From MAILER-DAEMON Tue Feb 3 09:00:50 2009 Date: 03 Feb 2009 09:00:50 -0400 From: Mail System Internal Data Subject: DON'T DELETE THIS MESSAGE -- FOLDER INTERNAL DATA Message-ID: <1233666050@mta.ca> X-IMAP: 1231334861 0000000064 Status: RO This text is part of the internal format of your mail folder, and is not a real message. It is created automatically by the mail system software. If deleted, important folder data will be lost, and it will be re-created with the data reset to initial values. From rrosebru@mta.ca Wed Jan 7 09:25:27 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 07 Jan 2009 09:25:27 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LKYMf-0007kn-Hz for categories-list@mta.ca; Wed, 07 Jan 2009 09:22:29 -0400 Date: Wed, 07 Jan 2009 09:00:03 +0100 From: Andree Ehresmann To: Categories list Subject: categories: Seminar MaMuX MIME-Version: 1.0 Content-Type: text/plain;charset=ISO-8859-1;DelSp="Yes";format="flowed" Content-Disposition: inline Content-Transfer-Encoding: quoted-printable Sender: categories@mta.ca Precedence: bulk Reply-To: Andree Ehresmann Message-Id: Status: O X-Status: X-Keywords: X-UID: 1 Transmitted from Moreno Andreatta Journ=E9e commune des s=E9minaires mamuphi et MaMuX Samedi 17 janvier 2009 ENS (matin=E9e) et IRCAM (apr=E8s midi) Programme de la journ=E9e (entr=E9e libre dans la mesure des places disponib= les) : 11h ? 13h (ENS, Salle S. Weil) - Christian Houzel : Th=E9orie des =20 faisceaux et linguistique 15h ? 18h (Ircam, Salle I. Stravinsky) - Andr=E9e C. Ehresmann et =20 Jean-Paul Vanbremeersch : MENS, un mod=E8le math=E9matique pour des =20 syst=E8mes cognitifs R=E9sum=E9s et rep=E8res bibliographiques : Th=E9orie des faisceaux et linguistique (Christian Houzel) Les productions des langues naturelles se pr=E9sentent comme des =20 concat=E9nations d'=E9l=E9ments. On peut traduire math=E9matiquement la =20 concat=E9nation par la loi de composition d'un mono=EFde. Mais toute suite = =20 de mots ne constitue pas une phrase ; il faut une structure =20 syntaxique. De telles structures constituent les morphismes d'une =20 cat=E9gorie mono=EFdale. Les th=E9ories interpr=E9tatives, comme la phonolog= ie =20 ou la s=E9mantique introduisent des filtres additionnels, qu'il para=EEt =20 convenable de prendre en compte au moyen d'une topologie convenable. =20 Une th=E9orie interpr=E9tative est alors repr=E9sent=E9e par un faisceau sur= =20 un site convenable. MENS, un mod=E8le math=E9matique pour des syst=E8mes cognitifs (Andr=E9e C. = =20 Ehresmann et Jean-Paul Vanbremeersch) Comment des processus mentaux d'ordre sup=E9rieur =E9mergent-ils du =20 fonctionnement du cerveau? Telle est la question que nous abordons =20 dans le mod=E8le MENS (Memory Evolutive Neural Systems), d=E9velopp=E9 dans = =20 notre livre (Ehresmann & Vanbremeersch, 2007); les objets mentaux y =20 sont mod=E9lis=E9s par des cat-neurones (neurones de cat=E9gorie), ou =20 'neurones d'ordre sup=E9rieur', liant une multiplicit=E9 =20 d'hyper-assembl=E9es de neurones Ce mod=E8le math=E9matique est une application aux syst=E8mes cognitifs de = =20 notre mod=E8le g=E9n=E9ral "Syst=E8mes Evolutifs =E0 M=E9moire" pour des sys= t=E8mes =20 complexes autonomes, tels que les syst=E8mes biologiques ou sociaux. Il =20 est bas=E9 sur la th=E9orie des cat=E9gories (Eilenberg & Mac Lane, 1945) = =20 qui permet de d=E9crire un processus de "complexification" par liage et =20 classification (via colimites et limites projectives). Nous montrons =20 comment des objets de complexit=E9 croissante peuvent =E9merger par une =20 suite de complexifications, d=E8s lors qu'un certain "principe de =20 multiplicit=E9" ("degeneracy" pour Edelman, 1989; Edelman & Gally, 2001) =20 est v=E9rifi=E9. Le mod=E8le MENS permet de d=E9crire le d=E9veloppement d'une "alg=E8bre des= =20 objets mentaux" (au sens de Changeux, 1983) et d'une m=E9moire =20 s=E9mantique =E0 partir du syst=E8me neuronal (en accord avec les donn=E9es = =20 neurologiques). Ceci m=E8ne =E0 la formation d'un invariant global, le =20 noyau arch=E9typal, confirm=E9 par la d=E9couverte r=E9cente, dans le cervea= u, =20 du "neural connection core" (Hagmann & al., 2008). Ce noyau arch=E9typal =20 int=E8gre les exp=E9riences saillantes et/ou r=E9guli=E8rement r=E9-enforc= =E9es =20 (sensitives, motrices, =E9motionnelles, proc=E9durales, s=E9mantiques). Il = =20 est =E0 la base de la notion de Soi et du d=E9veloppement de la =20 conscience, caract=E9ris=E9e en particulier par les processus d'extension = =20 temporelle (r=E9trospection et prospection). MENS soul=E8ve les probl=E8mes de l'=E9mergence, de la conscience, du Soi et= =20 du rapport corps/esprit. Quelques rep=E8res bibliographiques : - Changeux, J.-P., 1983, L'homme neuronal, Fayard, Paris. - Edelman, G.M., 1989, The remembered Present, Basic Books, New York. - Edelman, G.M. and Gally, J.A., 2001, Degeneracy and complexity in =20 biological systems, Proc. Natl. Acad. Sci. USA 98, 13763-13768. - Ehresmann, A.C. and Vanbremeersch J.-P., 2007, Memory Evolutive =20 Systems: Hierarchy, Emergence, Cognition, Elsevier, Amsterdam. - Eilenberg, S. and Mac Lane, S., 1945, General theory of natural =20 equivalences, Trans. Am. Math. Soc. 58, 231-294. - Hagmann, P., Cammoun, L., Gigandet, X., Meuli, R., Honey, C.J., Van =20 J. Wedeen & Sporns, O., 2008, Mapping the Structural Core of Human =20 Cerebral Cortex, PLoS Biology 6, Issue 7, 1479-1493. Online: =20 www.plosbiology.org Autres s=E9ances du s=E9minaire mamuphi : - Samedi 7 f=E9vrier 2009 (salle S. Weil) - Ren=E9 Guitart - Samedi 7 mars 2009 (salle des Actes) - Pierre Lochak - Samedi 4 avril 2009 (salle Beckett) - Jean B=E9nabou : Magie des =20 topos, ou topos et magie? - Samedi 9 mai 2009 (salle S. Weil) - s=E9ance =E0 d=E9finir Contacts Pour tout renseignement, contacts et propositions : Fran=E7ois Nicolas (fnicolas[at]ens.fr) Charles Alunni (charles.alunni[at]ens.fr) Moreno Andreatta (andreatta[at]ircam.fr) Autres s=E9ances du s=E9minaire MaMuX : - Vendredi 23 janvier : Musique et Cognition. Autour de l?apport de =20 John Sloboda (s=E9ance exceptionnelle du s=E9minaire organis=E9e en =20 collaboration avec Ir=E8ne Deli=E8ge et sous l?=E9gide de l?ESCOM, =20 Association europ=E9enne pour les sciences cognitives de la musique) - Vendredi 6 f=E9vrier 2009 : Combinatorial Block-Designs. Avec la =20 participation de Reinhard Laue (Universit=E4t Bayreuth, Allemagne), =20 Franck Jedrzejewski (CEA Saclay, INST/UESMS) et Tom Johnson =20 (compositeur) - Vendredi 6 mars 2009 : Math=E9matiques/Musique et S=E9miotique. Les =20 unit=E9s s=E9miotiques temporelles (s=E9ance organis=E9e en collaboration av= ec =20 le MIM, Laboratoire Musique et Informatique de Marseille) - Vendredi 3 avril 2009 : S=E9ance =E0 d=E9finir - Vendredi 8 mai 2009 : S=E9ance =E0 d=E9finir Contacts Pour tout renseignement, contacts et propositions : Moreno Andreatta (andreatta[at]ircam.fr) Carlos Agon Amado (agonc[at]ircam.fr) Adresses : S=E9minaire mamuphi (math=E9matiques/musique/philosophie) http://www.entretemps.asso.fr/maths/ ENS, Salle S. Weil 45, rue d?Ulm 75005 Paris S=E9minaire MaMuX (Math=E9matiques/Musique et relations avec d'autres discip= lines) http://recherche.ircam.fr/equipes/repmus/mamux/ Ircam, Salle I. Stravinsky 1, place I. Stravinsky 75004 Paris Le programme complet de la journ=E9e est disponible en pdf =E0 l'adresse : http://recherche.ircam.fr/equipes/repmus/mamux/MamuPhiXJanvier2009.pdf From rrosebru@mta.ca Wed Jan 7 12:25:23 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 07 Jan 2009 12:25:23 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LKbCM-0003UT-Pk for categories-list@mta.ca; Wed, 07 Jan 2009 12:24:02 -0400 Date: Wed, 7 Jan 2009 16:12:13 +0000 (GMT) From: Jocelyn Paine To: categories@mta.ca Subject: categories: Web-based category theory demonstrations MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: categories@mta.ca Precedence: bulk Reply-To: Jocelyn Paine Message-Id: Status: O X-Status: X-Keywords: X-UID: 2 This is to reannounce a selection of Web-based category theory demonstrations that I've put up at http://www.j-paine.org/cgi-bin/webcats/webcats.php . The page contains a number of buttons such as "generate and demonstrate an equaliser" and "generate and demonstrate a limit". Clicking on one will generate an example of the construct in the category of finite sets, and display it as a listing of its objects and arrows, and as a diagram. My latest demo generates examples of exponential objects, using the same notation as the Wikipedia article at http://en.wikipedia.org/wiki/Exponential_object . Bug reports, and suggestions for improvement, would be very welcome. Jocelyn Paine http://www.j-paine.org http://www.spreadsheet-factory.com From rrosebru@mta.ca Thu Jan 8 08:49:49 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 08 Jan 2009 08:49:49 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LKuIj-0006zI-Qa for categories-list@mta.ca; Thu, 08 Jan 2009 08:47:53 -0400 Mime-Version: 1.0 (Apple Message framework v753.1) Content-Type: text/plain; charset=US-ASCII; delsp=yes; format=flowed Content-Transfer-Encoding: 7bit From: Ross Street Subject: categories: Publications of Brian Day Date: Thu, 8 Jan 2009 12:45:34 +1100 To: categories Sender: categories@mta.ca Precedence: bulk Reply-To: Ross Street Message-Id: Status: RO X-Status: X-Keywords: X-UID: 4 I would like to draw your attention to the following page of Brian's publications. I try to keep it within a month or so of being up to date. The first two items on the list are scanned copies of his Masters and PhD theses: [Thesis1] Relationship of Spanier's Quasi-topological Spaces to k- Spaces (Master of Science Thesis, University of Sydney, 1968) . [Thesis2] Construction of Biclosed Categories (PhD Thesis, University of New South Wales, 1970) . Best wishes to all for 2009, Ross From rrosebru@mta.ca Fri Jan 9 09:44:07 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 09 Jan 2009 09:44:07 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LLHcb-00043J-Uj for categories-list@mta.ca; Fri, 09 Jan 2009 09:41:58 -0400 Date: Thu, 08 Jan 2009 17:00:00 -0500 From: Walter Tholen MIME-Version: 1.0 To: categories@mta.ca Subject: categories: Paper available Content-Type: text/plain; charset=us-ascii; format=flowed Content-Transfer-Encoding: 7bit Sender: categories@mta.ca Precedence: bulk Reply-To: Walter Tholen Message-Id: Status: O X-Status: X-Keywords: X-UID: 5 The paper "On the categorical meaning of Hausdorff and Gromov distances, I" by Andrei Akhvlediani, Maria Manuel Clementino and myself is available at http://arxiv.org/abs/0901.0618 and on my homepage at http://math.yorku.ca/~tholen/ The paper expands on ideas offered in Maria Manuel Clementino's talk at CT08 and in my talks at the Octoberfest in Montreal and at the Borceux-Bourn Birthday Conference in Brussels in October. We welcome comments. Regards, Walter Tholen. From rrosebru@mta.ca Fri Jan 9 09:44:07 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 09 Jan 2009 09:44:07 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LLHe2-0004CJ-Ci for categories-list@mta.ca; Fri, 09 Jan 2009 09:43:26 -0400 To: cfp@clip.dia.fi.upm.es Subject: categories: 10 PhD, PostDoc, and Engineering Positions offered!! From: CFP Date: Fri, 09 Jan 2009 11:01:05 +0100 Sender: categories@mta.ca Precedence: bulk Reply-To: CFP Message-Id: Status: O X-Status: X-Keywords: X-UID: 6 10 PhD, PostDoc, and Engineering Positions offered!! ----------------------------------------------------------------------- | HATS: Highly Adaptable and Trustworthy Software using Formal Models | ----------------------------------------------------------------------- HATS is a new Integrated Project funded by the European Union, within the programme "Future and Emerging Technologies" (FET) of the 7th Framework Programme (subject to contract) starting March 2009. The project partners from Chalmers Technical University, Gothenborg, Sweden University of Oslo, Norway Royal Institute of Technology, Stockholm, Sweden Technical University of Madrid, Spain IMDEA Software, Spain Technical University of Kaiserslautern, Germany, University of Bologna, Italy, Centrum voor Wiskunde en Informatica (CWI), Amsterdam, Netherlands Norwegian Computer Center, Oslo, Norway Fredhopper B.V., Amsterdam, Netherlands Fraunhofer Institute for Experimental SE, Kaiserslautern, Germany, Katholieke Universiteit Leuven, Belgium are jointly advertising several 3-5 year PhD, PostDoc, and Engineering positions. The goal of HATS is a tool-supported framework and formal methodology for the development of long-lived and trustworthy software systems. Specifically, HATS will turn software product family (SWPF) development into a rigorous approach. The technical core of the project is an Abstract Behavioral Specification language which will allow precise description of SWPF features and components and their instances. For further information see: http://www.hats-project.eu Topic areas: Applicants should have a background and/or interest in one of the topics software modeling, modeling and programming languages, formal methods, verification, language-based security, type systems, or concurrency theory. The following positions are offered: * 2 PhD positions with emphasis on formal modeling and verification at Chalmers University of Technology. One of the positions is in the EU project CHARTER which is closely related to HATS. Application deadline is 9th February 2009. Contact: Prof. Reiner Haehnle. Further details and information on how to apply at http://www.chalmers.se/cse/EN/news/vacancies/positions/two-ph-d-student * A Research Software Engineer at Fredhopper (Amsterdam). The position will comprise of industrial research on modeling and verification of key components of Fredhopper's flagship product within the EU-funded HATS research project. Fredhopper is the Nr. 1 provider of Search & Merchandising solutions for online business in Europe and industrial leader in the HATS project. Apply by 31 January 2009 for the most optimal procedure. Contact for project information: Dr. Nikolay Diakov. More information and how to apply at: http://www.fredhopper.com/public/company-opps.php?cat=0&subcat=0#research-software-engineer * 2 PostDoc positions at the University of Bologna. The emphasis is on formal modeling and verification of the kind of concurrent systems studied in Hats using various techniques, including behavioural techniques and type systems. Application deadline is 31 January (later applications may also be taken into account). Contact: Prof. Davide Sangiorgi, see: http://www.cs.unibo.it/~sangio/Hats/vacancies.txt * 3 PhD positions with emphasis on static analysis and security at the Technical University of Madrid/IMDEA Software. One of the positions is in the DOVES Spanish project, which is closely related to HATS. The application deadline is 25 January. Later applications may also be taken into account if the positions are not covered. Contact: Prof. German Puebla. Further details and information on how to apply at http://clip.dia.fi.upm.es/Job_Openings/hats-doves-phd-grants.html * 1 PhD and 1 PostDoc position in the area of software modeling and verification at the University of Kaiserslautern. The emphasis in the area of software modeling is on semantically founded integration of behavioral software models, feature-based descriptions of variability and programs. The emphasis in verification is on modular techniques for object-oriented models and model refinement. Application deadline is January 31. Later applications may also be taken into account. Contact: Prof. A. Poetzsch-Heffter. Further details and information on how to apply at http://softech.informatik.uni-kl.de/Homepage/OffeneStellen * Further positions will be announced at this space! Applicants should have (or expect to have at the start of employment): * For a PhD position: a good Masters level or excellent Bachelor level degree (or equivalent) in computer science, mathematics, or a closely related discipline with knowledge in the areas above. Please see also individual requirements at each site which can differ. * For a Postdoc position: a PhD in computer science or mathematics, preferably with research experience in one of the listed topic areas. * For a software engineer position: a Masters or PhD level level degree (or equivalent) in computer science, mathematics, or a closely related discipline with good knowledge in the areas of program verification, automata theory or discrete math. Knowledge of Java and some programming experience count as a plus. Regardless of the specific application instructions, each application should contain: 1) a full CV including letters of recommendation 2) a research statement, indicating the research directions you are interesting in and what relevant experience you have 3) transcripts of degree results where available. To apply, please follow the links given above. Expressions of interest received by 15 January 2009 are guaranteed full consideration. Specific application deadlines may vary. Early contact would be appreciated. From rrosebru@mta.ca Fri Jan 9 09:44:07 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 09 Jan 2009 09:44:07 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LLHbW-0003wn-7u for categories-list@mta.ca; Fri, 09 Jan 2009 09:40:50 -0400 Date: Thu, 8 Jan 2009 10:46:56 -0500 (EST) From: Michael Barr To: Categories list Subject: categories: Tripleableness via split equivalence relations MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed Sender: categories@mta.ca Precedence: bulk Reply-To: Michael Barr Message-Id: Status: O X-Status: X-Keywords: X-UID: 7 I have a memory that someone (Linton or Manes, maybe) proved a variation on the PTT involving split ERs. Can someone provide a reference? I thought it would be in LNM 80, but I couldn't find it there. Michael From rrosebru@mta.ca Fri Jan 9 09:44:27 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 09 Jan 2009 09:44:27 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LLHel-0004GM-JU for categories-list@mta.ca; Fri, 09 Jan 2009 09:44:11 -0400 Date: Fri, 9 Jan 2009 14:45:10 +0200 (EET) Subject: categories: Category Theory Papers From: "Georgios Nassopoulos" To: categories@mta.ca MIME-Version: 1.0 Content-Type: text/plain;charset=iso-8859-7 Content-Transfer-Encoding: quoted-printable Sender: categories@mta.ca Precedence: bulk Reply-To: "Georgios Nassopoulos" Message-Id: Status: O X-Status: X-Keywords: X-UID: 8 A new paper, A functorial approach to group C*-algebras, is at http://users.uoa.gr/~gnassop as well as past papers: -Spectral Decomposition and Duality in Commutative Locally C*- Algebras -Duality, uniqueness of topology and automatic continuity of *-homomorphisms in bornological locally C*-algebras -On a comparison of real with complex involutive complete algebras -A characterization of the base category V by its single object Pr. G. F .Nassopoulos From rrosebru@mta.ca Fri Jan 9 21:44:26 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 09 Jan 2009 21:44:26 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LLSqU-0000CU-UG for categories-list@mta.ca; Fri, 09 Jan 2009 21:41:02 -0400 Date: Fri, 9 Jan 2009 11:30:14 -0500 (EST) From: Michael Barr To: Categories list Subject: categories: Re: Tripleableness via split equivalence relations MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed Sender: categories@mta.ca Precedence: bulk Reply-To: Michael Barr Message-Id: Status: O X-Status: X-Keywords: X-UID: 9 It turns out that what I asked about is in TTT, Section 9.1. It starts on p. 250 of the electronic version, p. 303 of the print edition. The result is due to Jack Duskin. Michael From rrosebru@mta.ca Fri Jan 9 21:44:26 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 09 Jan 2009 21:44:26 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LLSrj-0000Ee-BT for categories-list@mta.ca; Fri, 09 Jan 2009 21:42:19 -0400 From: vs27@mcs.le.ac.uk To: categories@mta.ca Subject: categories: Re: Paper available Date: 09 Jan 2009 18:03:12 +0000 Mime-Version: 1.0 Content-Type: text/plain; format=flowed; charset=ISO-8859-1 Sender: categories@mta.ca Precedence: bulk Reply-To: vs27@mcs.le.ac.uk Message-Id: Status: O X-Status: X-Keywords: X-UID: 10 Hi Walter, let me advert my paper on a similar and related subject http://arxiv.org/abs/math/0602463 "Flatness, preorders and generalized metric spaces" that treats completions of non symmetric spaces. It took some time to be written but it is going to appear (in an improved version) in the Georgian Mathematical Journal. Cheers, V. On Jan 9 2009, Walter Tholen wrote: >The paper >"On the categorical meaning of Hausdorff and Gromov distances, I" >by Andrei Akhvlediani, Maria Manuel Clementino and myself is available at >http://arxiv.org/abs/0901.0618 >and on my homepage at >http://math.yorku.ca/~tholen/ > >The paper expands on ideas offered in Maria Manuel Clementino's talk at >CT08 and in my talks at the Octoberfest in Montreal and at the >Borceux-Bourn Birthday Conference in Brussels in October. >We welcome comments. > >Regards, >Walter Tholen. > > > > > > From rrosebru@mta.ca Sat Jan 10 13:00:33 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 10 Jan 2009 13:00:33 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LLhAI-0003rf-CB for categories-list@mta.ca; Sat, 10 Jan 2009 12:58:26 -0400 Date: Fri, 09 Jan 2009 23:08:42 -0800 From: Vaughan Pratt MIME-Version: 1.0 To: categories@mta.ca Subject: categories: Re: Paper available Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Sender: categories@mta.ca Precedence: bulk Reply-To: Vaughan Pratt Message-Id: Status: O X-Status: X-Keywords: X-UID: 11 Vincent's paper vs27@mcs.le.ac.uk wrote: > Hi Walter, let me advert my paper > on a similar and related subject > http://arxiv.org/abs/math/0602463 > "Flatness, preorders and generalized metric spaces" > that treats completions of non symmetric spaces. > Cheers, > V. reminds me of a question I've been meaning to ask for several years, in fact since my CT'04 talk on communes over bimodules, but wasn't quite sure how to formulate. In any setting, ordinary or enriched, it is possible to introduce presheaves immediately after defining "category," even before defining "functor." Ordinarily one does not do so because functors are more fundamental to category theory than presheaves, being an essential stepping stone to the notion of natural transformation, Mac Lane's motivating entity for the whole CT enterprise. But just as dessert tends to lose its appeal when complete demolition of the main course is a prerequisite, so are applications of CT most effective for a foreign (non-CT) audience when they don't assume that the whole CT enchilada has been digested. For applications of presheaves it is helpful to know what is the absolute minimum of CT required by the audience. Just as it is not necessary to understand the principle of the internal combustion engine when getting one's driver's license by showing that one can control such an engine, it should not be necessary to know what a functor, natural transformation, adjunction, or colimit is to freely construct a presheaf on a small category J as a colimit. The following construction should suffice for those who know nothing more about CT than the definition of category. Grow a presheaf category C starting with C = J (with Set^{J^op} as the unstated secret goal) as follows. Independently adjoin objects x to C. For each such x and each object j in J, further adjoin morphisms from j to x (more generally in the V-enriched case, assign an object of V to C(j,x)), with composites of the morphisms of C(j,x) with those of J chosen subject only to the requirement that C remain a category. For any objects x,y of C, with x not in J (y in J is ok), populate C(x,y) with as many morphisms f,g,... as possible (in the V-enriched case, a suitable limit), again choosing composites with morphisms from any j to x arbitrarily, subject to the requirements that (i) if for all j and all morphisms a: j --> x, fa = ga, then f = g, and (ii) again that C remain a category (which then determines all remaining composites x --> y --> z). A pre-question here is, did I inadvertently leave anything out? My main question is, is there a reference for this process that I can cite? Any such reference must make the point that the prerequisites for this process include categories but exclude the rest of CT (as prerequisites---obviously some additional parts of CT are directly derivable, the point is that they're not prerequisites for the student). Ordinarily one reason for not bothering with such a thing would be that one can avoid even the categories by talking about equational theories with only unary operations. My application however is to communes, which are trickier to describe from a purely algebraic perspective (they're chupological rather than coalgebraic), but very natural from the above colimit-based perspective. Vaughan From rrosebru@mta.ca Tue Jan 13 19:32:32 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 13 Jan 2009 19:32:32 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LMsh9-0006TN-Pk for categories-list@mta.ca; Tue, 13 Jan 2009 19:29:15 -0400 To: mfpsmail@linus.math.tulane.edu, categories@mta.ca Content-Type: text/plain; charset=US-ASCII; format=flowed; delsp=yes Content-Transfer-Encoding: 7bit Mime-Version: 1.0 (Apple Message framework v930.3) Subject: categories: MFPS Deadlines Revised and Extended! Date: Mon, 12 Jan 2009 07:44:44 -0600 From: MFPS Sender: categories@mta.ca Precedence: bulk Reply-To: MFPS Message-Id: Status: RO X-Status: X-Keywords: X-UID: 12 Dear Colleagues, The deadlines for submissions to MFPS 25 have been revised and extended. The new deadlines are: - January 20 Title and Short Abstract submission deadline - January 24 Paper submission deadline The other dates remain the same. Details about submission requirements and information about the meeting can be found at the MFPS 25 Home page http://www.math.tulane.edu/~mfps/mfps25.htm Submissions can be made to EasyChair by pointing your browser at http://www.easychair.org/conferences/?c=.120373;conf=mfps25 Mathematical Foundations of Programming Semantics http://www.math.tulane.edu/~mfps From rrosebru@mta.ca Tue Jan 13 19:32:59 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 13 Jan 2009 19:32:59 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LMskb-0006lw-8m for categories-list@mta.ca; Tue, 13 Jan 2009 19:32:49 -0400 Date: Tue, 13 Jan 2009 12:28:00 +0100 (CET) Subject: categories: Special volumes in honour of Francis Borceux and of Dominique Bourn From: "Marino Gran" To: categories@mta.ca MIME-Version: 1.0 Content-Type: text/plain;charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable Sender: categories@mta.ca Precedence: bulk Reply-To: "Marino Gran" Message-Id: Status: O X-Status: X-Keywords: X-UID: 13 =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D SPECIAL VOLUMES IN HONOUR OF FRANCIS BORCEUX AND OF DOMINIQUE BOURN ON TH= E OCCASION OF THEIR SIXTIETH BIRTHDAY Last year Francis Borceux and Dominique Bourn celebrated their 60th birthday, and an international meeting in their honour took place at the Royal Academy in Brussels last October (see http://www.math.ua.ac.be/bbdays/). We are glad to announce that there will be a Special Volume of the Cahier= s de Topologie et G=E9om=E9trie Diff=E9rentielle Cat=E9goriques dedicated t= o Francis Borceux, and a Special Volume of Theory and Applications of Categories dedicated to Dominique Bourn. Submission of papers on areas in which Francis Borceux and Dominique Bour= n have worked are particularly encouraged. The deadline for submission for both volumes is 31 May 2009. Please find the instructions for submission of papers below. With our best wishes for the New Year, Jiri Adamek, Andr=E9e Ehresmann, Marino Gran, George Janelidze, Rudger Kieboom, Jiri Rosicky, Walter Tholen and Enrico Vitale =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D - SPECIAL VOLUME FOR FRANCIS BORCEUX (CAHIERS): Please email your submission to Marino Gran (marino.gran@uclouvain.be) as an attached PDF file: you may suggest one of the Guest Editors Jiri Adamek Andr=E9e Ehresmann Marino Gran George Janelidze Rudger Kieboom for this Special Volume to be assigned to your paper. Please be sure that you receive an e-mail acknowledging the receipt of your submission. All papers will be carefully refereed following the standards of Cahiers de Topologie et G=E9om=E9trie Diff=E9rentielle Cat=E9goriques. =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D - SPECIAL VOLUME FOR DOMINIQUE BOURN (TAC): Please email your submission to Enrico Vitale (enrico.vitale@uclouvain.be= ) as an attached PDF file: you may suggest one of the Guest Editors Andr=E9e Ehresmann George Janelidze Jiri Rosicky Walter Tholen Enrico Vitale for this Special Volume to be assigned to your paper. Please be sure that you receive an e-mail acknowledging the receipt of your submission. All papers will be carefully refereed following the standards of Theory and Applications of Categories. From rrosebru@mta.ca Fri Jan 16 00:03:03 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 16 Jan 2009 00:03:03 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LNfs7-0001BA-Vh for categories-list@mta.ca; Thu, 15 Jan 2009 23:59:52 -0400 Date: Thu, 15 Jan 2009 19:25:05 -0500 (EST) From: Rory Lucyshyn-Wright To: categories@mta.ca Subject: categories: Paper available: "A Lax-Algebraic Approach to Domain-Theoretic Topology" MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed Sender: categories@mta.ca Precedence: bulk Reply-To: Rory Lucyshyn-Wright Message-Id: Status: O X-Status: X-Keywords: X-UID: 14 My paper "A Lax-Algebraic Approach to Domain-Theoretic Topology" is available on my web site, at "http://www.math.yorku.ca/~rorylw/". The paper documents and builds upon results presented in my talk at the 2008 OctoberFest in Montreal. Your comments are welcome. Regards, Rory Lucyshyn-Wright From rrosebru@mta.ca Sat Jan 17 12:35:38 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 17 Jan 2009 12:35:38 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LOE5l-000197-5a for categories-list@mta.ca; Sat, 17 Jan 2009 12:32:13 -0400 From: "mail.btinternet.com" To: Subject: categories: Bangor mathematics web pages Date: Sat, 17 Jan 2009 10:41:13 -0000 MIME-Version: 1.0 Content-Type: text/plain;format=flowed; charset="iso-8859-1";reply-type=original Content-Transfer-Encoding: 7bit Sender: categories@mta.ca Precedence: bulk Reply-To: "mail.btinternet.com" Message-Id: Status: O X-Status: X-Keywords: X-UID: 15 These have now transferred to http://www.math.bangor.ac.uk/ Please update your links. Ronnie Brown Previously this was http://www.informatics.bangor.ac.uk/public/mathematics From rrosebru@mta.ca Sun Jan 18 20:54:51 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 18 Jan 2009 20:54:51 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LOiMl-0002pr-SE for categories-list@mta.ca; Sun, 18 Jan 2009 20:51:48 -0400 Date: Sun, 18 Jan 2009 20:32:14 +0000 (GMT Standard Time) From: Eugenia Cheng To: categories@mta.ca Subject: categories: PSSL 88: new talk deadline MIME-Version: 1.0 Content-Type: TEXT/PLAIN; format=flowed; charset=US-ASCII Sender: categories@mta.ca Precedence: bulk Reply-To: Eugenia Cheng Message-Id: Status: O X-Status: X-Keywords: X-UID: 16 PSSL 88 - supplementary announcement Dear all, We are delighted by the large number of registrations and talk proposals we have had for the PSSL in honour of the joint 60th birthdays of Martin Hyland and Peter Johnstone. However, we have already had more talks proposed than we can accommodate. Therefore if you would like to propose a talk and have not already done so, we now ask you to let us know by January 31st rather than the end of February as originally planned. The deadline for applying for funding is also January 31st, as before. The PSSL announcement email and registration form can be found here: http://cheng.staff.shef.ac.uk/pssl88/announce2.html Apologies for the inconvenience. Eugenia Cheng --- e.cheng@sheffield.ac.uk PSSL home page http://cheng.staff.shef.ac.uk/pssl88/ From rrosebru@mta.ca Mon Jan 19 13:35:43 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 19 Jan 2009 13:35:43 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LOxyF-0001nF-OZ for categories-list@mta.ca; Mon, 19 Jan 2009 13:31:31 -0400 Mime-Version: 1.0 (Apple Message framework v753.1) Content-Transfer-Encoding: 7bit Content-Type: text/plain; charset=US-ASCII; format=flowed To: categories@mta.ca From: Steve Awodey Subject: categories: Carnegie Mellon Summer School in Logic and Formal Epistemology Date: Mon, 19 Jan 2009 10:35:23 -0500 Sender: categories@mta.ca Precedence: bulk Reply-To: Steve Awodey Message-Id: Status: O X-Status: X-Keywords: X-UID: 17 Carnegie Mellon Summer School in Logic and Formal Epistemology In the summer of 2009, the Department of Philosophy at Carnegie Mellon University will hold a three-week summer school in logic and formal epistemology for promising undergraduates in philosophy, mathematics, computer science, linguistics, and other sciences. The goals are to o introduce students to cross-disciplinary fields of research at an early stage in their career; and o forge lasting links between the various disciplines. The summer school will be held from Monday, June 8 to Friday, June 26, 2009. There will be morning and afternoon lectures and daily problem sessions, as well as planned outings and social events. The summer school is free. That is, we will provide o full tuition, and o dormitory accommodations on the Carnegie Mellon campus. So students need only pay round trip travel to Pittsburgh and living expenses while there. There are no grades, and the courses do not provide formal course credit. Instructions for applying can be found on the summer school web page, http://www.phil.cmu.edu/summerschool Materials must be received by the Philosophy Department by March 15, 2009. This year's topics are: Categories and Structures Monday, June 8 to Friday, June 12 Instructor: Steve Awodey Decisions and Games Monday, June 15 to Friday, June 19 Instructor: Teddy Seidenfeld Logic and Formal Verification Monday, June 22 to Friday, June 26 Instructor: Jeremy Avigad The summer school is open to undergraduates, as well as to students who will be completing their first year of graduate school. Applicants need not be US citizens. There is a $20 nonrefundable application fee. Inquiries may be directed to Jeremy Avigad (avigad@cmu.edu). From rrosebru@mta.ca Tue Jan 20 11:57:51 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 20 Jan 2009 11:57:51 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LPIwa-0001Ty-3l for categories-list@mta.ca; Tue, 20 Jan 2009 11:55:12 -0400 Date: Mon, 19 Jan 2009 11:13:41 -0700 Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 To: categories@mta.ca Subject: categories: terminology in definitions of limits Content-Transfer-Encoding: quoted-printable Sender: categories@mta.ca Precedence: bulk Message-Id: From: peasthope@shaw.ca Status: RO X-Status: X-Keywords: X-UID: 18 Folk, Each definition of a limit which I've=20 seen contains something I would describe=20 as a "probe object" or "test object". The=20 definition of map object in L&S page 313=20 for example, has X with a criterion asserted=20 