From MAILER-DAEMON Fri Sep 21 15:47:32 2007 Date: 21 Sep 2007 15:47:32 -0300 From: Mail System Internal Data Subject: DON'T DELETE THIS MESSAGE -- FOLDER INTERNAL DATA Message-ID: <1190400452@mta.ca> X-IMAP: 1183469172 0000000042 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 Tue Jul 3 10:24:16 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 03 Jul 2007 10:24:16 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1I5iDt-0001Qp-HK for categories-list@mta.ca; Tue, 03 Jul 2007 10:15:17 -0300 Date: Mon, 2 Jul 2007 22:34:04 +0100 (BST) From: "Prof. Peter Johnstone" To: Categories mailing list Subject: categories: CT Advisory Committee MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: RO X-Status: X-Keywords: X-UID: 1 Dear fellow-categorists, On behalf of the international CT Advisory Committee, I am delighted to announce that Maria Manuel Clementino has agreed to join the Committee with immediate effect. The current membership of the Committee, in alphabetical order, is thus as follows: Maria Manuel Clementino Peter Johnstone (Secretary) Bill Lawvere (Chair) Ross Street Walter Tholen Myles Tierney Richard Wood It might be appropriate at this point to remind people of the Committee's function. It has no official status, and no executive authority: its sole function is to offer advice, and the benefit of our collective experience, to those who may be thinking of organizing international conferences in Category Theory, with the aim of ensuring that such conferences should take place on a reasonably regular basis. Anyone who might be thinking of organizing such a meeting is welcome to contact any member of the Committee -- but particularly the undersigned -- at any time. Peter Johnstone From rrosebru@mta.ca Tue Jul 3 10:24:17 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 03 Jul 2007 10:24:17 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1I5iEc-0001Ue-Gr for categories-list@mta.ca; Tue, 03 Jul 2007 10:16:02 -0300 Mime-Version: 1.0 (Apple Message framework v752.2) Content-Type: text/plain; charset=US-ASCII; delsp=yes; format=flowed Content-Transfer-Encoding: 7bit From: Pedro Resende Subject: categories: New junior research positions in mathematics at IST Date: Mon, 2 Jul 2007 22:58:55 +0100 To: Categories list Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 2 I append below an announcement that may be of interest to some readers of the categories list. Best, Pedro. ########### NEW JUNIOR RESEARCH POSITIONS IN MATHEMATICS AT IST The Center for Mathematical Analysis, Geometry, and Dynamical Systems of Instituto Superior Tecnico plans to open soon 4 research positions in mathematics in one of the areas in which the faculty of the Center is currently active, privileging the following: differential equations and dynamical systems (3 maximum); geometry and topology (including string theory and mathematical-physics) (3 maximum). All positions are for a period of 5 years, subject to annual evaluations. The Center is a research and scientific training unit of Instituto Superior Tecnico (http://www.ist.utl.pt/). It was established in 1991 and develops its activity in mathematics with special emphasis on nonlinear analysis, dynamical systems, geometry, and topology. The applicants should hold a Ph.D. in Mathematics or in a related area relevant to the scientific interests of the faculty of the Center, for at least 3 years. They must have a strong curriculum and show a very strong research promise. Details about these new positions and how to apply will be available soon in the Center's web page: http://camgsd.math.ist.utl.pt. The expected application deadline for this program is August 31st, 2007. From rrosebru@mta.ca Sat Jul 7 08:01:53 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 07 Jul 2007 08:01:53 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1I77sG-0003dl-D3 for categories-list@mta.ca; Sat, 07 Jul 2007 07:50:48 -0300 Date: Fri, 6 Jul 2007 12:55:50 -0400 (EDT) From: Michael Barr To: Categories list Subject: categories: Isbell duality MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 3 I have seen a reference to Isbell duality. Can anyone point me to a definition and any results? From rrosebru@mta.ca Sat Jul 7 08:01:53 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 07 Jul 2007 08:01:53 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1I77rW-0003cI-FK for categories-list@mta.ca; Sat, 07 Jul 2007 07:50:02 -0300 Subject: categories: Paper: Euler characteristic as a divergent sum From: Tom Leinster To: categories@mta.ca Content-Type: text/plain Date: Fri, 06 Jul 2007 16:50:52 +0100 Mime-Version: 1.0 Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 4 The following paper is available: "The Euler characteristic of a category as the sum of a divergent series" The Euler characteristic of a cell complex is often thought of as the alternating sum of the number of cells of each dimension. When