knowledge of French is expected for teaching. The five positions are permanent positions, starting october 2002. Pour plus d'information sur les deux laboratoires / URL links of the two labs http://www.liafa.jussieu.fr http://www.pps.jussieu.fr Contact : Daniel KROB - Directeur du LIAFA - dk(a)liafa.jussieu.fr Pierre-Louis CURIEN - Directeur de PPS - curien(a)pps.jussieu.fr

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colimits of categories
by david carlton 31 Jan '02

31 Jan '02

Is there a good reference for the construction of colimits of categories? Here, by 'categories', I mean 1-categories; and I'm considering 1Cat as a weak 2-category. I've been playing around with this for the last week; I can construct limits without much trouble (at least if the index category is a 1-category; I assume that changing the index category to a 2-category wouldn't cause any substantial problems), but constructing colimits seems noticeably messier. It's not too bad if your index category is filtered, but in general it seems like a pain. I frequently see statements like 'nCat is expected to have all limits and colimits', so I assume that this has been verified in the case of n=1 somewhere. Also, while I'm asking, does the decategorification operation (from nCat into (n-1)Cat) commute with colimits? I was somewhat surprised to see that decategorification from 1Cat into 0Cat does commute with filtered colimits; so I'm wondering to what extent that statement generalizes. I.e. can I replace 1Cat by nCat, can I remove the word 'filtered', and for that matter can I replace colimits by limits? (I know decategorification doesn't commute with arbitrary limits of 1Cats - indeed, that's arguably where much of the fun of higher category theory comes into play - though I haven't thought too much about whether or not it commutes with filtered limits.) I have reason to hope that decategorification doesn't commute with filtered colimits of 2-categories, but no hard evidence; trying to check that seems like enough of a pain that I'm hoping somebody else has done it first. I haven't thought much about non-filtered colimits since I can't even construct them; I'd be surprised offhand if decategorification commuted with arbitrary colimits. Then again, I was surprised to see that it commuted with filtered colimits, so clearly my intuition isn't the most reliable guide in this case. David Carlton carlton(a)math.stanford.edu 29-Jan-2002 20:56:41 -0400,2784;000000000000-00000000

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Max Kelly recovering quickly
by Ross Street 31 Jan '02

31 Jan '02

Category Theorists may not know that Max Kelly had a heart operation last Friday (25 January 2002). He was given a sextuple bypass. I have heard today from Imogen Kelly that "Max was a lot brighter [yesterday] and is now doing everything by himself. He'll probably come home on Friday." Imogen's bulletin from Tuesday was as follows: ----------------------------------------------------------------

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PSSL 76 - Second Announcement
by Carsten Butz 31 Jan '02

31 Jan '02

PERIPATETIC SEMINAR ON SHEAVES AND LOGIC (PSSL 76) Second Announcement http://www.it-c.dk/research/theory/Seminars/pssl76.html Dear friends and colleagues, The 76th PSSL will be held at the IT-University of Copenhagen over the weekend 2-3 March, 2002. As usual we welcome talks on sheaves, category theory, logic, and related areas such as applications in (theoretical) computer science. As the meeting is informal in nature talks on work in progress are also welcome. Those interested in attending the meeting are kindly asked to complete the registration form below and return it to Carsten Butz (butz(a)it-c.dk) preferably before Monday, February 18. We maintain a webpage for this seminar at http://www.it-c.dk/research/theory/Seminars/pssl76.html which contains some travel information and details about accommodation. We suggest that you make a reservation at the following hotel: Leda Hotel Svanevej 6 2400 Copenhagen NV Tel: +45 35 83 12 22 Fax: +45 35 83 12 24 Email: leda(a)ledahotel.dk Payment: American Express, Cash, Check, Dankort, Diners Club, Eurocard, MasterCard, VISA Rate: DKK 600 (one Euro is about DKK 7.50) The hotel is in walking distance from the IT-University. Please mention that you will be visiting the IT-University to get the special rate of DKK 600. If your budget is tight the webpage suggests some other places further away where you might want to stay. If you need assistance or if you cannot access information on the webpage please do not hesitate to contact us at butz(a)it-c.dk. Looking forward to seeing you here in Copenhagen, Lars Birkedal (IT-C) Carsten Butz (IT-C, butz(a)it-c.dk) Thomas Hildebrandt (IT-C) Anders Kock (Aarhus University) ------------------------------------------------------- PSSL 76 Registration Form Name: Affiliation: Address: Email: I wish to attend the 76th meeting of the PSSL in Copenhagen. *I would like to give a talk entitled: *I have reserved accommodation on my own - at "Leda Hotel" for Friday/Saturday/Sunday night(s) - at another place (please specify) for Friday/Saturday/Sunday night(s) *Please reserve accommodation for me - at "Leda Hotel" for Friday/Saturday/Sunday night(s) - at another place (please specify) for Friday/Saturday/Sunday night(s) *Delete if inappropriate. 30-Jan-2002 19:55:13 -0400,4210;000000000001-00000000