for every object X in the category. Is there any sense in my terminology? Thanks, ... Peter E. =20 From rrosebru@mta.ca Tue Jan 20 11:57:52 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 20 Jan 2009 11:57:52 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LPIvK-0001LK-Fs for categories-list@mta.ca; Tue, 20 Jan 2009 11:53:54 -0400 Date: Mon, 19 Jan 2009 20:11:26 +0100 From: "Bockermann Bockermann" To: categories@mta.ca Subject: categories: adjunction of symmetric monoidal closed categories MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 7bit Content-Disposition: inline Sender: categories@mta.ca Precedence: bulk Reply-To: "Bockermann Bockermann" Message-Id: Status: O X-Status: X-Keywords: X-UID: 19 Dear mathematicians, I wonder if the following is true. Has anybody a reference, if this is the case? Let V and W be two complete and cocomplete symmetric monoidal closed categories and L: V <--> W :R an adjunction of (lax) symmetric monoidal functors. Let D be a small V- category. Is it true that there is a V-isomorphism V-Fun(D,RW) = R(W-Fun(LD,W)) ? (If not, is this at least the case if L is strict symmetric monoidal?) Thank you for any help. Tony From rrosebru@mta.ca Tue Jan 20 19:30:07 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 20 Jan 2009 19:30:07 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LPPzk-0003yw-PX for categories-list@mta.ca; Tue, 20 Jan 2009 19:26:56 -0400 From: Colin McLarty To: categories@mta.ca Date: Tue, 20 Jan 2009 12:15:54 -0500 MIME-Version: 1.0 Content-Language: en Subject: categories: Re: terminology in definitions of limits Content-Type: text/plain; charset=us-ascii Content-Disposition: inline Content-Transfer-Encoding: 7bit Sender: categories@mta.ca Precedence: bulk Reply-To: Colin McLarty Message-Id: Status: O X-Status: X-Keywords: X-UID: 20 I often call them "test objects" in talking with students (by analogy with "test particles" in General Relativity). I don't think I have ever done it in print. But I did use "T" as the typical name of such an object in my book. I am curious to know what others think. best, Colin ----- Original Message ----- From: categories@mta.ca Date: Tuesday, January 20, 2009 11:01 am Subject: categories: terminology in definitions of limits To: categories@mta.ca > Folk, > > Each definition of a limit which I've > seen contains something I would describe > as a "probe object" or "test object". The > definition of map object in L&S page 313 > for example, has X with a criterion asserted > for every object X in the category. > > Is there any sense in my terminology? > > Thanks, ... Peter E. > > > > From rrosebru@mta.ca Tue Jan 20 19:30:07 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 20 Jan 2009 19:30:07 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LPPyr-0003vt-9j for categories-list@mta.ca; Tue, 20 Jan 2009 19:26:01 -0400 Mime-Version: 1.0 (Apple Message framework v624) Content-Type: text/plain; charset=US-ASCII; format=flowed Content-Transfer-Encoding: 7bit From: Paul Taylor Subject: categories: Foundations for Computable Topology Date: Tue, 20 Jan 2009 17:11:56 +0000 To: Categories list Sender: categories@mta.ca Precedence: bulk Reply-To: Paul Taylor Message-Id: Status: O X-Status: X-Keywords: X-UID: 21 Foundations for Computable Topology www.PaulTaylor.EU/ASD/foufct/ This paper is an overview of the whole of the Abstract Stone Duality research programme. I was invited to write it for a volume on Foundations of Mathematics that is more inclined towards philosophy than technicalities and has contributions from categorists, set theorists and philosophers. I advertised this in July, but the production timescale of this book has slipped somewhat, so I would still welcome comments. In particular, I have some questions below about citations for the history of category theory. The plan of the paper is as follows: 1. Foundations should be designed FOR mathematics. 2. The formal link between category theory and symbolic logic. 3. Using this as a methodology to design the new theory. 4. Stone duality between topology and algebra over sets 5. Stone duality as a monad, with applications to topology 6. The axiomatic "monadic framework". 7. The subobject classifier and Sierpinski space. 8. Axiomatic development of set theory using the Euclidean principle and topology using the Phoa principle. 9. Discrete mathematics using overt discrete spaces, arithmetic universes, recursion, description. 10. The "underlying set" axiom, which makes the full subcategory of overt discrete spaces into a topos. 11. Scott continuity as an axiom. 12. Beyond local compactness. The version of the last section as it appeared in July was COMPLETELY SCRAPPED, and replaced with a discussion of "equideductive logic", about which I talked at meetings in Sussex in September and Padova in October. Even in the present version, I still intend to replace the last few pages with a "conclusion". Briefly, equideductive logic is the (surprisingly interesting) logic of regular monos in a CCC with all finite limits. It is exactly what is required to perform Dana Scott's "equilogical space" construction, but without using the set theoretic interpretation based on the set of points of the basic spaces. I have done further work on this, but I am nowhere near being ready to advertise it. This paper does not discuss computation, but Andrej Bauer did some interesting programming during the summer: math.andrej.com/2008/08/24/efficient-computation-with-dedekind-reals/ SOME HOSTORICAL QUESTIONS Recall that the purpose of my paper is to give a general overview of the philosophy and motivations of ASD, along with a statement of all of the axioms for reference. I am therefore looking for citations that are also of a survey, historical or philosophical flavour, rather than the original technical source. The numbers refer to the subsections or paragraphs -- the paper is written in a narrative style, without Definition--Lemma--Theorem--Proof. The non-bracketed text is quoted from my paper. 2.6 [In a discussion of the relationship between category theory and symbolic logic.] Systems such as linear logic that do not obey all of the structural rules correspond to different categorical structures. These might, for example, be \emph{tensor} products~($\otimes$), which categorists understood long before they did predicate logic. 3.7 [In a critique of point--set topology.] Sheaves in algebraic geometry were based on open sets and not points 3.8 These books [on point--set topology] ... make little attempt to explore the full extent of even the world that is measured out by their own co-ordinate system. This was only begun when the analogy with the $\exists\land$-fragment of logic was recognised. 5.1 For this, we need a way of formulating (potentially infinitary) algebraic theories that works over an arbitrary category $\S$, and not just over the category of sets. Such an account is provided by the categorical notion of \emph{monad}. [Has anyone ever tried to write a textbook that covers the material of Modern or Universal Algebra using monads?] 6.12 The problem of finding splittings is actually not a new one: it was well known in homological algebra, which provided Jon Beck's original inspiration. [Can you give me a simple example of the use of splittings in homological algebra, and the difficulty in finding them?] 9.1 Finite limits and stable effective quotients of equivalence relations were studied in category theory long before it considered logic, because categories of finitary algebras inherit them from sets. 9.12 For terms and parameters of these types, Scott continuity is a \emph{theorem}, essentially the one of Henry Rice and Norman Shapiro. Paul Taylor pt09 @ PaulTaylor.EU www.PaulTaylor.EU/ASD/foufct From rrosebru@mta.ca Wed Jan 21 09:03:04 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 21 Jan 2009 09:03:04 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LPcgU-00001E-9c for categories-list@mta.ca; Wed, 21 Jan 2009 08:59:54 -0400 Mime-Version: 1.0 (Apple Message framework v624) Content-Type: text/plain; charset=US-ASCII; format=flowed Content-Transfer-Encoding: 7bit From: Paul Taylor Subject: categories: Re: terminology in definitions of limits Date: Tue, 20 Jan 2009 16:39:09 +0000 To: Sender: categories@mta.ca Precedence: bulk Reply-To: Paul Taylor Message-Id: Status: O X-Status: X-Keywords: X-UID: 22 Peter E observed that > each definition of a limit which I've seen contains something > I would describe as a "probe object" or "test object" although I am not sure whether his question is about the name for this (for which either of his suggestions is reasonable), or what. Limits are, of course, examples of right adjoints, and the situation that Peter describes is a case of the adjoint correspondence (considered as a trivial diagram) test object -----> diagram ============================================================== test object ------> limit of diagram So the left adjoint is a "forgetful" functor, which takes the test object and considers it as a trivial diagram, ie with identities as edges. Giving the test object a "name" in the sense of an English word is not such a big deal. However, I would argue that it is important to give it a "name" in the sense of using a particular letter uniformly for it. For this purpose, I propose the Greek letter capital Gamma. The reason for this choice is that the same role is played in symbolic logic by the "context", ie the collection of parameters, along with their types and hypotheses, that occurs in any mathematical statement. In type theory, the letter Gamma is traditionally and uniformly used for this purpose. (Can some type or proof theorist tell me who introduced or established this convention?) Indeed, I use this convention both for this test object and for other parts of the anatomy of an adjunction systematically throughout my book, "Practical Foundations of Mathematics" (CUP, 1999). In so far as there was a previous convention in category theory for the name of this object, it was "U". This came from sheaf theory, where, by the Yoneda lemma, we need only consider maps from hom(-,U), where U belongs to the base category. This category was primordially the lattice of open subsets of a topological space, so the convention came from that of using "U" for an open set. I believe that German-speaking authors were responsible for this, though I don't know what German word it was that began with U. Speaking of sheaf theory, when and to whom was it first apparent that the category of sheaves depends only on the lattice of open sets, and not on the points of a topological space? Paul Taylor www.PaulTaylor.EU pt09 @ PaulTaylor.EU From rrosebru@mta.ca Wed Jan 21 09:04:18 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 21 Jan 2009 09:04:18 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LPcka-0000KM-Pc for categories-list@mta.ca; Wed, 21 Jan 2009 09:04:08 -0400 Date: Tue, 20 Jan 2009 23:34:48 -0800 From: Vaughan Pratt MIME-Version: 1.0 To: categories@mta.ca Subject: categories: Re: terminology in definitions of limits Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Sender: categories@mta.ca Precedence: bulk Reply-To: Vaughan Pratt Message-Id: Status: O X-Status: X-Keywords: X-UID: 23 Colin McLarty wrote: > I often call them "test objects" in talking with students (by analogy > with "test particles" in General Relativity). I don't think I have ever > done it in print. But I did use "T" as the typical name of such an > object in my book. > > I am curious to know what others think. From a game-theoretic standpoint one can be either taking the test or administering it. Both sides call it the test, showing that the name is stable under perp (change of team). However that's not to say that "test" gives a helpful perspective in either case. A right adjoint defined by its adjunction is simply a specification of *all* homsets to it, and dually, in the case of left adjoints, of all the homsets from it. What you're calling a "test" object there is for me merely the variable being universally quantified over in the definition of "all." Whether a student is going to find it helpful thinking of a universally quantified variable as a "test object" is going to be less a question of what the student thinks about that perspective than what the teacher thinks about it and whether they can convey their point of view. The mathematically talented student who immediately sees it is merely being universally quantified over may be more puzzled than helped. But then how many of us are so lucky as to have a significant number of mathematically talented students in our classes? Vaughan From rrosebru@mta.ca Wed Jan 21 19:57:58 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 21 Jan 2009 19:57:58 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LPmvH-0007S5-4z for categories-list@mta.ca; Wed, 21 Jan 2009 19:55:51 -0400 Message-ID: <20090121161100.50sl8rgbkkow8w8s@webmail.u-picardie.fr> Date: Wed, 21 Jan 2009 16:11:00 +0100 From: Andree Ehresmann To: categories@mta.ca Subject: categories: In answer to Paul Taylor MIME-Version: 1.0 Content-Type: text/plain;charset=ISO-8859-1;DelSp="Yes";format="flowed" Content-Disposition: inline Content-Transfer-Encoding: quoted-printable Sender: categories@mta.ca Precedence: bulk Reply-To: Andree Ehresmann Status: O X-Status: X-Keywords: X-UID: 24 In answer to Paul Taylor Charles Ehresmann has realized as soon as 1951 (cf. "Charles =20 Ehresmann: Oeuvres compl=E8tes et comment=E9es", Part I, p. 153) that in a = =20 pseudogroup of transformations only the open sets of the associated =20 topology are used, not the points, whence the idea of replacing the =20 pseudogroup of transformations by a groupoid and the topology by a =20 paratopology (i.e., a complete distributive lattice). He formalized this idea in later works, in particular in the 1957 =20 seminal paper "Gattungen von lokalen Strukturen" [Oeuvres, Part II, p. =20 126], where he replaces the pseudogroup of transformations by a local =20 groupoid, and even, more generally, by a local category, that is a =20 category equipped with a "local" order compatible with its structure =20 (in modern term it is a category internal to a category of locales); =20 and he develops the theory of complete local species of structures =20 over a local groupoid, which generalizes that of a sheaf. Andr=E9e From rrosebru@mta.ca Wed Jan 21 19:57:58 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 21 Jan 2009 19:57:58 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LPmu0-0007Mz-QO for categories-list@mta.ca; Wed, 21 Jan 2009 19:54:32 -0400 Date: Wed, 21 Jan 2009 15:10:40 +0000 (GMT) From: Ulrike Tillmann To: categories@mta.ca Subject: categories: Oxford position MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=iso-8859-1; format=flowed Content-Transfer-Encoding: QUOTED-PRINTABLE Content-ID: Sender: categories@mta.ca Precedence: bulk Reply-To: Ulrike Tillmann Message-Id: Status: O X-Status: X-Keywords: X-UID: 25 We are about to advertise the position described below. A University Lectureship is the standard position at Oxford and should be= =20 comparable roughly with an Assistant or Associate Professorship in North= =20 American universities. I would be happy to receive any informal inquiries. Please note the deadline of 20 February. Ulrike Tillmann %%%%%%%%%%% Ad %%%%%%%%%% UNIVERSITY OF OXFORD Mathematical, Physical and Life Sciences Division Mathematical Institute in association with Keble College University Lecturership in Pure Mathematics The Mathematical Institute proposes to appoint a University Lecturer in Pur= e=20 Mathematics with effect from 1 October 2009. The successful candidate will= be=20 appointed to a Fellowship at Keble College under arrangements described in = the=20 further particulars. The combined University and College salary will be on= a=20 scale up to =A356,917 per annum. The successful candidate must have a record of outstanding research in some= =20 branch of pure mathematics. Preference will be given to applicants whose= =20 research interests are close to algebraic topology, broadly interpreted. Further particulars, containing details of the application procedure and of= the=20 duties, may be obtained from the Administrative Assistant (Vacancies), The= =20 Mathematical Institute, 24-9 St Giles' Street, Oxford OX1 3LB=20 (vacancies@maths.ox.ac.uk) or by visiting http://www.maths.ox.ac.uk/notices/vacancies/ The closing date for applications is 20 February 2009. Please quote refere= nce=20 number BK/09/006. The University is an Equal Opportunities Employer. From rrosebru@mta.ca Wed Jan 21 19:58:13 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 21 Jan 2009 19:58:13 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LPmxE-0007aC-D9 for categories-list@mta.ca; Wed, 21 Jan 2009 19:57:52 -0400 MIME-Version: 1.0 Date: Wed, 21 Jan 2009 10:48:57 -0600 Subject: categories: Re: terminology in definitions of limits From: Charles Wells To: Vaughan Pratt , catbb Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 7bit Sender: categories@mta.ca Precedence: bulk Reply-To: Charles Wells Message-Id: Status: O X-Status: X-Keywords: X-UID: 26 Calculus teachers do something similar when they make an epsilon-delta proof into a game: The opponent picks an epsilon (the test object) and you have to come up with a delta. There is one big difference between epsilon-delta proofs and limits. To show that something is a limit you have to find, for each test object, the unique arrow specified by the definition of limit. Thus you are producing a function (indeed, a bijection). The delta for a given epsilon is not unique, and