the complex is infinite, the sum diverges. Nevertheless, it can sometimes be evaluated; in particular, this is possible when the complex is the nerve of a finite category. This provides an alternative definition of the Euler characteristic of a category, which is in many cases equivalent to the original one. http://arxiv.org/abs/0707.0835 Many thanks to Clemens Berger for suggesting the original idea. Best wishes, Tom From rrosebru@mta.ca Tue Jul 10 10:20:30 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 10 Jul 2007 10:20:30 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1I8FUy-00054v-Sn for categories-list@mta.ca; Tue, 10 Jul 2007 10:11:25 -0300 To: categories@mta.ca Subject: categories: Post-doc position in the European project Credo Date: Mon, 9 Jul 2007 16:28:19 +0200 (CEST) From: F.S.de.Boer@cwi.nl (Frank de Boer) Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 5 Postdoc in CREDO project The position is within the IST-33826 research project CREDO "Modeling and analysis of evolutionary structures for distributed services". The project aims at the development and application of an integrated suite of tools for compositional modeling, testing, and validation of software for evolving networks of dynamically reconfigurable components. More information on this project can be found at http://www.cwi.nl/projects/credo. The candidate is expected to work on a object-oriented software development method and architecture to support the dynamic composition of highly reconfigurable component-based software systems. The method structures applications as a network of adaptive concurrent computational tasks that interact using mobile channels. The research focusses on studying: (i) the effects of runtime reconfiguration of the network of mobile channels, and (ii) the effects runtime changes/upgrades of the computational tasks. In addition, the applicability of light-weight and automated verification and model checking techniques and tools will be evaluated in a real-world case study. The candidate should have a PhD degree and a background in software engineering, concurrency and distributed systems, and practical software development or formal methods. The postdoc is offered a full-time position for the remaining duration of the CREDO project (till September 2009). To ensure intensive knowledge transfer from industry to university and vice versa the position will be hosted by the research group on coordination languages of the Centre for Mathematics and Computer Science (CWI, Amsterdam, The Netherlands) and Almende BV which is one of the case study partners in the project. To apply, please send your letter of application, together with curriculum vitae, and possible letters of references to Alfons Salden (alfons@almende.com) and Frank de Boer (F.S.de.Boer@cwi.nl). From rrosebru@mta.ca Tue Jul 10 10:20:31 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 10 Jul 2007 10:20:31 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1I8FVs-0005AC-Rz for categories-list@mta.ca; Tue, 10 Jul 2007 10:12:20 -0300 Date: Mon, 09 Jul 2007 23:41:24 +0100 From: Reiko Heckel MIME-Version: 1.0 To: categories@mta.ca Subject: categories: Lecturer in Computer Science, University of Leicester Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: quoted-printable Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 6 Dear all the department of CS at Leicester is advertising a lectureship with focus on software engineering, in particular software evolution and model transformation, preferably with some formal background in=20 algebraic or categorical methods, graph transformation, rewriting, etc. The deadline for application is July 31, the post is available from October (and should be filled soon after). Please find further details below and don't hesitate to contact Jose or myself if you have any questions. Best wishes Reiko ---------------------------------------------------------------------- Lecturer in Computer Science, University of Leicester Salary Grade 8: =A332,976 to =A340,335 per annum Available from 1 October 2007 The University of Leicester seeks to appoint a Lecturer in Computer Science who can contribute to existing research in model-based software evolution, including meta-modelling and model transformation, model-driven development and re-engineering of legacy systems. Preference will be given to candidates with an interest in formal techniques who can contribute to and make use of the expertise that the Department has in algebraic and categorical structures and methods, including graph transformations and rewriting. Informal enquiries are welcome and should be addressed to Professor Jos=E9 Fiadeiro (jose@mcs.le.ac.uk), Head of Department, or Professor Reiko Heckel (reiko@mcs.le.ac.uk). Downloadable application forms and further particulars are available from www.le.ac.uk/personnel/jobs/a3331p.html. If you require a hard