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CFP: Domain Theory Workshop in Honour of Dana Scott's 70'th
by cat-dist＠mta.ca 30 Jan '02

30 Jan '02

birthday

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bases for locally compact spaces
by Paul Taylor 30 Jan '02

30 Jan '02

Bases for spaces Has anyone come across this was of seeing locally compact spaces? We say that a system B_n of VECTORS in a VECTOR SPACE is a BASIS if any other vector U can be expressed as a sum of scalar multiples of basic vectors. Likewise, we say that a system B_n of OPEN SUBSETS of a TOPOLOGICAL SPACE is a BASIS if any other open set U can be expressed as a "sum" (disjunction) of basic opens. How do we find out which basis elements contribute to the sum, and by what scalar multiple? By applying the DUAL BASIS A_n to the given element U, ie A_n.U Then U = sum_n A_n.U * B_n where - "sum" means linear sum, disjunction or existential quantification, - "scalars" in the case of topology range over the Sierpinski space, - the dot denotes - inner product of a dual vector with a vector to yield a scalar, - that U is an element of the family A_n, or - lambda application, - `*' denotes multiplication by a scalar or a vector, or conjunction. In topology, each A_n is a Scott-open family of open subsets. Unfortunately, in general it need not be a filter. In the case where it is a filter, it corresponds by the Hofmann--Mislove theorem to a compact saturated subspace K_n. Then if A_n.U is true, B_n < K_n < U where < denotes non-strict subset inclusion. In this case K_n provides a basis of compact neighbourhoods. Anyway, if A_n.B_n is true then B_n is itself compact open, and more generally A_n.U implies B_n << U ("way below"). Thus, A_n.U is defined in terms of - the traditional definition of local compactness as the existence of a compact subspace between B_n and U - continuous lattices as B_n << U. As you might have guessed, I discovered this during my current work on domain theory in Abstract Stone Duality, and have lambda-terms for A_n and B_n. Indeed, if such a basis exists for a space X then X is a Sigma-split subspace of Sigma^N (in the sense of my recently-announced paper "Subspaces in Abstract Stone Duality"), where i: X -> Sigma^N by x |--> lambda n. B_n.x I: Sigma^X -> Sigma^2 N by U |--> lambda psi. some n. A_n.U * psi.n make Sigma^X a retract of Sigma^2 N. Conversely, given i and I,we define a basis indexed, not by numbers themselves, but by lists (k) of numbers, by B_k.x = all n in k. (i.x).n A_k.U = (I.U).(lambda n.n in k) Paul Taylor (no academic affiliation) ASD web page: http://www.dcs.qmul.ac.uk/~pt/ASD 30-Jan-2002 19:52:11 -0400,2568;000000000001-00000000

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AMAST'2002 **** NEW EXTENDED DEADLINE ****
by Christophe Ringeissen 30 Jan '02