so there is no natural function giving a delta for each epsilon. I am pretty sure this makes epsilon-delta proofs harder for non-talented students than proving something is a limit. I know some calculus teachers talk about there being a function that takes epsilon to delta, but I suspect it is a mistake to bring that up. Charles Wells On Wed, Jan 21, 2009 at 1:34 AM, Vaughan Pratt wrote: > > Colin McLarty wrote: > >> I often call them "test objects" in talking with students (by analogy >> with "test particles" in General Relativity). I don't think I have ever >> done it in print. But I did use "T" as the typical name of such an >> object in my book. >> >> I am curious to know what others think. >> > > From a game-theoretic standpoint one can be either taking the test or > administering it. Both sides call it the test, showing that the name is > stable under perp (change of team). > > However that's not to say that "test" gives a helpful perspective in > either case. A right adjoint defined by its adjunction is simply a > specification of *all* homsets to it, and dually, in the case of left > adjoints, of all the homsets from it. What you're calling a "test" > object there is for me merely the variable being universally quantified > over in the definition of "all." > > Whether a student is going to find it helpful thinking of a universally > quantified variable as a "test object" is going to be less a question of > what the student thinks about that perspective than what the teacher > thinks about it and whether they can convey their point of view. The > mathematically talented student who immediately sees it is merely being > universally quantified over may be more puzzled than helped. > > But then how many of us are so lucky as to have a significant number of > mathematically talented students in our classes? > > Vaughan > > > > -- professional website: http://www.cwru.edu/artsci/math/wells/home.html blog: http://www.gyregimble.blogspot.com/ abstract math website: http://www.abstractmath.org/MM//MMIntro.htm personal website: http://www.abstractmath.org/Personal/index.html From rrosebru@mta.ca Wed Jan 21 19:59:25 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 21 Jan 2009 19:59:25 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LPmyH-0007iP-NR for categories-list@mta.ca; Wed, 21 Jan 2009 19:58:57 -0400 MIME-Version: 1.0 Date: Wed, 21 Jan 2009 10:01:03 -0800 Subject: categories: Re: terminology in definitions of limits From: John Baez To: categories@mta.ca Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 7bit Sender: categories@mta.ca Precedence: bulk Reply-To: John Baez Message-Id: Status: O X-Status: X-Keywords: X-UID: 27 Dear Categorists - On Tue, Jan 20, 2009 at 11:34 PM, Vaughan Pratt wrote: > Colin McLarty wrote: > >> I often call them "test objects" in talking with students (by analogy with >> "test particles" in General Relativity). I don't think I have ever done it >> in print. > > > From a game-theoretic standpoint one can be either taking the test or > administering it. [..] What you're calling a "test" object there is for > me merely the variable being universally quantified over in the definition > of "all." When I teach limits I call Colin's "test object" a "competitor" to the true limit, or "pretender to the throne", and describe the universal property as saying "whatever you can do, I can do better". This game-theoretic approach to universal properties becomes more interesting when dealing with n-categorical weak limits: the two players take turns making moves. First the proponent picks a cone, then the challenger picks a cone, then the proponent picks a map between cones, then the challenger picks a map between cones, then the proponent picks a map between maps between cones, etc.. This idea is important in opetopic n-categories, and there's also an omega-categorical version - a nice discussion appears starting at the bottom of page 32 of this paper by Makkai: http://www.math.mcgill.ca/makkai/equivalence/equivinpdf/equivalence.pdf "The Hero has to answer each move of the Challenger [...] If Hero can keep it up forever, he wins; otherwise he loses." Best, jb From rrosebru@mta.ca Thu Jan 22 22:27:34 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 22 Jan 2009 22:27:34 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LQBes-0002K0-5Z for categories-list@mta.ca; Thu, 22 Jan 2009 22:20:34 -0400 Date: Wed, 21 Jan 2009 20:47:04 -0500 (EST) From: Michael Barr To: Charles Wells , catbb Subject: categories: Re: terminology in definitions of limits MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed Sender: categories@mta.ca Precedence: bulk Reply-To: Michael Barr Message-Id: Status: O X-Status: X-Keywords: X-UID: 28 This is getting peripheral to the main point. AS far as I recall, I thought of T as a test object. As for epsilon-delta, Bishop required that delta be prescribed as a constructible function of epsilon in order that a function be continuous. He required that the convergence be uniform on every closed interval, so that this function on a closed interval was independent of the points in the interval. Michael On Wed, 21 Jan 2009, Charles Wells wrote: > Calculus teachers do something similar when they make an epsilon-delta proof > into a game: The opponent picks an epsilon (the test object) and you have > to come up with a delta. > There is one big difference between epsilon-delta proofs and limits. To > show that something is a limit you have to find, for each test object, the > unique arrow specified by the definition of limit. Thus you are producing a > function (indeed, a bijection). The delta for a given epsilon is not unique, > and so there is no natural function giving a delta for each epsilon. I am > pretty sure this makes epsilon-delta proofs harder for non-talented students > than proving something is a limit. I know some calculus teachers talk about > there being a function that takes epsilon to delta, but I suspect it is a > mistake to bring that up. > > Charles Wells > From rrosebru@mta.ca Thu Jan 22 22:28:49 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 22 Jan 2009 22:28:49 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LQBgE-0002NU-Mi for categories-list@mta.ca; Thu, 22 Jan 2009 22:21:58 -0400 From: "mail.btinternet.com" To: "catbb" Subject: categories: Re: terminology in definitions of limits Date: Thu, 22 Jan 2009 11:16:38 -0000 MIME-Version: 1.0 Content-Type: text/plain;format=flowed;charset="iso-8859-1";reply-type=original Content-Transfer-Encoding: 7bit Sender: categories@mta.ca Precedence: bulk Reply-To: "mail.btinternet.com" Message-Id: Status: O X-Status: X-Keywords: X-UID: 29 Without getting into discussion of the `game' aspect, I feel category theorists should speak out against the epsilon-delta approach to limits as against the neighbourhood f(M) \subseteq N approach, where the notation easily describes the pictures. The epsilon-delta approach is in terms of measurement of a neighbourhood, i.e. one step away from the neighbourhood, and less actual (I almost wrote `real'!), and students find that step difficult. The utility of epsilon-delta is in terms of calculation, rather than geometry and structure. The `only measurable things are real' approach is based on the notion that numbers are the most important aspect of science, rather than one tool to investigate structure. Ronnie From rrosebru@mta.ca Thu Jan 22 22:29:21 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 22 Jan 2009 22:29:21 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LQBgm-0002P5-Cx for categories-list@mta.ca; Thu, 22 Jan 2009 22:22:32 -0400 Date: Thu, 22 Jan 2009 11:17:36 +0000 (GMT) From: Richard Garner To: categories@mta.ca Subject: categories: Re: terminology in definitions of limits MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed Sender: categories@mta.ca Precedence: bulk Reply-To: Richard Garner Message-Id: Status: O X-Status: X-Keywords: X-UID: 30 I have always used the phrase "test object" in a slightly different sense. Namely, to refer to a tractably small collection of objects that one may use, not only to detect, but also to calculate some right adjoint. Thus in Set, one may take the terminal object; in Set/X, the elements 1-->X; in Cat, the ordinals 1, 2 and 3; in presheaf categories, the representables; and so on. The best case is that these test objects are colimit dense, since then your calculations always yield a right adjoint as soon as the functor you start with preserves colimits. Richard From rrosebru@mta.ca Thu Jan 22 22:30:34 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 22 Jan 2009 22:30:34 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LQBhr-0002Rx-80 for categories-list@mta.ca; Thu, 22 Jan 2009 22:23:39 -0400 Date: Thu, 22 Jan 2009 10:07:13 -0200 From: "Eduardo J. Dubuc" MIME-Version: 1.0 To: Charles Wells , catbb Subject: categories: Re: terminology in definitions of limits Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Sender: categories@mta.ca Precedence: bulk Reply-To: "Eduardo J. Dubuc" Message-Id: Status: O X-Status: X-Keywords: X-UID: 31 of course, by choice (and many times without choice), there are lots of functions \delta = f(\epsilon). It is a good question to see when there is a continous such "f". e.d. Charles Wells wrote: > Calculus teachers do something similar when they make an epsilon-delta proof > into a game: The opponent picks an epsilon (the test object) and you have > to come up with a delta. > There is one big difference between epsilon-delta proofs and limits. To > show that something is a limit you have to find, for each test object, the > unique arrow specified by the definition of limit. Thus you are producing a > function (indeed, a bijection). The delta for a given epsilon is not unique, > and so there is no natural function giving a delta for each epsilon. I am > pretty sure this makes epsilon-delta proofs harder for non-talented students > than proving something is a limit. I know some calculus teachers talk about > there being a function that takes epsilon to delta, but I suspect it is a > mistake to bring that up. > > Charles Wells > > On Wed, Jan 21, 2009 at 1:34 AM, Vaughan Pratt wrote: > >> Colin McLarty wrote: >> >>> I often call them "test objects" in talking with students (by analogy >>> with "test particles" in General Relativity). I don't think I have ever >>> done it in print. But I did use "T" as the typical name of such an >>> object in my book. >>> >>> I am curious to know what others think. >>> >> From a game-theoretic standpoint one can be either taking the test or >> administering it. Both sides call it the test, showing that the name is >> stable under perp (change of team). >> >> However that's not to say that "test" gives a helpful perspective in >> either case. A right adjoint defined by its adjunction is simply a >> specification of *all* homsets to it, and dually, in the case of left >> adjoints, of all the homsets from it. What you're calling a "test" >> object there is for me merely the variable being universally quantified >> over in the definition of "all." >> >> Whether a student is going to find it helpful thinking of a universally >> quantified variable as a "test object" is going to be less a question of >> what the student thinks about that perspective than what the teacher >> thinks about it and whether they can convey their point of view. The >> mathematically talented student who immediately sees it is merely being >> universally quantified over may be more puzzled than helped. >> >> But then how many of us are so lucky as to have a significant number of >> mathematically talented students in our classes? >> >> Vaughan >> >> >> >> > > From rrosebru@mta.ca Thu Jan 22 22:32:01 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 22 Jan 2009 22:32:01 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LQBjF-0002W7-7K for categories-list@mta.ca; Thu, 22 Jan 2009 22:25:05 -0400 Date: Thu, 22 Jan 2009 10:21:04 -0500 (EST) From: Michael Barr To: "Advances in Set-Theoretic Topology, the Organizing Committee" , Subject: categories: Re: Request to referee the manuscript no. ER-29 MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed Sender: categories@mta.ca Precedence: bulk Reply-To: Michael Barr Message-Id: Status: O X-Status: X-Keywords: X-UID: 32 I do not do free work for journals published by publishers who make enormous profits and pay nothing in return either to the authors or reviewers. In choosing to publish your proccedings in such a journal rather than in the many journals that charge between 0 and and a tenth what Elsevier does, you have chosen a path that ultimately would lead to the destruction of scholarship. It is insulting to ask me to cooperate in such a venture. Sincerely yours, Michael Barr On Fri, 23 Jan 2009, Advances in Set-Theoretic Topology, the Organizing Committee wrote: > > Dear Professor Barr, > > We would like to ask you to referee the enclosed manuscript that has been > submitted for possible publication in the Special Issue of the journal > "Topology and its Applications" dedicated to the Proceedings of the > Conference "Advances in Set-Theoretic Topology" (in Honour of Tsugunori > Nogura on his 60th Birthday). > > In order to facilitate timely processing of the whole volume of the > proceedings, we would appreciate having a referee report by April 20, 2009. > > Please, let us know by the return e-mail whether you are willing to referee > this manuscript. If you are unable to referee this paper, we would appreciate > it very much if you could kindly indicate us three people who in your opinion > could serve as ponential referees for this article. > > We are looking forward to your feedback on our request by January 31. > > Best Wishes, > > ---- > > Szymon Dolecki (Burgundy University, France) > Yasunao Hattori (Shimane University, Japan) > Dmitri Shakhmatov (Ehime University, Japan) > Gino Tironi (University of Trieste, Italy) > > Guest Editors of the Special Issue of > "Topology and its Applications" > dedicated to the Proceedings of the Conference > "Advances in Set-Theoretic Topology" > (in Honour of Tsugunori Nogura on his 60th Birthday) > > erice@dmitri.math.sci.ehime-u.ac.jp > From rrosebru@mta.ca Thu Jan 22 22:32:54 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 22 Jan 2009 22:32:54 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LQBk0-0002Xz-7L for categories-list@mta.ca; Thu, 22 Jan 2009 22:25:52 -0400 Mime-Version: 1.0 (Apple Message framework v753.1) Content-Type: text/plain; charset=ISO-8859-1; format=flowed From: Jeremy Gibbons Subject: categories: WGP'09: Workshop on Generic Programming Call for Papers Date: Thu, 22 Jan 2009 22:14:40 +0000 To: categories@mta.ca Sender: categories@mta.ca Precedence: bulk Reply-To: Jeremy Gibbons Message-Id: Status: O X-Status: X-Keywords: X-UID: 33 ACM SIGPLAN Workshop on Generic Programming 2009 Edinburgh, UK, August 30, 2009 http://wiki.portal.chalmers.se/cse/WGP09 Goals of the workshop Generic programming is about making programs more adaptable by making them more general. Generic programs often embody non-traditional kinds of polymorphism; ordinary programs are obtained from them by suitably instantiating their parameters. In contrast with normal programs, the parameters of a generic program are often quite rich in structure; for example they may be other programs, types or type constructors, class hierarchies, or even programming paradigms. Generic programming techniques have always been of interest, both to practitioners and to theoreticians, and for at least 20 years generic programming techniques have been a specific focus of research in the functional and object-oriented programming language communities. Generic programming has gradually spread to more and more mainstream languages and is today widely used also in industry. This workshop will bring together leading researchers and practitioners in generic programming from around the world, and feature papers capturing the state of the art in this important area. We welcome contributions on all aspects, theoretical as well as practical, of * adaptive object-oriented programming, * aspect-oriented programming, * concepts (as in the STL / C++ sense) * component-based programming, * generic programming, * meta-programming, * polytypic programming, * programming with modules, * and so on. Organisers: Chair Patrik Jansson, CSE.Chalmers.se co-Chair Sibylle Schupp, STS.TUHH.de Programme Committee: Edwin Brady, U. of St Andrews, Peter Gottschling, TU Dresden Patrik Jansson, Chalmers Chair Barry Jay, U. of T., Sydney Jaakko J=E4rvi, Texas A&M Oleg Kiselyov, FNMOC Andres L=F6h, Utrecht U. Fritz Ruehr, Willamette U. Sibylle Schupp, TU Hamburg Harburg, Co-Chair Marcin Zalewski, Chalmers, We plan to have formal proceedings, published by the ACM. Submission details Deadline for submission: Sunday 090510 Notification of acceptance: Monday 090601 Final submission due: Tuesday 090616 Workshop: Sunday 090830 Authors should submit papers, in postscript or PDF format, formatted for A4 paper, to the WGP09 EasyChair instance by 10th of May 2009. The length should be restricted to 12 pages in standard (two-column, 9pt) ACM format. Accepted papers are published by the ACM and will additionally appear in the ACM digital library. History of the Workshop on Generic Programming This year: * Edinburgh, UK 2009 (affiliated with ICFP09) Earlier Workshops on Generic Programming have been held in * Victoria, BC, Canada 2008 (affiliated with ICFP), * Portland 2006 (affiliated with ICFP), * Utrecht 2005 (informal workshop), * Dagstuhl 2002 (IFIP WG2.1 Working Conference), * Nottingham 2001 (informal