copy, please contact Personnel Services - tel: 0116 252 2758, fax: 0116 252 5140, email: recruitment3@le.ac.uk Please note that CVs will only be accepted in support of a fully completed application form. Closing Date: 31 July 2007 --=20 Dr Reiko Heckel Professor in Software Engineering Department of Computer Science University of Leicester Leicester LE1 7RH United Kingdom Tel +44 (0)116 252 3406 Fax +44 (0)116 252 3915 http://www.cs.le.ac.uk/people/rh122 From rrosebru@mta.ca Tue Jul 10 14:42:08 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 10 Jul 2007 14:42:08 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1I8JeF-0003Y1-8n for categories-list@mta.ca; Tue, 10 Jul 2007 14:37:15 -0300 Mime-Version: 1.0 (Apple Message framework v752.3) Content-Transfer-Encoding: 7bit Content-Type: text/plain; charset=US-ASCII; delsp=yes; format=flowed To: categories@mta.ca From: Steven R. Costenoble Subject: categories: Maps of monads - references Date: Tue, 10 Jul 2007 09:25:28 -0400 Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 7 In Toposes, Triples, and Theories, Barr and Wells define a morphism of triples (which, being a student of Peter May, I will call a map of monads) in the context of two monads on a given category C. I have a situation where I have two categories C and D, a monad S on C, a monad T on D, and a functor F: C -> D. There is a fairly obvious generalization of the TTT definition, to say that a map from S to T is a natural transformation FS -> TF making certain diagrams commute. My guess is that someone else noticed this long ago, so I'm looking for references to where this has appeared in the literature. I'm particularly interested in references that include the fact (at least, I'm pretty sure it's a fact) that such maps are in one-to-one correspondence with extensions of F to a functor between the respective Kleisli categories of S and T. Thanks in advance. --Steve Costenoble From rrosebru@mta.ca Tue Jul 10 20:05:02 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 10 Jul 2007 20:05:02 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1I8OfF-0001K5-36 for categories-list@mta.ca; Tue, 10 Jul 2007 19:58:37 -0300 Mime-Version: 1.0 (Apple Message framework v752.2) Content-Type: text/plain; charset=US-ASCII; delsp=yes; format=flowed To: categories@mta.ca Content-Transfer-Encoding: 7bit From: Steve Vickers Subject: categories: Re: Maps of monads - references Date: Tue, 10 Jul 2007 20:39:24 +0100 Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 8 See Ross Street "The formal theory of monads", JPAA 2 (1972) 149-168 for the general definition, in the abstract setting of a 2-category instead of Cat. Actually, there are two obvious generalizations of the TTT definition ("monad functors" and "monad opfunctors"), for the two possible directions of F. Steve Vickers. On 10 Jul 2007, at 14:25, Steven R. Costenoble wrote: > In Toposes, Triples, and Theories, Barr and Wells define a morphism > of triples (which, being a student of Peter May, I will call a map of > monads) in the context of two monads on a given category C. I have a > situation where I have two categories C and D, a monad S on C, a > monad T on D, and a functor F: C -> D. There is a fairly obvious > generalization of the TTT definition, to say that a map from S to T > is a natural transformation FS -> TF making certain diagrams commute. > My guess is that someone else noticed this long ago, so I'm looking > for references to where this has appeared in the literature. I'm > particularly interested in references that include the fact (at > least, I'm pretty sure it's a fact) that such maps are in one-to-one > correspondence with extensions of F to a functor between the > respective Kleisli categories of S and T. > > Thanks in advance. > > --Steve Costenoble > > > From rrosebru@mta.ca Tue Jul 10 20:05:02 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 10 Jul 2007 20:05:02 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1I8Oh9-0001QH-Hk for categories-list@mta.ca; Tue, 10 Jul 2007 20:00:35 -0300 Date: Tue, 10 Jul 2007 17:54:35 -0400 (EDT) From: Michael Barr To: categories@mta.ca Subject: categories: Re: Maps of monads - references MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 9 I think that somewhere Harry Appelgate did something like that, probably in his Ph.D. thesis. Whether he ever published it, I cannot now say. Michael On Tue, 10 Jul 2007, Steven R. Costenoble wrote: > In Toposes, Triples, and Theories, Barr and Wells define a morphism > of triples (which, being a student of Peter May, I will call a map of > monads) in the context of two monads on a given category C. I have a > situation where I have two categories C and D, a monad S on C, a > monad T on D, and a functor F: C -> D. There is a fairly obvious > generalization of the TTT definition, to say that a map from S to T > is a natural transformation FS -> TF making certain diagrams