30 Jan '02

[Apologies for multiple copies] AMAST'2002 **** NEW EXTENDED DEADLINE: FEBRUARY 15, 2002 **** In response to multiple requests, the submission deadline is extended until FEBRUARY 15, 2002 ---------------------------------------------------------------------------- AMAST 2002 CALL FOR PAPERS 9-th International Conference on Algebraic Methodology And Software Technology AMAST 2002, September 9-13, 2002 St. Gilles les Bains, Reunion Island, France * Important Dates: Paper submissions February 15, 2002 (EXTENDED DEADLINE) Notification of paper acceptance April 27, 2002 Camera ready papers June 1, 2002 AMAST 2002 conference September 9-13, 2002 * Topics: As in previous years, we invite papers reporting original research on setting software technology on a firm mathematical basis. Of particular interest is research on using algebraic, logic, and other formalisms suitable as foundations for software technology, as well as software technologies developed by means of logic and algebraic methodologies. * Submissions: We invite prospective authors to submit electronically previously unpublished papers of high quality. Papers must be no longer than 15 pages (6 pages for system demonstrations) and should be prepared using LaTeX and the LNCS style that can be downloaded from the URL: http://www.springer.de/comp/lncs/authors.html Please send a fully self-contained PostScript file to amast(a)loria.fr As in the past, the AMAST'2002 proceedings will be published by Springer-Verlag in the Lecture Notes in Computer Science Series. * Program Committee: V.S. Alagar, E. Astesiano, M. Bidoit, D. Bolignano, M. Broy, J. Fiadeiro, B. Fischer, K. Futatsugi, A. Haeberer, N. Halbwachs, A. Haxthausen, D. Hutter, P. Inverardi, B. Jacobs, M. Johnson, H. Kirchner (PC chair), P. Klint, T. Maibaum, Z. Manna, J. Millen, P. Mosses, F. Orejas, R. de Queiroz, T. Rus, C. Ringeissen (PC chair assistant), D. Sannella, P.-Y. Schobbens, G. Scollo, A. Tarlecki, M. Wirsing * Local Organization Chair: Teodor Knapik, Univ. de la Reunion * Further information: For regularly updated details of the conference organization send email to amast(a)loria.fr or visit the AMAST'2002 web page: http://www.loria.fr/conferences/amast2002 30-Jan-2002 09:06:02 -0400,4748;000000000000-00000000

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Re: Operads
by Martin Markl, Mathematical Institute of the Academy 30 Jan '02

30 Jan '02

PROPs invented by Mac Lane in the 1960 do the job; operad is then a special case of a PROP. For example, Hopf algebras and various other bialgebras are described by PROPs. I believe you can find more details in @article{maclane:BAMS65, author={S. {Mac~Lane}}, title={Categorical Algebra}, journal={Bull. Amer. Math. Soc.}, year=1965, volume=71, pages={40--106}} There is also a more special notion called bioperad introduced recently by Wee Liang Gan - see his paper math.QA/0201074 posted on xxx.lanl.gov. Sincerely, Martin > Date: Mon, 19 Nov 2001 09:56:13 -0000 > From: S.J.Vickers(a)open.ac.uk > To: categories(a)mta.ca > Cc: univalg(a)yahoogroups.com > Subject: categories: Operads > > There's some discussion on the Universal Algebra list at present on operads. > > I'm not very familiar with them. What I understand from the discussion is > they capture single sorted algebraic theories with respect to a symmetric > monoidal product ox. For each natural number n an object of n-ary operators > O_n is given, and an algebra A has operations O_n ox A^(n) -> A where A^(n) > is A ox ... ox A n times. > > If you do this sort of thing with respect to categorical product, then it > already contains the information of the Lawvere theory category (for > single-sorted finitary algebraic theories), since hom(m,n) is hom(m,1)^n and > you take hom(m,1) to be O_m. But with a monoidal product this doesn't work. > It seemed to me that for proper generality the operad ought to have objects > O_mn (m, n natural numbers) representing the object of operations from A^(m) > to A^(n). Is there a name for that? > > Steve Vickers > Department of Pure Maths > Faculty of Maths and Computing > The Open University > ----------- > Tel: 01908-653144 > Fax: 01908-652140 > Web: http://mcs.open.ac.uk/sjv22 > > > > > 29-Jan-2002 08:18:52 -0400,3550;000000000001-00000000

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