workshop), * Ponte de Lima 2000 (affiliated with MPC), * Marstrand 1998 (affiliated with MPC). There were also (closely related) DGP workshops in Oxford (June 3-4 2004), and a Spring School on DGP in Nottingham (April 24-27 2006, which had a half-day workshop attached). Additional information: The WGP steering committee consists of J Gibbons, R Hinze and J Jeuring. Jeremy.Gibbons@comlab.ox.ac.uk, Deputy Director Oxford University Computing Laboratory, TEL: +44 1865 283508 Wolfson Building, Parks Road, FAX: +44 1865 283531 Oxford OX1 3QD, UK. URL: http://www.comlab.ox.ac.uk/people/Jeremy.Gibbons From rrosebru@mta.ca Fri Jan 23 19:39:16 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 23 Jan 2009 19:39:16 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LQVVN-0002JQ-Gu for categories-list@mta.ca; Fri, 23 Jan 2009 19:32:05 -0400 Date: Fri, 23 Jan 2009 08:00:52 -0500 (EST) From: Michael Barr To: Categories list Subject: categories: abc conjecture proved? MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed Sender: categories@mta.ca Precedence: bulk Reply-To: Michael Barr Message-Id: Status: RO X-Status: X-Keywords: X-UID: 34 Although this has nothing to do with categories, it should be of interest to all mathematicians. According to this: http://groups.google.com/group/sci.math.research/browse_thread/thread/43d73791ca5d5cbd?hl=en someone is claiming proof of the abc conjecture by adapting somehow the valid proof for polynomial rings F[x] over a field that uses formal differentiation (this can be found, e.g. in Lang's Algebra). The abc conjecture easily implies the Fermat Last Theorem as well as a number of generalizations (such as the impossibility x^n + y^m = z^p with obvious exceptions) and more. It would be an astounding result. Michael From rrosebru@mta.ca Sat Jan 24 22:11:31 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 24 Jan 2009 22:11:31 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LQuMC-0007Re-2J for categories-list@mta.ca; Sat, 24 Jan 2009 22:04:16 -0400 Date: Sat, 24 Jan 2009 16:23:28 -0500 From: Michael Winter To: categories@mta.ca Subject: categories: CFP - RelMiCS 11 / AKA 6 MIME-Version: 1.0 Content-Type: text/plain;charset=ISO-8859-1;DelSp="Yes";format="flowed" Content-Disposition: inline Content-Transfer-Encoding: quoted-printable Sender: categories@mta.ca Precedence: bulk Reply-To: Michael Winter Message-Id: Status: RO X-Status: X-Keywords: X-UID: 35 Announcement and Call for Papers for the =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D 11th International Conference on Relational Methods in Computer Science (RelMiCS 11) =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D 6th International Conference on Applications of Kleene Algebra (AKA 6) =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D November 1 to 5, 2009 Doha, Qatar =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D 1) Conference Over the past fifteen years, the RelMiCS meetings have been a main forum for researchers who use the calculus of relations and similar algebraic =20 formalisms as methodological and conceptual tools. The workshop series on Applications of Kleene algebra started with a Dagstuhl seminar in 2001 and has been co- organised with the RelMiCS conference since. Due to their considerable =20 overlap, the two events have a joint PC and joint proceedings.Their scope comprises relation algebra, fixpoint calculi, semiring theory, iteration =20 algebras, process algebras and dynamic algebras. Applications include formal algebraic =20 modelling, the semantics, analysis and development of programs, formal language theory and combinatorial optimisation. We invite submissions on the general topics of Relation Algebra and Kleene Algebra in computer science. Special focus will lie on formal methods for software engineering, logics of programs and links with neighbouring disciplines. Particular topics of the =20 conference cover, but are not limited to the theory of - relation algebras and Kleene algebras - related formalisms such as process algebras, fixed point calculi, idempote= nt semirings, quantales, allegories, dynamic algebras, cylindric =20 algebras and their applications in areas such as - verification, analysis and development of programs and algorithms - relational formal methods such as B or Z, tabular methods, - algebraic approaches to logics of programs, modal and dynamic logics, interval and temporal logics - algebraic semantics of programming languages - graph theory and combinatorial optimisation - games, automata and language theory - mechanised and automated reasoning, decision procedures - spatio-temporal reasoning, knowledge acquisition, preference and scaling methods - information systems. The predecessors of this conference were held in Dagstuhl (January 1994), Parati (September 1995), Hammamet (January 1997), Warsaw (September 1998), Quebec (January 2000), Dagstuhl (February 2001), Oisterwijk (October 2001), Malente (April 2003), St. Catherines (January 2005), Manchester (September 2006) and Frauenwoerth (April 2008). 2) Program committee Jihad Al'Jaam (Doha, Qatar University) Rudolf Berghammer (Kiel, Germany; Program Co-Chair) Harrie de Swart (Tilburg, Netherlands) Jules Desharnais (Laval, Canada) Rehab Duwairi (Doha, Qatar University) Marcelo Frias (Buenos Aires, Argentina) Hitoshi Furusawa (Kagoshima, Japan) Peter Hoefner (Augsburg, Germany) Ali Jaoua (Doha, Qatar University; General Chair of =20 RelMiCS/AKA 09) Peter Jipsen (Chapman, USA) Wolfram Kahl (McMaster, Canada) Yasuo Kawahara (Kyushu, Japan) Larissa Meinicke (Sydney, Australia) Ali Mili (Tunis, TN, Newark, USA) Bernhard M=F6ller (Augsburg, Germany; Program Co-Chair) Carroll Morgan (Sydney, Australia) Ewa Orlowska (Warsaw, Poland) Susanne Saminger (Linz, Austria) Gunther Schmidt (Munich, Germany) Renate Schmidt (Manchester, UK) Georg Struth (Sheffield, UK) Michael Winter (Brock, Canada) 3) Invited Speakers First Invited Speaker Prof.Dr. H.C.M. de Swart Chair of Logic, Department of Philosophy Tilburg University, Dante building, room 255 P.O. Box 90153, 5000 LE Tilburg The Netherlands Phone: (0031) 13 466 2415 Fax: (0031) 13 4662892 E-mail: H.C.M.deSwart@uvt.nl URL: http://www.tilburguniversity.nl/faculties/humanities/dphil/staff/swart/ Second Invited Speaker Prof. Dr. Rohit Parikh Distinguished Professor CS, Math, Philosophy Brooklyn College and CUNY Grad Center USA Phone: 212-817-8197 URL: http://web.cs.gc.cuny.edu/~kgb/ 4) Important Dates Call for Papers: Jan 15 2009 Submission of papers: April 15 2009 Notification: June 20 2009 Final versions due (firm deadline): July 20 2009 Registration Oct. 1 2009 Conference Nov 1-5 2009 5) Proceedings and Submission All papers will be formally reviewed. We plan to publish the =20 proceedings in the series Lecture Notes in Computer Science ready at the conference. The proceedings editors will be R. Berghammer, A. Jaoua and B. M=F6ller. Submissions must be in English, in postscript or pdf format, and =20 provide sufficient information to judge their merits. They must be unpublished and not =20 submitted for publication elsewhere. They may not exceed 15 pages in Springer LNCS style and must be produced with LaTeX. Additional material may be provided by a clearly marked appendix or a reference to a manuscript on a website. This ma= y be considered at the discretion of the PC. Deviation from these requirements may cause immediate rejection. One author of each accepted paper is expected to present the paper at the conference. Detailed instructions for electronic submission can be found at the conference website. Formatting instructions and the LNCS style files can be obtained via http://www.springer.de/comp/lncs/authors.html. As for the earlier conferences of this series, it is also intended to =20 publish a selection of the best papers in revised and extended form in a special =20 issue of the Journal of Logic and Algebraic Programming (JLAP). 6) Student Programme The conference will be accompanied by a PhD training program. Details will be published in due time in a special call and on the conference website. 7) Venue Doha is the capital city of Qatar. With a population of about 1500.000 =20 inhabitants it is the largest city of Qatar and its economic and cultural center. =20 The city is located on the Persian Gulf. The university of Qatar at Doha was opened in t= he year 1973. Doha is also home of many international schools. Doha has an international airport that is served by many international (e.g., Turkish Airway, by British Airways from London-Heathrow, Lufthansa fr= om Frankfurt, KLM from Amsterdam and Qatar Airways from New York-JFK and Osaka-Kansai). 8) Organization Ali Jaoua (General chair and local organizer) Rudolf Berghammer and Bernhard M=F6ller (Program co-chairs) Further details can be found under http://www.qu.edu.qa/RelMiCs11/ From rrosebru@mta.ca Mon Jan 26 08:55:28 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 26 Jan 2009 08:55:28 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LRQu3-00010t-U0 for categories-list@mta.ca; Mon, 26 Jan 2009 08:49:24 -0400 Date: Mon, 26 Jan 2009 08:15:08 +0000 From: Tim Porter To: "categories@mta.ca" Subject: categories: Lie groups and Lie algebras MIME-Version: 1.0 Content-Type: text/plain;charset=3DISO-8859-1;DelSp=3D"Yes";format=3D"flowe= Message-Id: Status: O X-Status: X-Keywords: X-UID: 36 d" Content-Disposition: inline Content-Transfer-Encoding: 7bit Sender: categories@mta.ca Precedence: bulk Reply-To: Tim Porter In the relationship between Lie groups and Lie algebras, there is the neat result that the Lie functor L : LieGrp->LieAlg restricts to an equivalence on the simply connected Lie groups, and that the fibre over any given Lie algebra is the category of those G which are isomorphic to quotients of the one simply connected one of them and hence there is a Galois theory interpretation in terms of central extensions. I am sure that this sort of situation must be much more general than just this case, and is somehow linked to abstract Galois theories. I am hoping that someone can point out really neat categorical results on this (in the literature). I am sure I ought to know them but ... It does not seem to be in Borceux-Janelidze, and my own library on this area is very sadly thin on the ground. Thanks in advance, Tim --=20 Gall y neges e-bost hon, ac unrhyw atodiadau a anfonwyd gyda hi, gynnwys deunydd cyfrinachol ac wedi eu bwriadu i'w defnyddio'n unig gan y sawl y cawsant eu cyfeirio ato (atynt). Os ydych wedi derbyn y neges e-bost hon trwy gamgymeriad, rhowch wybod i'r anfonwr ar unwaith a dil=EBwch y neges. Os na fwriadwyd anfon y neges atoch chi, rhaid i chi beidio =E2 defnyddio, cadw neu ddatgelu unrhyw wybodaeth a gynhwysir ynddi. Mae unrhyw farn neu safbwynt yn eiddo i'r sawl a'i hanfonodd yn unig ac nid yw o anghenraid yn cynrychioli barn Prifysgol Bangor. Nid yw Prifysgol Bangor yn gwarantu bod y neges e-bost hon neu unrhyw atodiadau yn rhydd rhag firysau neu 100% yn ddiogel. Oni bai fod hyn wedi ei ddatgan yn uniongyrchol yn nhestun yr e-bost, nid bwriad y neges e-bost hon yw ffurfio contract rhwymol - mae rhestr o lofnodwyr awdurdodedig ar gael o Swyddfa Cyllid Prifysgol Bangor. www.bangor.ac.uk This email and any attachments may contain confidential material and is solely for the use of the intended recipient(s). If you have received this email in error, please notify the sender immediately and delete this email. If you are not the intended recipient(s), you must not use, retain or disclose any information contained in this email. Any views or opinions are solely those of the sender and do not necessarily represent those of the Bangor University. Bangor University does not guarantee that this email or any attachments are free from viruses or 100% secure. Unless expressly stated in the body of the text of the email, this email is not intended to form a binding contract - a list of authorised signatories is available from the Bangor University Finance Office. www.bangor.ac.uk From rrosebru@mta.ca Mon Jan 26 15:45:00 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 26 Jan 2009 15:45:00 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LRXFv-0007Ic-Rv for categories-list@mta.ca; Mon, 26 Jan 2009 15:36:23 -0400 Subject: categories: request for comments: "A survey of graphical languages for monoidal categories" To: categories@mta.ca (Categories List) Date: Mon, 26 Jan 2009 11:02:01 -0400 (AST) MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit From: selinger@mathstat.dal.ca (Peter Selinger) Sender: categories@mta.ca Precedence: bulk Reply-To: selinger@mathstat.dal.ca (Peter Selinger) Message-Id: Status: O X-Status: X-Keywords: X-UID: 37 Dear Category Theorists, as you know, there is a proliferation of monoidal categories with additional structure, many of which have graphical languages. For example: autonomous, balanced, braided, compact closed, pivotal, ribbon, rigid, sovereign, spherical, tortile, traced. I have recently written a survey article on all of these graphical languages (and more). The goal was not to re-prove known theorems, but simply to collect most known facts in one location, with references to the primary literature. I have also tried to put a systematic perspective on things. Consequently, I included many results and conjectures that don't seem to appear in the literature at all, or for which only special cases seem to be known. Since this paper will not be refereed in the usual sense (it is supposed to appear as a book chapter), I am instead inviting comments and corrections from all interested parties. I am particularly interested in missing references for any of the results or conjectures, and of course any other corrections you might have. The article is available from: http://www.mathstat.dal.ca/~selinger/papers.html#graphical I hope this will be useful. Thanks! -- Peter ---------------------------------------------------------------------- P. Selinger: A survey of graphical languages for monoidal categories December 2008. 59 pages. Abstract: This article is intended as a reference guide to various notions of monoidal categories and their associated string diagrams. It is hoped that this will be useful not just to mathematicians, but also to physicists, computer scientists, and others who use diagrammatic reasoning. We have opted for a somewhat informal treatment of topological notions, and have omitted most proofs. Nevertheless, the exposition is sufficiently detailed to make it clear what is presently known, and to serve as a starting place for more in-depth study. Where possible, we provide pointers to more rigorous treatments in the literature. Where we include results that have only been proved in special cases, we indicate this in the form of caveats. From rrosebru@mta.ca Mon Jan 26 15:45:00 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 26 Jan 2009 15:45:00 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LRXGx-0007R9-UC for categories-list@mta.ca; Mon, 26 Jan 2009 15:37:28 -0400 Date: Mon, 26 Jan 2009 07:10:48 -0800 (PST) From: Bill Rowan To: Tim Porter , Subject: categories: Re: Lie groups and Lie algebras MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed Sender: categories@mta.ca Precedence: bulk Reply-To: Bill Rowan Message-Id: Status: O X-Status: X-Keywords: X-UID: 38 There is a much more general form of the functor that takes a Lie algebra to its envelloping ring. This is not precisely what you asked, but if it would be helpful, try looking at my 1992 thesis, Enveloping rings of universal algebras, University Microfilms, and the paper a bit later in Algebra Universalis. Bill Rowan On Mon, 26 Jan 2009, Tim Porter wrote: > In the relationship between Lie groups and Lie algebras, there is the > neat result that the Lie functor L : LieGrp->LieAlg restricts to an > equivalence on the simply connected Lie groups, and that the fibre > over any given Lie algebra is the category of those G which are > isomorphic to quotients of the one simply connected one of them and > hence there is a Galois theory interpretation in terms of central > extensions. > > I am sure that this sort of situation must be much more general than > just this case, and is somehow linked to abstract Galois theories. I > am hoping that someone can point out really neat categorical results > on this (in the literature). I am sure I ought to know them but ... > > It does not seem to be in Borceux-Janelidze, and my own library on > this area is very sadly thin on the ground. > > > Thanks in advance, > > Tim > > > > --=20 > Gall y neges e-bost hon, ac unrhyw atodiadau a anfonwyd gyda hi, > gynnwys deunydd cyfrinachol ac wedi eu bwriadu i'w defnyddio'n unig > gan y sawl y cawsant eu cyfeirio ato (atynt). Os ydych wedi derbyn y > neges e-bost hon trwy gamgymeriad, rhowch wybod i'r anfonwr ar > unwaith a dil=EBwch y neges. Os na fwriadwyd anfon y neges atoch chi, > rhaid i chi beidio =E2 defnyddio, cadw neu ddatgelu unrhyw wybodaeth a > gynhwysir ynddi. Mae unrhyw farn neu safbwynt yn eiddo i'r sawl a'i > hanfonodd yn unig ac nid yw o anghenraid yn cynrychioli barn > Prifysgol Bangor. Nid yw Prifysgol Bangor yn gwarantu > bod y neges e-bost hon neu unrhyw atodiadau yn rhydd rhag firysau neu > 100% yn ddiogel. Oni bai fod hyn wedi ei ddatgan yn uniongyrchol yn > nhestun yr e-bost, nid bwriad y neges e-bost hon yw ffurfio contract > rhwymol - mae rhestr o lofnodwyr awdurdodedig ar gael o Swyddfa > Cyllid Prifysgol Bangor. www.bangor.ac.uk > > This email and any attachments may contain confidential material and > is solely for the use of the intended recipient(s). If you have > received this email in error, please notify the sender immediately > and delete this email. If you are not the intended recipient(s), you > must not use, retain or disclose any information contained in this > email. Any views or opinions are solely those of the sender and do > not necessarily represent those of the Bangor University. > Bangor University does not guarantee that this email or > any attachments are free from viruses or 100% secure. Unless > expressly stated in the body of the text of the email, this email is > not intended to form a binding contract - a list of authorised > signatories is available from the Bangor University Finance > Office. www.bangor.ac.uk > > > From rrosebru@mta.ca Tue Jan 27 08:29:47 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 27 Jan 2009 08:29:47 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LRmz7-0003YA-Mv for categories-list@mta.ca; Tue, 27 Jan 2009 08:24:05 -0400 Mime-Version: 1.0 (Apple Message framework v753.1) Content-Transfer-Encoding: quoted-printable Content-Type: text/plain; charset=ISO-8859-1; delsp=yes; format=flowed To: Categories list From: =?UTF-8?Q?Jonathan_CHICHE_=E9=BD=90=E6=AD=A3=E8=88=AA?