commute. > My guess is that someone else noticed this long ago, so I'm looking > for references to where this has appeared in the literature. I'm > particularly interested in references that include the fact (at > least, I'm pretty sure it's a fact) that such maps are in one-to-one > correspondence with extensions of F to a functor between the > respective Kleisli categories of S and T. > > Thanks in advance. > > --Steve Costenoble > > > From rrosebru@mta.ca Tue Jul 10 20:05:02 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 10 Jul 2007 20:05:02 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1I8OgW-0001OT-QQ for categories-list@mta.ca; Tue, 10 Jul 2007 19:59:56 -0300 Date: Tue, 10 Jul 2007 15:54:06 -0400 (EDT) From: Bill Lawvere To: categories@mta.ca Subject: categories: CT 07 June 17 - 23, 2007 MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 10 The category meeting in Carvoeiro, Portugal held from June 17th to 23rd, 2007 proved to be one of the most enjoyable and scientifically promising of the series. This was possible because of the thoughtful and dedicated organization by Diana Rodelo, Manuela Sobral, Maria Manuel Clementino, Jorge Picado, Lourdes Sousa, Gonzalo Gutierres, and Maria Joao Ferreira. They created a wonderful atmosphere which made possible the collaboration and friendship between the senior researchers who were there and the many very intelligent and active young people, who will be contributing their original research to future meetings. Of course, I was particularly honored by the fact that the conference banquet took note of my 70th birthday and was attended by several of my cherished students and colleagues. I was gratified to meet the many young researchers whom I had not previously known; they gave me the special gift of hope for the future of our science. My friends and colleagues join me in heartily thanking the organizers, the scientific committee, and the sponsoring organizations for having created a most memorable occasion. Bill Lawvere ************************************************************ F. William Lawvere, Professor emeritus Mathematics Department, State University of New York 244 Mathematics Building, Buffalo, N.Y. 14260-2900 USA Tel. 716-645-6284 HOMEPAGE: http://www.acsu.buffalo.edu/~wlawvere ************************************************************ From rrosebru@mta.ca Tue Jul 10 22:28:16 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 10 Jul 2007 22:28:16 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1I8QuU-0000gI-TN for categories-list@mta.ca; Tue, 10 Jul 2007 22:22:30 -0300 MIME-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Content-Transfer-Encoding: quoted-printable Subject: categories: Re: Maps of monads - references Date: Tue, 10 Jul 2007 17:31:21 PDT From: To: Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 11 There's also: The formal theory of monads II, R. Street and S. Lack,J. Pure Appl. Algebra 175 (1-3) (2002) 243-265; MR2003m:18007 (preprint available from the homepages of the authors). Street's work is about 2-categories of monads and many people needed the simply categorical level, because of the Linear Logic connection. So there are several printed versions of the restricted result, including one of our group, I believe, in Relating Categorical Semantics for Intuitionistic Linear Logic, (M. Maietti, P. Maneggia, V. de Paiva and E. Ritter) in Applied Categorical Structures, volume 13(1):1--36, 2005.=20 But given our application we prove it for comonads, lifting both to Eilenberg-Moore coalgebras and to co-Kleisli categories. Dr Valeria de Paiva PARC 3333 Coyote Hill Road Palo Alto, CA 94304 USA -----Original Message----- From: Steve Vickers [mailto:s.j.vickers@cs.bham.ac.uk]=20 Sent: Tuesday, July 10, 2007 12:39 PM To: categories@mta.ca Subject: categories: Re: Maps of monads - references See Ross Street "The formal theory of monads", JPAA 2 (1972) 149-168 for the general definition, in the abstract setting of a 2-category instead of Cat. Actually, there are two obvious generalizations of the TTT definition ("monad functors" and "monad opfunctors"), for the two possible directions of F. Steve Vickers. On 10 Jul 2007, at 14:25, Steven R. Costenoble wrote: > In Toposes, Triples, and Theories, Barr and Wells define a morphism of > triples (which, being a student of Peter May, I will call a map of > monads) in the context of two monads on a given category C. I have a=20 > situation where I have two categories C and D, a monad S on C, a monad > T on D, and a functor F: C -> D. There is a fairly obvious=20 > generalization of the TTT definition, to say that a map from S to T is > a natural transformation FS -> TF making certain diagrams commute. > My guess is that someone else noticed this long ago, so I'm looking=20 > for references to where this has appeared in the literature. I'm=20 > particularly interested in references that include