November 2002 - Categories - categories.org.au

Category Theory and Program Construction
by Claus Gwiggner 29 Nov '02

29 Nov '02

Hello, what is the relation between Category Theory and (Computer) Program Construction ? Don't hesitate to substitute "(Computer) Program Construction" by another, maybe weaker expression, if you feel to. Thanks, Claus 29-Nov-2002 19:56:58 -0400,3356;000000000000-00000000

2 1

Irish School of Constructive Mathematics
by Galchin Vasili 27 Nov '02

27 Nov '02

Hello CAT community, I discovered this topos and intuitionistic logic site and I wanted to call to other people's attention for feedback: http://www.cs.tcd.ie/Micheal.MacanAirchinnigh/Web%20Pages/IRISH_VDM/Master.… In particluar, I have been reading: http://www.cs.tcd.ie/Micheal.MacanAirchinnigh/Web%20Pages/IRISH_VDM/WRITING… and http://www.cs.tcd.ie/Micheal.MacanAirchinnigh/Web%20Pages/IRISH_VDM/WRITING… I would like feedback because I have a more immature view of topos and intuitionistic logic. Regards, Bill Halchin

1 0

Category of generalized diagrams over a given category C
by Philippe Gaucher 26 Nov '02

26 Nov '02

Hello, Given a category C, I am interesting in the category DC defined as follows: an object is a functor F:I-->C where I is a small category, and a morphism from F:I-->C to G:J-->C is a functor from phi:I-->J together with a natural transformation from F to G o phi. If C is locally small (resp. complete, cocomplete, cartesian closed), then so is DC (see CTGDC vol XVIII-4 (1977) "Decompositions et lax-completions", Guitart et Van Den Bril). My question (for today) is : consider the "forgetful functor" from DC to Cat (the category of small categories) sending F:I-->C to I. Does this functor commute with colimits ? The paper above seems to claim that the commutativity holds if the colimit is a coproduct (see p376). What about general colimits ? Thanks in advance for any help or any other pointer for DC. pg. 25-Nov-2002 20:24:28 -0400,1614;000000000000-00000000

2 1

Re: Category of generalized diagrams over a given category
by Steve Lack 26 Nov '02

26 Nov '02

Philippe Gaucher writes: > > Hello, > > Given a category C, I am interesting in the category DC defined as follows: > an object is a functor F:I-->C where I is a small category, and a morphism > from F:I-->C to G:J-->C is a functor from phi:I-->J together with a > natural transformation from F to G o phi. > > If C is locally small (resp. complete, cocomplete, cartesian closed), then > so is DC (see CTGDC vol XVIII-4 (1977) "Decompositions et > lax-completions", Guitart et Van Den Bril). > > My question (for today) is : consider the "forgetful functor" from DC to > Cat (the category of small categories) sending F:I-->C to I. Does this > functor commute with colimits ? The paper above seems to claim that the > commutativity holds if the colimit is a coproduct (see p376). What about > general colimits ? > If C has a terminal object then the functor DC-->Cat has a right adjoint and so preserves any colimits which exist. However now many colimits do exist in DC (apart from coproducts). I don't have the paper of Guitart and Van Den Bril in front of me, but if I remember correctly, DC is the underlying category of a 2-category D'C, and D'C is the free completion of C (seen as a 2-category with no non-identity 2-cells) under lax colimits. And the 2-functor D'C-->Cat preserves lax colimits. Steve Lack. 28-Nov-2002 16:35:02 -0400,1567;000000000000-00000000

1 0

Co-Invertors in the category of CoComplete categories
by Christopher Townsend 25 Nov '02

25 Nov '02

Is anyone aware of an explicit description of the coinvertor of a diagram -> [R^op,Set] -> [C^op,Set] in CoComp (the two arrows are f,g, and there is a natural transofrmation, \alpha:f->g, to be coinverted). C,R are small categories, and the category CoComp is the category of (small) cocomplete categories. Thank you, Christopher Townsend (Open University) 25-Nov-2002 14:56:54 -0400,1581;000000000000-00000000

2 1

Categories, Cognition and Neurosciences
by Andree Ehresmann 24 Nov '02

24 Nov '02

This is to announce a Conference which should attract people interested in applications of categories to Cognition and Neurosciences. Indeed it is organized: "to facilitate development of theoretical tools and methodology required to further our understanding of the brain.... One of its main goals is to provide a platform for experimental neuroscientists to closely interact and exchange ideas with mathematicians working in the areas of category theory and higher dimensional algebra " The "International Conference on Theoretical Neurobiology" will be held at the National Brain Research Centre (Deemed University), New Delhi, India, from February 24 to 28, 2003. More information can be found on the website <http://www.nbrc.ac.in/international_conference_on_theo.htm>http://www.nbrc.ac.in/international_conference_on_theo.htm 28-Nov-2002 16:35:02 -0400,880;000000000000-00000000