= Subject: categories: Model Theory and Category Theory Date: Tue, 27 Jan 2009 10:02:44 +0100 Sender: categories@mta.ca Precedence: bulk Reply-To: =?UTF-8?Q?Jonathan_CHICHE_=E9=BD=90=E6=AD=A3=E8=88=AA?= Message-Id: Status: O X-Status: X-Keywords: X-UID: 39 Hello, I am looking for references regarding the interplay between Model =20 Theory and Category Theory. I came across an announcement related to =20 this topic recently, possibly on this list, but I cannot find it =20 anymore. There has been a thread about it on the n-Category caf=E9 a =20 few months ago also. Do you have any other reference? What would be =20 the best place to start? Thanks in advance, Jonathan=20= From rrosebru@mta.ca Tue Jan 27 08:29:47 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 27 Jan 2009 08:29:47 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LRmyC-0003V0-Hz for categories-list@mta.ca; Tue, 27 Jan 2009 08:23:08 -0400 From: David Roberts To: Categories list Content-Type: text/plain; charset=US-ASCII; format=flowed; delsp=yes Content-Transfer-Encoding: 7bit Mime-Version: 1.0 (Apple Message framework v930.3) Subject: categories: bicategory of fractions and homotopy category Date: Tue, 27 Jan 2009 16:31:44 +1030 Sender: categories@mta.ca Precedence: bulk Reply-To: David Roberts Message-Id: Status: O X-Status: X-Keywords: X-UID: 40 Hi all, has anyone come across this situation? I have a 2-category where the underlying category has a model structure, and the class of equivalences (from the 2-cat structure) is contained in the weak equivalences. The class of weak equivalences admits a bicategory of fractions, and so one can consider that bicategory as the homotopy 'category' in some sense. Cheers, David Roberts From rrosebru@mta.ca Tue Jan 27 20:56:33 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 27 Jan 2009 20:56:33 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LRybZ-0005FF-Ot for categories-list@mta.ca; Tue, 27 Jan 2009 20:48:33 -0400 From: Colin McLarty To: Categories list Date: Tue, 27 Jan 2009 08:33:55 -0500 MIME-Version: 1.0 Content-Language: en Subject: categories: Re: Model Theory and Category Theory Content-Type: text/plain; charset=iso-8859-1 Content-Disposition: inline Content-Transfer-Encoding: quoted-printable Sender: categories@mta.ca Precedence: bulk Reply-To: Colin McLarty Message-Id: Status: O X-Status: X-Keywords: X-UID: 41 So far as I know the most explicit=2C extensive account of how model theorists do use categories---and ought to use them more freely and explicitly---is in AUTHOR =3D =7BMacintyre=2C Angus=7D=2C TITLE =3D =7BModel Theory=3A Geometrical and Set-Theoretic Aspec= ts and Prospects=7D=2C JOURNAL =3D =7BBulletin of Symbolic Logic=7D=2C YEAR =3D =7B2003=7D=2C volume =3D =7B9=7D=2C number =3D =7B2=7D=2C pages =3D =7B197--212=7D=2C And there are some pointed remarks=2C about a tendency to avoid explicitl= y using categorical tools that are in effect already being used=2C in Pillay=27s part of Author =3D =7BBuss=2C Samuel and Kechris=2C Alexander and Pillay=2C= Anand and Shore=2C Richard=7D=2C TITLE =3D =7BThe Prospects for Mathematical Logic in the Twenty-First Century=7D=2C JOURNAL =3D =7BBulletin of Symbolic Logic=7D=2C YEAR =3D =7B2001=7D=2C volume =3D =7B7=7D=2C number =3D =7B2=7D=2C pages =3D =7B169--96=7D=2C Unsystematic uses occur throughout the literature=2C often without using the word =22category=2E=22 I would mention especially = AUTHOR =3D =7Bvan den Dries=2C Lou=7D=2C TITLE =3D =7BTame Topology and O-minimal Structures=7D=2C PUBLISHER =3D =7BCambridge University Press=7D=2C YEAR =3D =7B1998=7D=2C address =3D =7BCambridge=7D=2C editor =3D =7BHaskell=2C Dierdre and Pillay=2C Anand and Steinhor= n=2C Charles=7D=2C TITLE =3D =7BModel Theory=2C Algebra=2C and Geometry=7D=2C PUBLISHER =3D =7BCambridge University Press=7D=2C YEAR =3D =7B2000=7D=2C number =3D =7B39=7D=2C series =3D =7BMathematical Sciences Research Center Publications=7D= =2C best=2C Colin ----- Original Message ----- From=3A Jonathan CHICHE =3F=3F=3F =3Cjonathan=2Echiche=40polytechnique=2E= edu=3E Date=3A Tuesday=2C January 27=2C 2009 7=3A32 am Subject=3A categories=3A Model Theory and Category Theory To=3A Categories list =3Ccategories=40mta=2Eca=3E =3E Hello=2C =3E = =3E I am looking for references regarding the interplay between Model = =3E Theory and Category Theory=2E I came across an announcement related = =3E to = =3E this topic recently=2C possibly on this list=2C but I cannot find it = = =3E anymore=2E There has been a thread about it on the n-Category caf=E9 = a = =3E few months ago also=2E Do you have any other reference=3F What would = be = =3E = =3E the best place to start=3F =3E = =3E Thanks in advance=2C =3E = =3E Jonathan = =3E = =3E = From rrosebru@mta.ca Tue Jan 27 20:57:35 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 27 Jan 2009 20:57:35 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LRycy-0005MU-9y for categories-list@mta.ca; Tue, 27 Jan 2009 20:50:00 -0400 Mime-Version: 1.0 (Apple Message framework v753.1) Content-Type: text/plain; charset=UTF-8; delsp=yes; format=flowed To: Categories list From: Philip Scott Subject: categories: Re: Model Theory and Category Theory Date: Tue, 27 Jan 2009 12:58:55 -0500 Sender: categories@mta.ca Precedence: bulk Reply-To: Philip Scott Message-Id: Status: O X-Status: X-Keywords: X-UID: 42 Dear Jonathan: There will be an upcoming workshop June 19-20 at the CRM (Centre de =20 Recherches Mathematiques) at the University of Montreal, dedicated to Michael Makkai's 70th birthday, which is =20 exactly on this theme. Its local organizers are Robert Seely and me, along with two model theorists (Bradd Hart =20 and Tommy Kucera), who were students of Makkai. This was announced on this list some time ago, but a more up-to-date =20 announcement with the official CRM webpage will shortly be made available from CRM. I will post information soon. = Cheers, = Phil Scott =09 On 27-Jan-09, at 4:02 AM, Jonathan CHICHE =E9=BD=90=E6=AD=A3=E8=88=AA = wrote: > Hello, > > I am looking for references regarding the interplay between Model =20 > Theory and Category Theory. I came across an announcement related =20 > to this topic recently, possibly on this list, but I cannot find it =20= > anymore. There has been a thread about it on the n-Category caf=C3=A9 = a =20 > few months ago also. Do you have any other reference? What would be =20= > the best place to start? > > Thanks in advance, > > Jonathan From rrosebru@mta.ca Tue Jan 27 20:58:20 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 27 Jan 2009 20:58:20 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LRye3-0005Re-4z for categories-list@mta.ca; Tue, 27 Jan 2009 20:51:07 -0400 MIME-Version: 1.0 Date: Tue, 27 Jan 2009 12:54:42 -0600 Subject: categories: Re: bicategory of fractions and homotopy category From: Michael Shulman To: David Roberts , Categories list Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 7bit Sender: categories@mta.ca Precedence: bulk Reply-To: Michael Shulman Message-Id: Status: O X-Status: X-Keywords: X-UID: 43 Hi David, This is something I've thought about as well. If your model category is a Cat-model category, then by Hovey's general results on enriched model categories, its homotopy category is automatically enriched over Ho(Cat), the category of categories and natural-isomorphism-classes of functors. A Ho(Cat)-enriched category is like a "bicategory without coherence," and the question is about lifting that structure to a coherent bicategory. However, in this case I believe you can actually always obtain a strict 2-category equivalent to the bicategory of fractions by just looking at the full sub-2-category of your model 2-category spanned by the fibrant and cofibrant objects. Since any Ho(Cat)-category that is equivalent (as a Ho(Cat)-category) to a bicategory must itself underlie a bicategory, you can use this to get a "homotopy bicategory" without needing the calculus of fractions (which model category theory is basically designed to avoid). There is lots of good stuff about Cat-model categories in Steve Lack's paper "Homotopy-theoretic aspects of 2-monads": http://arxiv.org/abs/math.CT/0607646. Best, Mike On Tue, Jan 27, 2009 at 12:01 AM, David Roberts wrote: > Hi all, > > has anyone come across this situation? I have a 2-category where the > underlying category has a model structure, and the class of equivalences > (from the 2-cat structure) is contained in the weak equivalences. The > class > of weak equivalences admits a bicategory of fractions, and so one can > consider that bicategory as the homotopy 'category' in some sense. > > Cheers, > > David Roberts > > > From rrosebru@mta.ca Tue Jan 27 20:58:32 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 27 Jan 2009 20:58:32 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LRyeu-0005Vb-CP for categories-list@mta.ca; Tue, 27 Jan 2009 20:52:00 -0400 Date: Wed, 28 Jan 2009 08:26:38 +1100 Subject: categories: Re: bicategory of fractions and homotopy category From: Steve Lack To: David Roberts , categories Mime-version: 1.0 Content-type: text/plain; charset="US-ASCII" Content-transfer-encoding: 7bit Sender: categories@mta.ca Precedence: bulk Reply-To: Steve Lack Message-Id: Status: O X-Status: X-Keywords: X-UID: 44 Dear David, I have written about this sort of thing in the paper Homotopy-theoretic aspects of 2-monads, Journal of Homotopy and Related Structures 2:229-260, 2007; also arXiv:math.CT/0607646. Regards, Steve Lack. On 27/01/09 5:01 PM, "David Roberts" wrote: > Hi all, > > has anyone come across this situation? I have a 2-category where the > underlying category has a model structure, and the class of equivalences > (from the 2-cat structure) is contained in the weak equivalences. The > class > of weak equivalences admits a bicategory of fractions, and so one can > consider that bicategory as the homotopy 'category' in some sense. > > Cheers, > > David Roberts > > From rrosebru@mta.ca Tue Jan 27 20:59:51 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 27 Jan 2009 20:59:51 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LRyfj-0005Z3-GU for categories-list@mta.ca; Tue, 27 Jan 2009 20:52:51 -0400 Date: Wed, 28 Jan 2009 09:56:28 +1100 Subject: categories: Re: adjunction of symmetric monoidal closed categories From: Steve Lack To: Bockermann Bockermann , categories Mime-version: 1.0 Content-type: text/plain; charset="US-ASCII" Content-transfer-encoding: 7bit Sender: categories@mta.ca Precedence: bulk Reply-To: Steve Lack Message-Id: Status: O X-Status: X-Keywords: X-UID: 45 On 20/01/09 6:11 AM, "Bockermann Bockermann" wrote: > Dear mathematicians, > I wonder if the following is true. Has anybody a reference, if this is > the case? > > Let V and W be two complete and cocomplete symmetric monoidal closed > categories and > L: V <--> W :R > an adjunction of (lax) symmetric monoidal functors. Let D be a small V- > category. > Is it true that there is a V-isomorphism > V-Fun(D,RW) = R(W-Fun(LD,W)) ? > > (If not, is this at least the case if L is strict symmetric monoidal?) > > Thank you for any help. > Tony > > Dear Tony, I pointed out this fact in my reply (see below) to one of your earlier questions. In fact you don't need symmetry, and L is automatically strong monoidal. Regards, Steve Lack. %%%%% On 6/12/08 10:21 AM, "Bockermann Bockermann" wrote: > Dear mathematicians, > > could anybody give me a hint if the following assertion is true? > Let V be a complete and co-complete symmetric monoidal closed category. The > category sV of simplicial objects in V is also complete and co-complete > symmetric monoidal closed with the pointwise tensor. There is a V-adjunction > D:V<-->sV:Z > of the V-functor Z which evaluates in 0 and the discrete V-functor D. Does > this induce a V-Isomorphism of V-categories > V-Fun(K,ZC)~sV-Fun(DK,C) > for any small V-category K and any sV-category C? > > Please note that a similar statement is true for the non-enriched case [e.g. > Borceux2, Proposition 6.4.8.]. > > Thank you for any help. > > Tony > > Dear Tony, Yes, it is true. More generally, let F-|U:W-->V be a monoidal adunction. This means that V and W are monoidal categories, F and U are monoidal functors, monoidal natural transformations 1-->UF and FU-->1 satisfying the triangle equations. (A monoidal functor F:V-->W involves maps FX\otimes FY-->F(X\otimes Y) and I_W-->F(I_V), not necessarily invertible, but satisfying coherence conditions. In a monoidal adjunction, as above, the monoidal functor F is necessarily strong, so that the comparison maps are invertible. The comparison maps for U need not be invertible.) For a small V-category K and a W-category C we do indeed have an isomorphism V-Fun(K,UC) = U(W-Fun(FK,C)) of V-categories. I'll do my best to explain this via ascii. V-functors from K to UC are in bijection with W-functors from FK to C; this takes care of the object-part. For V-functors M,N:K-->UC, the hom-object V-Fun(K,UC)(M,N) is the equalizer of the evident maps ---> Pi_k UC(Mk,Nk) ---> Pi_{k,l} [K(k,l), UC(Mk,Nl)] in V, where the products run over all objects k and l of K. On the other hand, U(W-Fun(FK,C)(M,N)) is given by the equalizer of --> U(Pi_k C(Mk,Nk)) --> U Pi_{k,l} [FK(k,l),C(Mk,Nl)] or equivalently, since U is a left adjoint, the equalizer of --> Pi_k UC(Mk,Nk) --> Pi_{k,l} U[FK(k,l),C(Mk,Nl)] So we are now left to prove Lemma: U[FX,Y]=[X,UY], for X in V and Y in W. Proof: V(Z,U[FX,Y]) = W(FZ,[FX,Y]) = W(FZ\otimes FX,Y) = W(F(Z\otimes X),Y) = V(Z\otimes X,UY) = V(Z,[X,UY]) naturally in Z and so U[FX,Y]=[X,UY] as required. Regards, Steve Lack. From rrosebru@mta.ca Wed Jan 28 09:01:11 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 28 Jan 2009 09:01:11 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LS9vz-0006iw-P0 for categories-list@mta.ca; Wed, 28 Jan 2009 08:54:23 -0400 From: calco09 To: categories@mta.ca, Mime-Version: 1.0 (Apple Message framework v930.3) Subject: categories: [Calco'09] cfp: deadline is approaching Date: Wed, 28 Jan 2009 11:05:44 +0100 Sender: categories@mta.ca Precedence: bulk Reply-To: calco09 Message-Id: Status: O X-Status: X-Keywords: X-UID: 46 ***---------- Deadline is approaching -------- *** *------------------------------------------------------------------* * Call for Papers * * * * CALCO 2009 * * * * 3rd Conference on Algebra and Coalgebra in Computer Science * * CALCO Tools Day * * CALCO-jnr * * * September 6-10 2009, Udine, Italy * * * *------------------------------------------------------------------* * Abstract submission: February 2, 2009 * * Technical paper submission: February 7, 2009 * * Tools Day submission: February 24, 2009 * * Author notification: April 22, 2009 * *------------------------------------------------------------------* * http://www.dimi.uniud.it/calco09/ * *------------------------------------------------------------------* CALCO brings together researchers and practitioners to exchange new results about both traditional and emerging uses of algebras and =20 coalgebras in computer science. This is a high-level, bi-annual conference formed by joining the forces and reputations of CMCS (the International Workshop on Coalgebraic =20 Methods in Computer Science), and WADT (the Workshop on Algebraic Development Techniques). The first and second CALCO conferences took place 2005 in Swansea, Wales (http://www.cs.swan.ac.uk/calco/index.php), and 2007 in Bergen, Norway (http://www.ii.uib.no/calco07/). The second event will take place September 2009 in Udine, Italy. CALCO 2009 will be preceded by two events on September 6, 2009. * CALCO-jnr - a CALCO Young Researchers Workshop dedicated to presentations by PhD students and by those who completed their doctoral studies within the past few years. * CALCO Tools Day - providing the opportunity to give system demonstrations. See below for more information. There are separate submission procedures for the CALCO main conference, CALCO-jnr and CALCO Tools Day, respectively. Invited Speakers ------------------ Mai Gehrke (Nijmegen, NL) Conor McBride (Strathclyde, UK) Prakash Panangaden (McGill, Canada) Gordon Plotkin (Edinburgh, UK) Topics of Interest ------------------ We invite submissions of technical papers that report results of theoretical work on the mathematics of algebras and coalgebras, the way these results can support methods and techniques for software development, as well as experience with the transfer of resulting technologies into industrial practice. We encourage submissions in topics included or related to those in the lists below. * Abstract