the fact (at least, > I'm pretty sure it's a fact) that such maps are in one-to-one=20 > correspondence with extensions of F to a functor between the=20 > respective Kleisli categories of S and T. > > Thanks in advance. > > --Steve Costenoble > > > From rrosebru@mta.ca Wed Jul 11 15:19:51 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 11 Jul 2007 15:19:51 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1I8gbh-0006e5-IE for categories-list@mta.ca; Wed, 11 Jul 2007 15:08:09 -0300 Mime-Version: 1.0 (Apple Message framework v752.3) Content-Type: text/plain; charset=US-ASCII; delsp=yes; format=flowed Content-Transfer-Encoding: 7bit From: "Steven R. Costenoble" Subject: categories: Re: Maps of monads - references Date: Wed, 11 Jul 2007 09:04:47 -0400 To: categories@mta.ca Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 12 Thanks, all, for the many replies (private as well as to the list). Among other interesting references, almost everyone suggested Ross Street's "The formal theory of monads" as well as the recent followup by Street and Steve Lack, "The formal theory of monads II." I'll add those to my summer reading list. --Steve Costenoble On Jul 10, 2007, at 9:25 AM, Steven R. Costenoble wrote: > In Toposes, Triples, and Theories, Barr and Wells define a morphism > of triples (which, being a student of Peter May, I will call a map of > monads) in the context of two monads on a given category C. I have a > situation where I have two categories C and D, a monad S on C, a > monad T on D, and a functor F: C -> D. There is a fairly obvious > generalization of the TTT definition, to say that a map from S to T > is a natural transformation FS -> TF making certain diagrams commute. > My guess is that someone else noticed this long ago, so I'm looking > for references to where this has appeared in the literature. I'm > particularly interested in references that include the fact (at > least, I'm pretty sure it's a fact) that such maps are in one-to-one > correspondence with extensions of F to a functor between the > respective Kleisli categories of S and T. > > Thanks in advance. > > --Steve Costenoble > > > From rrosebru@mta.ca Thu Jul 12 09:26:50 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 12 Jul 2007 09:26:50 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1I8xeu-0001Rr-9K for categories-list@mta.ca; Thu, 12 Jul 2007 09:20:36 -0300 Date: Wed, 11 Jul 2007 21:20:58 -0400 (EDT) Subject: categories: Re: Isbell duality From: "Fred Linton" To: "Categories list" MIME-Version: 1.0 Content-Type: text/plain;charset=UTF-8 Content-Transfer-Encoding: 8bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 13 Michael asked: > I have seen a reference to Isbell duality. Can anyone point me to a > definition and any results? Perhaps John's 196x-ish "Structure of Categories" paper is what you seek. -- F. From rrosebru@mta.ca Fri Jul 13 10:24:34 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 13 Jul 2007 10:24:34 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1I9Kzo-0003AA-Fj for categories-list@mta.ca; Fri, 13 Jul 2007 10:15:44 -0300 To: categories@mta.ca Subject: categories: Lectureship in Computer Science From: rlc3@mcs.le.ac.uk (Roy L. Crole) Date: Fri, 13 Jul 2007 12:11:40 +0100 MIME-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 14 Dear Colleagues, The lectureship outlined below may be of interest to readers of categories and types. Please also pass the details on to others who may wish to apply. Roy Crole. ___________________________________________________________________ Lecturer in Computer Science, University of Leicester Salary Grade 8: =A332,976 to =A340,335 per annum Available from 1 October 2007 The University of Leicester seeks to appoint a Lecturer in Computer Science who can contribute to existing research in model-based software evolution, including meta-modelling and model transformation, model-driven development and re-engineering of legacy systems. Preference will be given to candidates with an interest in formal techniques who can contribute to and make use of the expertise that the Department has in algebraic and categorical structures and methods, including graph transformations and rewriting. Informal enquiries are welcome and should be addressed to Professor Jos=E9 Fiadeiro (jose@mcs.le.ac.uk), Head of Department, or Professor Reiko Heckel (reiko@mcs.le.ac.uk). Downloadable application forms and further particulars are available from www.le.ac.uk/personnel/jobs/a3331p.html. If you require a hard copy, please contact Personnel Services - tel: 0116 252 2758, fax: 0116 252 5140, email: recruitment3@le.ac.uk Please note that CVs will only be accepted in support of a fully completed application form. Closing Date: 31 July 2007 From rrosebru@mta.ca Fri Jul 13 10:24:34 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 13 Jul 2007 10:24:34 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1I9L13-0003KE-8n