1 0

FGC: Foundations of Global Computing
by Vladimiro Sassone 23 Nov '02

23 Nov '02

=09=09 FGC: Foundations of Global Computing =09=09=09 2nd EATCS Workshop =09 <http://www.cogs.susx.ac.uk/users/vs/fgc> =09=09 co-located with ICALP2003 =09 28-29 June 2003, Eindhoven, The Netherlands =09=09 Announcement and Call for papers =09=09 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Aims and Scope Foundations of Global Computing focuses on foundational aspects of global computing, and invites submissions of original scientific work thereof. A non-exclusive list of topics includes: * calculi, models, and semantic theories of concurrent, distributed, mobile, global-computing systems; * languages, security, types, protocols and algorithms for global computing. Further points of specific interest are grid computing, peer-to-peer systems, game-theoretic approaches, protocol analysis, trust management, language-based security, ... The workshop proceedings will be published in the ENTCS series and a selection of papers will appear in a special issue of a leading Computer Science journal. It will be held as a ICALP2003 satellite event under the auspices of the EATCS. Invited Speakers C=E9dric Fournet (Microsoft Research) Robert Harper (CMU) Martin Hofmann (LMU Munich) Li Gong (SUN Microsystems) (joint speaker with twin SecCo`03) Programme Committee Luca Cardelli (Microsoft) Rocco De Nicola (Florence) Andrew D. Gordon (Microsoft) Jan van Leeuwen=09(Utrecht) John C. Mitchell (Stanford) Eugenio Moggi=09(Genoa) Ugo Montanari (Pisa) Greg Morrisett (Cornell) Mogens Nielsen (Aarhus) Don Sannella (Edinburgh) Vladimiro Sassone (Sussex) Vasco T. Vasconcelos (Lisbon) Martin Wirsing (LMU Munich) Important Dates Submission 27 Apr 2003 (midnight GMT-11 -- Samoa time) Notification 2 Jun 2003 PreFinal version 15 Jun 2003 Final version 31 Jul 2003 Submissions Authors are invited to submit an extended abstract of their papers, presenting original contributions to the workshop themes. Submissions should be in English and not exceed 15 standard pages. They should be sent as PS or PDF files to fgc(a)cogs.susx.ac.uk and be accompanied by a text-only message containing: title, abstract and keywords, the authors' full names, and address and e-mail for correspondence. Simultaneous submission to other meetings with published proceedings is not allowed. Organising Committee * Erik de Vink (Eindhoven) 25-Nov-2002 14:56:54 -0400,1124;000000000000-00000000

1 0

Preprint:One setting for all: metric, topology, uniformity, approach structure
by Walter Tholen 22 Nov '02

22 Nov '02

This is to announce the availability of the paper "One setting for all: metric, topology, uniformity, approach structure" by M.M. Clementino, D. Hofmann and W. Tholen at http://www.mat.uc.pt/~mmc/preprints/ http://math.yorku.ca/Who/Faculty/Tholen/research.html Abstract For a complete lattice V which, as a category, is monoidal closed, and for a suitable Set-monad T we consider (T,V)-algebras and introduce (T,V)-proalgebras, in generalization of Lawvere's presentation of metric spaces and Barr's presentation of topological spaces. In this lax-algebraic setting, uniform spaces appear as proalgebras. Since the corresponding categories behave functorially in T and in V, one establishes a network of functors at the general level which describe the main connections between the structures mentioned in the title. Categories of (T,V)-algebras and of (T,V)-proalgebras turn out to be topological over Set. 25-Nov-2002 10:24:06 -0400,3120;000000000000-00000000

1 0

Workshop on Categorification and Higher-Order Geometry, 1st announcement
by Roger Picken 21 Nov '02

21 Nov '02

First announcement Workshop on Categorification and Higher-Order Geometry 23-24 July, 2003 Instituto Superior Tecnico, Lisbon, Portugal Confirmed main speakers to date: JOHN BAEZ, Univ. California at Riverside "Categorified Lie groups, Lie algebras, bundles and connections" LAWRENCE BREEN, Univ. Paris 13 (on non-abelian gerbes) LOUIS CRANE, Kansas State Univ. (to be announced) MIKHAIL KHOVANOV, Univ. California at Davis (on categorification of the Jones polynomial) STEPHAN STOLZ, Univ. Notre Dame (on elliptic objects) This workshop is a satellite event of the International Conference on Mathematical Physics, 28th July - 2nd August, 2003, Lisbon, Portugal (http://icmp2003.net/) Apart from the invited talks, there will be slots available for contributed talks. People interested in giving a contributed talk should contact the organisers as soon as possible to register their interest, and send a title and abstract before 31st January, 2003. The list of accepted talks will be announced before April 1st. Marco Mackaay: mmackaay(a)ualg.pt Roger Picken: rpicken(a)math.ist.utl.pt Due to the limitations of the budget it is unlikely that financial support will be available except for the main speakers and perhaps some local students. Further information will be provided on the conference homepage: http://www.math.ist.utl.pt/~rpicken/CHOG2003 21-Nov-2002 21:23:46 -0400,1246;000000000000-00000000

1 0

Positions available
by R J Steiner 21 Nov '02

21 Nov '02

Positions available There are two Lectureships in Mathematics available at the University of Glasgow. For details see http://www.gla.ac.uk/services/humanresources/recruit/24jan_546.htm. Richard Steiner<underline><color><param>0000,8000,0000</param><bigger> <nofill> --------------------------------------------------- Richard Steiner Department of Mathematics, University of Glasgow, University Gardens, Glasgow, Great Britain G12 8QW E-mail: r.steiner(a)maths.gla.ac.uk Telephone: (0141) 330 6538 Fax: (0141) 330 4111 22-Nov-2002 09:37:09 -0400,1674;000000000000-00000000

1 0