models and logics - Automata and languages, - Categorical semantics, - Modal logics, - Relational systems, - Graph transformation, - Term rewriting, - Adhesive categories * Specialised models and calculi - Hybrid, probabilistic, and timed systems, - Calculi and models of concurrent, distributed, mobile, and context-aware computing, - General systems theory and computational models (chemical, biological, etc) * Algebraic and coalgebraic semantics - Abstract data types, - Inductive and coinductive methods, - Re-engineering techniques (program transformation), - Semantics of conceptual modelling methods and techniques, - Semantics of programming languages * System specification and verification - Algebraic and coalgebraic specification, - Formal testing and quality assurance, - Validation and verification, - Generative programming and model-driven development, - Models, correctness and (re)configuration of hardware/middleware/architectures, - Process algebra Submission Guidelines --------------------- Prospective authors are invited to submit full papers in English presenting original research. Submitted papers must be unpublished and not submitted for publication elsewhere. Experience papers are welcome, but they must clearly present general lessons learned that would be of interest and benefit to a broad audience of both researchers and practitioners. As in 2005 and 2007, it is planned to =20 publish the proceedings in the Springer LNCS series. Final papers will be no more than 15 pages long in the format specified by Springer. It is recommended that submissions adhere to that format and length (see http://www.springer.de/comp/lncs/authors.html). Submissions that are clearly too long may be rejected immediately. Proofs omitted due to space limitations may be included in a clearly marked appendix. Both an abstract and the full paper must be submitted by their =20 respective submission deadlines. A special issue of the new high-quality open access journal Logical Methods in Computer Science (http://www.lmcs-online.org), consisting of extended versions of selected papers will be produced after the =20 conference if there are enough good papers that can be extended and revised to the standards of this journal. Important Dates (all in 2009) ----------------------------- February 2 Abstract submission due February 7 Technical paper submission due February 24 Submissions to CALCO Tools Day, see below April 22 Author notification May 22 Camera ready due ----------------------------- September 6 CALCO-jnr and CALCO Tools Day September 6-10 CALCO technical programme Programme Committee ------------------- Luca Aceto, Reykjavik University, IS Stephen Bloom, Stevens Institute of Technology, Hoboken, USA Marcello Bonsangue, Leiden University, NL Corina Cirstea, University of Southampton, UK Andrea Corradini, University of Pisa, I Jos=E9 Fiaderio, University of Leicester, UK Rolf Hennicker, University of Munich, D Furio Honsell, University of Udine, I Bart Jacobs, University of Nijmegen, NL Bartek Klin, University of Warsaw, PL Alexander Kurz, University of Leicester, UK (co-chair) Stefan Milius, University of Braunschweig, D Ugo Montanari, University of Pisa, I Larry Moss, Indiana University, Bloomington, USA Till Mossakowski, DFKI Lab Bremen and University of Bremen, D Dirk Pattinson, Imperial College London, UK Dusko Pavlovic, Kestrel Institute, USA Jean-Eric Pin, CNRS-LIAFA Paris, F John Power, University of Bath, UK Grigore Rosu, University of Illinois, Urbana, USA Jan Rutten, CWI and Free University, Amsterdam, NL Davide Sangiorgi, University of Bologna, I Lutz Schr=F6der, DFKI Lab Bremen and University of Bremen, D Eugene Stark, State University of New York, USA Andrzej Tarlecki, Warsaw University, PL (co-chair) Yde Venema, University of Amsterdam, NL James Worrell, University of Oxford, UK Steering Committee ------------------ Jiri Adamek, Michel Bidoit, Corina Cirstea, Jose Fiadeiro (co-chair, http://www.cs.le.ac.uk/people/jfiadeiro/), H.Peter Gumm, Magne Haveraaen, Bart Jacobs, Hans-Joerg Kreowski, Alexander Kurz, Marina Lenisa, Ugo Montanari, Larry Moss, Till Mossakowski, Peter Mosses, Fernando Orejas, Francesco Parisi-Presicce, John Power, Horst Reichel, Markus Roggenbach, Jan Rutten (co-chair, http://homepages.cwi.nl/=20 ~janr/), Andrzej Tarlecki Organising Committee -------------------- Fabio Alessi, Alberto Ciaffaglione, Pietro Di Gianantonio, Davide =20 Grohmann, Furio Honsell, Marina Lenisa (chair, http://www.dimi.uniud.it/~lenisa), Marino Miculan, Ivan Scagnetto, University of Udine, Italy Location ------------------------- The conference will be held in the city of Udine, the capital of the =20 historical region of Friuli, Italy. Located between the Adriatic sea and the =20 Alps, close to Venice, Austria and Slovenia, Udine is a city of Roman origins, funded =20= by Emperor Otto in 983. Rich of historical sites, Udine is also famous =20 for its outstanding wine and culinary traditions. CALCO Tools Day --------------- A special day at CALCO'09 is dedicated to tools based on algebraic and coalgebraic principles. These include systems/prototypes/tools developed specifically for design, checking, execution, and verification of (co)algebraic specifications, but also tools targeting different application domains but making core or interesting use of (co)algebraic techniques. Tool submissions should be no longer than 5 pages in the LNCS format; the accepted tool papers will be included in the final LNCS proceedings of the conference. The tools should be available on the web for download and evaluation. Each submission will be evaluated by at least three reviewers; one or more of the reviewers will be asked to download and run the tool. At least one of the authors of each tool paper must attend the conference to demo the tool. Submissions by e-mail to grosu@cs.uiuc.edu. Important Dates (all in 2009) February 24 Tools software and paper submissions due March 28 Author notification May 16 Camera ready due September 6 CALCO Tools Day Program Committee Luigi Liquori, INRIA, Sophia Antipolis, France http://www-sop.inria.fr/members/Luigi.Liquori/ Grigore Rosu, University of Illinois, Urbana, USA http://fsl.cs.uiuc.edu/index.php/Grigore_Rosu http://www.dimi.uniud.it/calco09/ From rrosebru@mta.ca Wed Jan 28 20:38:41 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 28 Jan 2009 20:38:41 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LSKsy-00021D-Ak for categories-list@mta.ca; Wed, 28 Jan 2009 20:36:00 -0400 MIME-Version: 1.0 Date: Wed, 28 Jan 2009 19:31:35 +0000 From: Paul Levy To: categories@mta.ca Subject: categories: initial algebra question X-Sender: P.B.Levy@cs.bham.ac.uk Content-Type: text/plain; charset="UTF-8" Content-Transfer-Encoding: quoted-printable Sender: categories@mta.ca Precedence: bulk Reply-To: Paul Levy Message-Id: Status: O X-Status: X-Keywords: X-UID: 47 Does anybody know a reference for the following (very easy) result? Let C and D be categories, and let F:C-->D and G:D-->C be functors. If (c,theta) is an initial algebra for GF, then (Fc, F theta) is an initi= al algebra for FG. thanks, Paul From rrosebru@mta.ca Thu Jan 29 09:19:00 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 29 Jan 2009 09:19:00 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LSWlt-0003RD-U8 for categories-list@mta.ca; Thu, 29 Jan 2009 09:17:29 -0400 MIME-Version: 1.0 Date: Thu, 29 Jan 2009 17:27:27 +0900 Subject: categories: Re: initial algebra question From: Makoto Hamana To: categories@mta.ca Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 7bit Sender: categories@mta.ca Precedence: bulk Reply-To: Makoto Hamana Message-Id: Status: O X-Status: X-Keywords: X-UID: 48 > Date: Wed, 28 Jan 2009 19:31:35 +0000 > From: Paul Levy > Does anybody know a reference for the following (very easy) result? > Let C and D be categories, and let F:C-->D and G:D-->C be functors. > If (c,theta) is an initial algebra for GF, then (Fc, F theta) is an initial algebra for FG. It is mentioned as Proposition 5.3 of Alex Simpson and Gordon Plotkin, Complete Axioms for Categorical Fixed-point Operators, LICS 2000. Best Regards, Makoto Hamana From rrosebru@mta.ca Thu Jan 29 14:14:46 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 29 Jan 2009 14:14:46 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LSbO4-0002xL-V4 for categories-list@mta.ca; Thu, 29 Jan 2009 14:13:12 -0400 Mime-Version: 1.0 (Apple Message framework v753.1) Content-Type: text/plain; charset=US-ASCII; delsp=yes; format=flowed Content-Transfer-Encoding: 7bit From: Steve Vickers Subject: categories: Re: initial algebra question Date: Thu, 29 Jan 2009 14:37:36 +0000 To: Paul Levy , categories@mta.ca Sender: categories@mta.ca Precedence: bulk Reply-To: Steve Vickers Message-Id: Status: O X-Status: X-Keywords: X-UID: 49 Dear Paul, I proved a "topical" version of this as Propn 2.3.7 in my "Topical Categories of Domains" (1999). "Topical" here means working in the 2-category of Grothendieck toposes and geometric morphisms instead of that of categories and functors. Instead of objects of a category and morphisms between them, it deals with points of a topos and natural transformations between them. (Note that I use the term "F-structures" instead of "F- algebras".) In this setting there are some subtleties of interpretation. An initial F-structure is defined as a point of the classifying topos [F- struct] for F-structures that is initial amongst all the generalized points - making [F-struct] a local topos. Nonetheless, the argument is essentially one that you might use with categories and functors. I remarked that my results were familiar from the category context as set out in Freyd's 1991 paper "Algebraically complete categories". I cannot remember if your result on FG-algebras and GF-algebras was in Freyd. All the best, Steve. On 28 Jan 2009, at 19:31, Paul Levy wrote: > Does anybody know a reference for the following (very easy) result? > > Let C and D be categories, and let F:C-->D and G:D-->C be functors. > > If (c,theta) is an initial algebra for GF, then (Fc, F theta) is an > initial algebra for FG. > > thanks, > Paul > > > From rrosebru@mta.ca Thu Jan 29 14:16:03 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 29 Jan 2009 14:16:03 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LSbQk-0003I9-3z for categories-list@mta.ca; Thu, 29 Jan 2009 14:15:58 -0400 From: "Noson" To: Subject: categories: New York City Category Seminar Date: Thu, 29 Jan 2009 11:47:45 -0500 MIME-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Content-Transfer-Encoding: 7bit Sender: categories@mta.ca Precedence: bulk Reply-To: "Noson" Message-Id: Status: RO X-Status: A X-Keywords: X-UID: 50 We would like to announce the formation of a Category Theory Seminar to be held at the Graduate Center of the City University of New York. We anticipate talks in applied and pure category theory. We also encourage students to make presentations on their work. New York City is central enough that someone prominent is always passing through. When: Commencing Spring 2009, weekly, Monday evenings 6:00 - 7:00 PM. Where: Room 4421 The Graduate Center, The City University of New York, 365 Fifth Avenue (at 34th street. Diagonally across from the Empire State Building) New York, NY 10016-4309 Web: http://www.sci.brooklyn.cuny.edu/~noson/CTseminar.html Please forward this e-mail on to anyone who might be interested. If you are interested in receiving announcements about the seminar, or know someone who would be or are interested in giving a talk, please drop me a line. All the best, Noson Yanofsky From rrosebru@mta.ca Thu Jan 29 14:17:32 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 29 Jan 2009 14:17:32 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LSbSB-0003VN-E4 for categories-list@mta.ca; Thu, 29 Jan 2009 14:17:27 -0400 Date: Thu, 29 Jan 2009 18:16:00 +0100 (CET) From: Lutz Strassburger To: Lutz Strassburger , Michel Parigot Subject: categories: Second CfP: "Structures and Deduction", Bordeaux, July 20-24, 2009 MIME-Version: 1.0 Content-Type: MULTIPART/MIXED; BOUNDARY="1753285643-486541765-1233248717=:8795" Content-ID: Content-Type: TEXT/PLAIN; CHARSET=ISO-8859-15; format=flowed Content-ID: Content-Transfer-Encoding: quoted-printable Sender: categories@mta.ca Precedence: bulk Reply-To: Lutz Strassburger Message-Id: Status: RO X-Status: X-Keywords: X-UID: 51 ******************************************************************* SECOND CALL FOR PAPERS International Workshop "Structures and Deduction" (SD09) July 20 - 24, 2009 organized as part of the European Summer School on Logic, Language and Information ESSLLI 2009 July 20 - 31, 2009 in Bordeaux ******************************************************************* ORGANIZERS: Michel Parigot (CNRS, Univ. Paris 7, France) Lutz Strassburger (INRIA Saclay-IdF, France) DESCRIPTION OF THE WORKSHOP: The topic of this workshop is the application of algebraic, geometric, and combinatorial methods in proof theory. In recent years many researchers have proposed approaches to understand and reduce "syntactic bureaucracy" in the presentation of proofs. Examples are proof nets, atomic flows, new deductive systems based on deep inference, and new algebraic semantics for proofs. These efforts have also led to new methods of proof normalisation and new results in proof complexity. The workshop is relevant to a wide range of people. The list of topics includes among others: algebraic semantics of proofs, game semantics, proof nets, deep inference, tableaux systems, category theory, deduction modulo, cut elimination, complexity theory, etc. The goal of the workshop is twofold: first, to bring together researchers from various fields who share the interest of understanding and dealing with structural properties of proofs and second, to provide an opportunity for PhD students and researchers to present and discuss their work with colleagues who work in the broad subject areas that are represented at ESSLLI. The workshop is intended to be a sequel of the ICALP-workshop SD05 in Lisbon 2005 . SUBMISSION DETAILS: Contributions can be regular papers, but also work in progress, programmatic/position papers or tutorials. Submissions should be formatted with the LNCS LaTeX style, take between two and fifteen pages and allow the committee to assess their merits with reasonable effort. The length limit can be relaxed for the versions that will be presented at the workshop, depending on the total bulk of the accepted contributions. Please use the SD'09 submission page=20 handled by the EasyChair conference system, to submit papers. The accepted papers will appear in the workshop proceedings published by=20 ESSLLI. One author of each accepted paper must attend the workshop in=20 order to present the paper. WORKSHOP FORMAT: The workshop is part of ESSLLI and is open to all ESSLLI participants. It will consist of five 90-minute sessions held over five consecutive days in the first week of ESSLLI. There will be 2 or 3 slots for paper presentation and discussion per session. On the first day the workshop organizers will give an introduction to the topic. INVITED SPEAKER: Fran=E7ois Lamarche (LORIA, Nancy) PROGRAM COMMITTEE: Lev Beklemishev (Moscow) Stefano Berardi (Torino) Agata Ciabattoni (Vienna) Alessio Guglielmi (Bath/Nancy) Martin Hyland (Cambridge) Grigori Mints (Stanford) Michel Parigot (Paris) Lutz Strassburger (Palaiseau) Kazushige Terui (Kyoto) IMPORTANT DATES: Deadline for submissions: February 15, 2009 Notification of acceptance: April 15, 2009 Deadline for final versions: May 11, 2009 Workshop dates: July 20 - 24, 2009 LOCAL ARRANGEMENTS: All workshop participants including the presenters will be required to register for ESSLLI. The registration fee for authors presenting a paper will correspond to the early student/workshop speaker registration fee. Moreover, a number of additional fee waiver grants will be made available by the ESSLLI local organizing committee on a competitive basis and workshop participants are eligible to apply for those. There will be no reimbursement for travel costs and accommodation. Workshop speakers who have difficulty in finding funding should contact the local organizing committee to ask for the possibilities for a grant. FURTHER INFORMATION: About the workshop: About ESSLLI: From rrosebru@mta.ca Fri Jan 30 11:49:36 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 30 Jan 2009 11:49:36 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LSvaI-0002ga-T3 for categories-list@mta.ca; Fri, 30 Jan 2009 11:47:11 -0400 Date: Thu, 29 Jan 2009 19:05:50 -0800 Subject: categories: Symmetric monoidal closed natural transformation? From: Mike Stay To: categories Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 7bit Sender: categories@mta.ca Precedence: bulk Reply-To: Mike Stay Message-Id: Status: O X-Status: X-Keywords: X-UID: 52 A symmetric monoidal functor F:C->D is closed if the morphism c_D(Phi_{x -o y, x}^{-1} o F(c_C^{-1}(1_{x -o y}))):F(x -o y) -> F(x) -o F(y) is an isomorphism, where x,y in C, Phi_{x,y}:F(x) tensor F(y) -> F(x tensor y) and c_C and c_D are currying in C, D. Could someone give me the definition of a symmetric monoidal closed natural transformation? I thought it would be a simple commuting diagram like the one involving Phi, but one of the arrows goes the wrong way. -- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike http://reperiendi.wordpress.com From rrosebru@mta.ca Fri Jan 30 14:19:00 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 30 Jan 2009 14:19:00 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LSxwE-0002TC-Ek for categories-list@mta.ca; Fri, 30 Jan 2009 