for categories-list@mta.ca; Fri, 13 Jul 2007 10:17:01 -0300 Date: Fri, 13 Jul 2007 12:22:53 +0100 (BST) From: "Prof. Peter Johnstone" To: Categories list Subject: categories: Re: Isbell duality MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 15 On Wed, 11 Jul 2007, Fred Linton wrote: > Michael asked: > >> I have seen a reference to Isbell duality. Can anyone point me to a >> definition and any results? > > Perhaps John's 196x-ish "Structure of Categories" paper is what you seek. > > -- F. I think it's more likely to refer to John's unpublished (indeed, unwritten) paper "Some concrete dualities". This appeared as an abstract in the AMS Notices in 1974 (vol. 21, pp. A567-8), and I heard John talk about it at an Oberwolfach meeting in 1975. In 1981 I asked John when we could expect to see the paper in print (since I was then writing "Stone Spaces", in which I wanted to refer to it), and he replied that he was still working on the write-up of his 1973 Oberwolfach talk. (The implication was that he'd get around to the 1975 talk when the earlier one was out of the way, but I'm pretty sure he never did.) Peter From rrosebru@mta.ca Fri Jul 13 13:24:10 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 13 Jul 2007 13:24:10 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1I9NtE-000151-7h for categories-list@mta.ca; Fri, 13 Jul 2007 13:21:08 -0300 Mime-Version: 1.0 (Apple Message framework v752.3) Content-Type: text/plain; charset=ISO-8859-1; delsp=yes; format=flowed From: Pierre-Louis Curien Subject: categories: Journees Jean-Yves Girard FREE REGISTRATION OPEN Date: Fri, 13 Jul 2007 17:46:42 +0200 To: categories@mta.ca, Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 16 Following earlier announcements, I am happy to inform you that a draft =20= programme of the ***************************** Journ=E9es Jean-Yves Girard Paris, Institut Henri Poincar=E9, September 10-12 ***************************** is now visible on the website of the event: http://www-lipn.univ-paris13.fr/jyg60/index-en.php Registration is also open on this site. (Registration is free, and serves several purposes: keeping a list of =20= participants, catering on Monday 10th evening, etc...) Please do register if you intend to attend the meeting. Best regards, on behalf of the organizing committee, Pierre-Louis Curien From rrosebru@mta.ca Sat Jul 14 11:09:24 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 14 Jul 2007 11:09:24 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1I9i9Z-0001zC-Pc for categories-list@mta.ca; Sat, 14 Jul 2007 10:59:21 -0300 Mime-Version: 1.0 (Apple Message framework v752.2) Content-Type: text/plain; charset=US-ASCII; delsp=yes; format=flowed Date: Fri, 13 Jul 2007 18:23:48 +0200 From: Marino Miculan Subject: categories: Call for papers: Proceedings of TYPES 2007 Content-Transfer-Encoding: 7bit To: categories@mta.ca Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 17 *** Call for papers: Proceedings of TYPES 2007 *** http://users.dimi.uniud.it/types07/ types07-cfp.html * OPEN TO ALL INTERESTED RESEARCHERS * The Post-Proceedings of the TYPES 2007 Annual Conference will be published, after a formal refereeing process, as a volume of the Lecture Notes in Computer Science (LNCS) series. Previous TYPES post- workshop proceedings include LNCS volumes 4502, 3895, 3085, 2646, 2277, 1657, 1512, 1158, 996 and 806. We hope this volume will give a good account of the papers presented at the conference and of recent research in the field in general. ** TOPICS ** We encourage you to submit research papers on the subject of the Types Coordination Action (see http://www.cs.chalmers.se/Cs/Research/ Logic/Types/objectives.html). Topics include, but are not limited to: - foundations of type theory and constructive mathematics - applications of type theory - dependently typed programming - industrial uses of type theory technology - meta-theoretic studies of type systems - implementation of proof-assistants - automation in computer-assisted reasoning - links between type theory and functional programming - formalizing mathematics using type theory Work within the scope of TYPES that was not presented at the workshop or whose authors are not formally involved in the Coordination Action may also be submitted for the proceedings. ** IMPORTANT DATES ** SUBMISSION DEADLINE: Monday, September 24, 2007. NOTIFICATION OF ACCEPTANCE: Monday, November 5, 2007. FINAL VERSION DUE: Monday, December 3, 2007. ** Submission guidelines ** We invite submission of high quality papers, written in English and typeset in LaTeX2e using the LNCS style. (See authors Instructions at Springer Online). Submissions should not have been published and should not be under consideration for publication elsewhere. Submissions should be no more than fifteen pages long in LNCS style. Please email your contribution as a self-contained PDF file to types07@dimi.uniud.it with subject "Submission to TYPES 2007 proceedings". In a separate email, give the title, authors and abstract of your submission, as well as email address of the corresponding author. All submissions will be acknowledged. LNCS is now published in full-text electronic version, as well as printed books. Thus we will need the final LaTeX source files of accepted submissions. The final versions of accepted submissions must be in the LaTeX2e LNCS style, and be as self-contained as possible. With the final version you will also be asked to complete a copyright form for LNCS accepted papers. We look forward to hearing from you. Marino Miculan, Ivan Scagnetto, Furio Honsell Editors of the TYPES 2007 Proceedings From rrosebru@mta.ca Mon Jul 16 21:42:59 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 16 Jul 2007 21:42:59 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1IAb2b-0000s4-Eh for categories-list@mta.ca; Mon, 16 Jul 2007 21:35:49 -0300 Date: Mon, 16 Jul 2007 19:30:53 -0500 From: "Yemon Choi" Reply-To: y.choi.97@cantab.net To: categories@mta.ca Subject: categories: categorical literature on Arens products? MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Content-Disposition: inline Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 18 Dear categorists (and anyone else reading), I have a question that's been bugging me for some time (in genesis, all the way back to 2002 I think). It concerns a certain construction of interest in the world of (Banach) algebras: given an algebra over a field one can equip its double dual with two natural algebra structures, in general distinct, which extend the original algebra structure. More generally any bilinear map from a pair of vector spaces to a third vector space admits two natural extensions to a bilinear map on the bidual spaces. Functional analysts know this through work of Arens, but reading through his original paper (Monatsh Math 1955) it becomes clear that most of the calculations work in any symmetric closed monoidal category and so I wondered if this kind of construction has been well-studied or is well-known/well-understood in the categorical community. (Arens comes close to this level of abstraction but requires his objects to be sets with structure.) Here are the details (parphrased by me into the SCMC setting), with apologies for the dodgy attempts at notation. We work in a fixed symmetric closed monoidal category V. Fix a distinguished object C in V (we are thinking of V as complex Banach spaces and C as the ground field). Denote the `tensor' in V by @, and isomorphism in V by ~ . For A in ob(V) define A' using the Hom-tensor adjunction in V, i.e. Hom_V ( __ @ A, C) ~ Hom_V( __, A'). As usual we have a natural transformation with components A --> A'', call this K. Given objects R, S, T in V let's write r(R,S,T) for the isomorphism R @ S @ T ~> S @ T @ R Now: given an arrow m: E@F --> G in V, we compose with the natural map K_G to get E@ F --> G'', then use the Hom-tensor adjunction to get an arrow E@F@G' --> C. Composing with the isomorphism r(G',E,F) gives us an arrow G' @ E @ F --> C and using Hom-tensor adjunction again gives us, finally, an arrow L(m) : G' @ E --> F' Note that in the case V=vector spaces, E an algebra, and F=G a left E-module with m the module action, L(m) is just the adjoint (right) action of E on the dual of F. Iterating this construction we get L^2(m): F'' @ G' --> E' and L^3(m): E'' @ F'' --> G'' which we might call the left Arens extension, or left Arens bidual, of m. The right Arens extension is constructed similarly: as before we produce from the original arrow m: E @ F --> G an arrow E @ F @ G' --> C. This time we compose with the isomorphism r(E,F,G')^{-1} to get an arrow F@ G' @ E --> C and apply Hom-tensor adjunction to get R(m): F @ G' --> E' Iterating this construction gives R^2(m): G' @ E'' --> F' and R^3(m): E'' @ F'' --> G'' which we call the right Arens extension, or right Arens bidual, of m. Then left and right Arens extensions have been studied by functional analysts, mainly in the particular case where E=F=G is a Banach algebra and m is the multiplication map; in this case both L^3(m) and R^3(m) define associative multiplication maps on the double dual A'', but in general these multiplication maps are not the same. (They coincide if A is a C^*-algebra, and it would be interesting if there was a categorical interpretation of the proof.) Two noticeable features of the work functional analysts have done on this area (in the case where V=Ban is Banach spaces and continuous linear maps) is that 1) the notation used to prove things is horrible, and usually looks a little like a proof by commutative diagrams would if it were written out as a line-by-line equational argument; 2) a lot of the proofs use analytic tools (Hahn-Banach theorem, weak compactness of various mappings) but look as if they should have `purely algebraic