14:17:58 -0400 MIME-Version: 1.0 Date: Fri, 30 Jan 2009 10:09:34 -0800 Subject: categories: Re: Symmetric monoidal closed natural transformation? From: Mike Stay To: categories Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 7bit Sender: categories@mta.ca Precedence: bulk Reply-To: Mike Stay Message-Id: Status: O X-Status: X-Keywords: X-UID: 54 On Thu, Jan 29, 2009 at 7:05 PM, Mike Stay wrote: > A symmetric monoidal functor F:C->D is closed if the morphism > c_D(Phi_{x -o y, x}^{-1} o F(c_C^{-1}(1_{x -o y}))):F(x -o y) -> F(x) -o F(y) > is an isomorphism, where x,y in C, > Phi_{x,y}:F(x) tensor F(y) -> F(x tensor y) > and c_C and c_D are currying in C, D. > > Could someone give me the definition of a symmetric monoidal closed > natural transformation? I thought it would be a simple commuting > diagram like the one involving Phi, but one of the arrows goes the > wrong way. Thanks to all those who responded, letting me know that precisely because of the arrow going the "wrong" way, it only makes sense to talk about symmetric monoidal closed natural isomorphisms. -- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike http://reperiendi.wordpress.com From rrosebru@mta.ca Fri Jan 30 15:28:34 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 30 Jan 2009 15:28:34 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LSz1h-0001g9-3c for categories-list@mta.ca; Fri, 30 Jan 2009 15:27:41 -0400 MIME-Version: 1.0 Date: Fri, 30 Jan 2009 01:18:39 -0600 Subject: categories: "Kantor dust" From: "Galchin, Vasili" To: Categories mailing list Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 7bit Sender: categories@mta.ca Precedence: bulk Reply-To: "Galchin, Vasili" Message-Id: Status: RO X-Status: X-Keywords: X-UID: 55 [Note from moderator: this may have been sent incorrectly earlier, apologies if you have received it twice.] Dear Category group, Here is a definition of Cantor dust .... http://en.wikipedia.org/wiki/Cantor_set. My question is from a constructivist viewpoint does this set really exist and if so, why? Very kind regards, Vasili From rrosebru@mta.ca Sat Jan 31 09:38:30 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 31 Jan 2009 09:38:30 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LTG1w-00066D-08 for categories-list@mta.ca; Sat, 31 Jan 2009 09:37:04 -0400 MIME-Version: 1.0 Date: Fri, 30 Jan 2009 16:40:24 -0600 Subject: categories: Re: "Kantor dust" From: "Galchin, Vasili" To: Bas Spitters Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 7bit Sender: categories@mta.ca Precedence: bulk Reply-To: "Galchin, Vasili" Message-Id: Status: O X-Status: X-Keywords: X-UID: 56 I don't think it exists from a constructivist viewpoint because it has to be constructed in a finite number of steps. Vasili On Fri, Jan 30, 2009 at 3:52 PM, Bas Spitters wrote: > On Friday 30 January 2009 08:18:39 Galchin, Vasili wrote: > > Here is a definition of Cantor dust .... > > http://en.wikipedia.org/wiki/Cantor_set. > > > > My question is from a constructivist viewpoint does this set really > > exist and if so, why? > > Yes, it exists. In fact, it is a continuous image of 2^N. > It is Bishop compact, fan-like and compact overt (choose your taste of > constructivism). > > Bas > > From rrosebru@mta.ca Sat Jan 31 09:38:30 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 31 Jan 2009 09:38:30 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LTG0y-00061X-Ns for categories-list@mta.ca; Sat, 31 Jan 2009 09:36:04 -0400 Date: Fri, 30 Jan 2009 22:52:57 +0100 From: Bas Spitters Subject: categories: Re: "Kantor dust" To: "Galchin, Vasili" MIME-version: 1.0 Content-type: text/plain; charset=iso-8859-1 Content-transfer-encoding: 7BIT Content-disposition: inline Sender: categories@mta.ca Precedence: bulk Reply-To: Bas Spitters Message-Id: Status: O X-Status: X-Keywords: X-UID: 57 On Friday 30 January 2009 08:18:39 Galchin, Vasili wrote: > Here is a definition of Cantor dust .... > http://en.wikipedia.org/wiki/Cantor_set. > > My question is from a constructivist viewpoint does this set really > exist and if so, why? Yes, it exists. In fact, it is a continuous image of 2^N. It is Bishop compact, fan-like and compact overt (choose your taste of constructivism). Bas From rrosebru@mta.ca Sat Jan 31 09:39:14 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 31 Jan 2009 09:39:14 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LTG3y-0006AQ-CE for categories-list@mta.ca; Sat, 31 Jan 2009 09:39:10 -0400 From: "Ronnie Brown" To: "categories" Subject: categories: It it a good idea to use the term 2-group outside of its use in group thoery? Date: Fri, 30 Jan 2009 23:34:26 -0000 MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Sender: categories@mta.ca Precedence: bulk Reply-To: "Ronnie Brown" Message-Id: Status: O X-Status: X-Keywords: X-UID: 58 I would like to raise an objection to using the term `2-group' as on = nlab and elsehere since for the group theorists this has a specialised = meaning: See the following wiki entry, especially the first 2 words:=20 "In mathematics, given a prime number p, a p-group is a periodic group = in which each element has a power of p as its order. That is, for each = element g of the group, there exists a nonnegative integer n such that g = to the power pn is equal to the identity element. Such groups are also = called primary."=20 I feel we should try to avoid and even to reduce confusion, = especially as there are claims that crossed modules, for example, can be = thought of as `2-dimensional groups' (I agree with this, of course!); = there are nice crossed modules M \to P in which M and P are 2-groups in = the group theoretic sense!=20 My favourite example is=20 \mu: Z_2 \times Z_2 \to Z_4=20 in which Z_4 acts by the twist (of order 2), and \mu maps each factor = Z_2 injectively into Z_4. This crossed module has non trivial = k-invariant. I think Johannes Huebschmann first observed this.=20 So an example oriented approach to crossed modules could well need the = term p-group in its standard group theoretic usage. Some examples of = finite crossed modules are in=20 R. Brown and C.D. Wensley, `Computation and homotopical applications of induced crossed modules', J. Symbolic Computation 35 (2003) 59-72. However I think one can be happy with the well established term = 2-groupoid.=20 I would just like this point to be discussed: terminology is important, = and confusing an established use might raise hackles unnecessarily.=20 Ronnie From rrosebru@mta.ca Sat Jan 31 09:41:00 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 31 Jan 2009 09:41:00 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LTG5g-0006FM-BM for categories-list@mta.ca; Sat, 31 Jan 2009 09:40:56 -0400 Date: Fri, 30 Jan 2009 17:22:49 -0800 (PST) From: John MacDonald To: categories@mta.ca Subject: categories: FMCS 2009 MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed Sender: categories@mta.ca Precedence: bulk Reply-To: John MacDonald Message-Id: Status: O X-Status: X-Keywords: X-UID: 59 FMCS 2009 17th Workshop on Foundational Methods in Computer Science University of British Columbia, VANCOUVER, Canada MAY 28th - 31st, 2009 FIRST ANNOUNCEMENT * * * The Department of Mathematics at the University of British Columbia in cooperation with the Pacific Institute of Mathematical Sciences is hosting the Foundational Methods in Computer Science workshop on May 28th - 31st, 2009, on the University of British Columbia Campus in Vancouver, Canada The workshop is an annual informal meeting intended to bring together researchers in mathematics and computer science. There is a focus on the application of category theory in computer science. However, all those who are interested in category theory or computer science are welcome to attend. There will be a welcoming reception on the evening of Thursday May 28. The scientific program starts on May 29, and consists of a day of tutorials aimed at students and newcomers to category theory, as well as a day and a half of research talks. The meeting ends at mid-day on May 31. Research talks There will be some invited presentations, but the majority of the talks are solicited from the participants. If you wish to give a talk please send a title and abstract to johnm@math.ubc.ca. Time slots are limited, so please respond early if you would like to be considered for a talk. Graduate student participation is particularly encouraged at FMCS. Accommodations A block of rooms has been reserved for participants at Gage Towers on the UBC campus. Registration If you would like to come to the meeting or will come to the meeting please send a brief email to johnm@math.ubc.ca with the words "would like to attend" or "may attend" or "will attend". This is just so the local organizer and organizing committee wiil have a first estimate of how many people may show up. The Second Announcement will be out soon with links to the conference webpage, registration and accommodation. Previous meetings Previous FMCS meetings were held in Pullman (1992), Portland (1993), Vancouver (1994), Kananaskis (1995), Pullman (1996), Portland (1998), Kananaskis (1999), Vancouver (2000), Spokane (2001), Hamilton (2002), Ottawa (2003), Kananaskis (2004), Vancouver (2005), Kananaskis (2006), Hamilton (2007), and Halifax (2008). Organizing committee: Robin Cockett (Calgary) John MacDonald (UBC) Phil Mulry (Colgate) Peter Selinger (Dalhousie) Local Organizers: John MacDonald (UBC) From rrosebru@mta.ca Sat Jan 31 09:42:38 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 31 Jan 2009 09:42:38 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LTG7G-0006Lh-8r for categories-list@mta.ca; Sat, 31 Jan 2009 09:42:34 -0400 MIME-Version: 1.0 Date: Fri, 30 Jan 2009 22:35:41 -0600 Subject: categories: Re: "Kantor dust" From: "Galchin, Vasili" To: Bas Spitters Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 7bit Sender: categories@mta.ca Precedence: bulk Reply-To: "Galchin, Vasili" Message-Id: Status: O X-Status: X-Keywords: X-UID: 60 i.e. a well-defined algorithm exists to construct Cantor dust but the Cantor dust cannot be constructed/built from the algorithm in a finite number of steps. Hence, Cantor dust represents potential infinity rather than actual infinity. This problem has nagged at me for a while. Regards, Vasili On Fri, Jan 30, 2009 at 4:40 PM, Galchin, Vasili wrote: > I don't think it exists from a constructivist viewpoint because it has to > be constructed in a finite number of steps. > > Vasili > > On Fri, Jan 30, 2009 at 3:52 PM, Bas Spitters wrote: > >> On Friday 30 January 2009 08:18:39 Galchin, Vasili wrote: >> > Here is a definition of Cantor dust .... >> > http://en.wikipedia.org/wiki/Cantor_set. >> > >> > My question is from a constructivist viewpoint does this set >> really >> > exist and if so, why? >> >> Yes, it exists. In fact, it is a continuous image of 2^N. >> It is Bishop compact, fan-like and compact overt (choose your taste of >> constructivism). >> >> Bas >> >> > From rrosebru@mta.ca Sat Jan 31 09:41:45 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 31 Jan 2009 09:41:45 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LTG6O-0006Ht-IH for categories-list@mta.ca; Sat, 31 Jan 2009 09:41:40 -0400 MIME-version: 1.0 Content-transfer-encoding: 7BIT Content-type: text/plain; charset=US-ASCII; delsp=yes; format=flowed To: categories@mta.ca From: Adam Eppendahl Subject: categories: Re: initial algebra question Date: Sat, 31 Jan 2009 10:36:24 +0800 Sender: categories@mta.ca Precedence: bulk Reply-To: Adam Eppendahl Message-Id: Status: O X-Status: X-Keywords: X-UID: 61 > Does anybody know a reference for the following (very easy) result? > Let C and D be categories, and let F:C-->D and G:D-->C be functors. > If (c,theta) is an initial algebra for GF, then (Fc, F theta) is an > initial algebra for FG. It is in Section 5 of Peter Freyd Remarks on Algebraically Compact Categories, LMS LNS 177, 1992. (modulo initial invariant = initial algebra). The full dinaturality of initial algebra delivery (as a diagram of functors) is in Section 4 of Adam Eppendahl Coalgebra-to-algebra Morphisms, ENTCS 29, 1999. where it is seen to follow from the lemma: If p is a coalgebra for GF and s is an algebra for FG, then morphisms from Fp to s correspond one-for-one to morphisms from p to Gs (even without an adjunction between G and F). Adam Eppendahl From rrosebru@mta.ca Sat Jan 31 09:43:35 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 31 Jan 2009 09:43:35 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LTG8A-0006PD-4Q for categories-list@mta.ca; Sat, 31 Jan 2009 09:43:30 -0400 From: spitters To: "Galchin, Vasili" Subject: categories: Re: "Kantor dust" Date: Sat, 31 Jan 2009 11:25:32 +0100 MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-15" Content-Transfer-Encoding: 7bit Content-Disposition: inline Sender: categories@mta.ca Precedence: bulk Reply-To: spitters Message-Id: Status: O X-Status: X-Keywords: X-UID: 62 It seems that what you are describing is usually called finitism. Bas On Saturday 31 January 2009 05:35:41 Galchin, Vasili wrote: > i.e. a well-defined algorithm exists to construct Cantor dust but the > Cantor dust cannot be constructed/built from the algorithm in a finite > number of steps. Hence, Cantor dust represents potential infinity rather > than actual infinity. This problem has nagged at me for a while. > > Regards, Vasili > From rrosebru@mta.ca Sun Feb 1 10:29:07 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 01 Feb 2009 10:29:07 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LTdIL-0005Bm-Nm for categories-list@mta.ca; Sun, 01 Feb 2009 10:27:33 -0400 Date: Sat, 31 Jan 2009 16:06:31 -0800 From: Vaughan Pratt MIME-Version: 1.0 To: categories list Subject: categories: Re: "Kantor dust" Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Sender: categories@mta.ca Precedence: bulk Reply-To: Vaughan Pratt Message-Id: Status: O X-Status: X-Keywords: X-UID: 63 Galchin, Vasili wrote: > i.e. a well-defined algorithm exists to construct Cantor dust but the Cantor > dust cannot be constructed/built from the algorithm in a finite number of > steps. Hence, Cantor dust represents potential infinity rather than actual > infinity. This problem has nagged at me for a while. Bill, if you mean this literally then you don't accept the existence of the set N of natural numbers either. If that's the case then for you it is very reasonable to reject the Cantor set K as well, e.g. because you're a finitist as Bas Spitters suggests. However if you're ok with the idea of a natural numbers object N in a topos, defined as an initial algebra for the functor F(X) = X+1, then you would need to draw a fairly fine line to reject as nonconstructive a Cantor set object K in a topos, defined as a final coalgebra for the functor F(X) = 2X (~ X+X, 2 being 1+1 in a topos). From this standpoint the existence of a Cantor set object is more plausible than a continuum object rather than less because more is needed. If you go with the double-induction approach of Pavlovic and Pratt, where the functor is F(X) = NX (~ X+X+X+...) then the topos needs a natural numbers object. If instead you go with Freyd's single-induction approach of connecting up (eliminating the gap between) the two halves of K+K, as preferred e.g. by Tom Leinster, then the topos needs structure sufficient tfor such gluing. I'm not aware of any reason why a topos with a Cantor set object K has to also have a natural number object N, though I'm not enough of a topos hacker myself to know how to produce one with K but without N (but would be happy to learn). Does such a topos exist in nature? And what can be said of the free topos with Cantor set object? Vaughan Pratt From rrosebru@mta.ca Sun Feb 1 10:29:07 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 01 Feb 2009 10:29:07 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LTdHV-00059N-5B for categories-list@mta.ca; Sun, 01 Feb 2009 10:26:41 -0400 Date: Sat, 31 Jan 2009 11:32:53 -0800 From: Toby Bartels To: categories Subject: categories: Re: It it a good idea to use the term 2-group outside of its use in group thoery? MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Disposition: inline Sender: categories@mta.ca Precedence: bulk Reply-To: Toby Bartels Message-Id: Status: O X-Status: X-Keywords: X-UID: 64 Ronnie Brown wrote: >I would like to raise an objection to using the term `2-group' as on nlab and elsehere since for the group theorists this has a specialised meaning: See the following wiki entry, especially the first 2 words: >"In mathematics, given a prime number p, a p-group is [...]" That the first 2 words are "In mathematics" rather than "In group theory, a branch of mathematics," means nothing. It's not like the Wikipedians had a discussion about it and determined that p-groups appear throughout mathematics. You do raise a good point, though. The term '2-group' is a special case of both 'p-group' and 'n-group', and these mean very different things. I wouldn't want to give up 'n-group', so I find '2-group' appropriate when (as on the n-Category Lab) one is discussing n-groups as well. But in your example about the structure of finite crossed modules, one can simply say 'crossed module', making a note that some literature calls a crossed module a '2-group' (or even 'strict 2-group'). >"[...] Such groups are also called primary." >there are claims that crossed modules, for example, can be thought of as `2-dimensional groups' In extreme cases, these show the way: both 'p-group' and 'n-group' are abbreviations, for 'p-primary group' and 'n-dimensional higher group'. So one can always use the full name or specify which usage one's paper follows. --Toby