proofs', i.e. the desired equations can often be derived purely from the closed structure on Ban. So if anyone can point me to any existing categorical/logical literature in this vein I'd be very grateful! In particular I would like to know why there are two equally `canonical' extensions, and whether there are universal properties underlying them. Also: in view of point 1) above, is there a better kind of graphical calculus for doing calculations? Best wishes Yemon -- Dr. Y. Choi 519 Machray Hall Department of Mathematics University of Manitoba Winnipeg. Manitoba Canada R3T 2N2 Tel: (204)-474-8734 -- Dr. Y. Choi 519 Machray Hall Department of Mathematics University of Manitoba Winnipeg. Manitoba Canada R3T 2N2 Tel: (204)-474-8734 From rrosebru@mta.ca Tue Jul 17 08:33:47 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 17 Jul 2007 08:33:47 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1IAlCs-0005D4-AM for categories-list@mta.ca; Tue, 17 Jul 2007 08:27:06 -0300 Mime-Version: 1.0 Date: Tue, 17 Jul 2007 12:59:29 +0200 To: categories@mta.ca From: Anders Kock Subject: categories: Arens product Content-Type: text/plain; charset="us-ascii" ; format="flowed" Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 19 In reply to Yemon Choi: The situation you describe has been studied in the context of symmetric monoidal closed categories, in some articles by me in the early 1970s (references below). The main point about double dualization in Banach spaces is that it is part of a V-enriched ("strong") monad on V (for suitable symmetric monoidal closed category V); and the two "Arens extensions" are special cases of the two canonical monoidal structures which any V-enriched monad on V admits. Commutative monads are those where the two structures agree. [1] Monads on symmetric monoidal closed categories, Archiv der Math. 21 (1970), 1-10. [2] On double dualization monads, Math. Scand 27 (1970), 151-165. [3] Bilinearity and Cartesian closed monads, Math. Scand 29 (1971), 161-174. [4] Strong functors and monoidal monads, Archiv der Math. 23 (1972), 113-120. [5] Closed categories generated by commutative monads, J. Austral. Math. Soc. 12 (1971), 405-424. The V-enrichment ("strength") of an endofunctor T on V can be encoded without reference to the closed structure of V as a transformation T(A)@B-->T(A@B) ("tensorial strength", introduced in [4]). Strong monads applied in functional-analytic contexts are also considered in my [6] Some problems and results in synthetic functional analysis , in Category Theoretic Methods in Geometry, Proceedings Aarhus 1983, Aarhus Various Publication Series 35 (1983) 168-191. All these papers, except [5], can be downloaded from my home page (go to the bottom of it), http://home.imf.au.dk/kock/ I hope the above references can be useful. Best wishes. Anders Kock From rrosebru@mta.ca Tue Jul 17 21:30:43 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 17 Jul 2007 21:30:43 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1IAxKz-0005Hf-Qb for categories-list@mta.ca; Tue, 17 Jul 2007 21:24:17 -0300 Date: Tue, 17 Jul 2007 14:11:46 -0400 (EDT) From: Jeff Egger Subject: categories: Actions of monoidal functors [was Re: Arens product] To: categories@mta.ca MIME-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 20 Dear all, Anders Kock's reply to Yemon Choi gives me a good opportunity to pose a question which I have been meaning to ask the list for a while: > The V-enrichment ("strength") of an endofunctor T on V can be encoded > without reference to the closed structure of V as a transformation > T(A)@B-->T(A@B) ("tensorial strength", introduced in [4]). This notion of "tensorial strength" is just a special case of what I would call "an action of a monoidal functor on a (mere) functor". Specifically, it is a right-action of the identity monoidal functor on the functor T. In general, given a monoidal functor M:V-->W and a functor T:V-->W, a right-action of M on T should be a n.t. of the form T(A)@M(B)-->T(A@B) satisfying the obvious associativity and unitality axioms. For instance, if we regard a G-graded algebra as a monoidal functor G-->Vec, then a right-action of this on a mere functor G-->Vec is precisely the same thing as a G-graded right-module. [Here the monoid G (G can also stand for grading-object!) is considered as a discrete monoidal category.] I have always assumed that this concept is well-known, but I haven't succeeded in finding a reference in the literature for it... perhaps some of the more well-read readers of this list could help me out? Cheers, Jeff. P.S. Upon reviewing [4], I see that there is a more general notion of tensorial strength which can be applied to a functor A-->B whenever A and B are tensored over some monoidal category V. There is a similar adaptation of the notion of action of a monoidal functor V-->W to functors A-->B whenever A is tensored over (or I would say, acted on by) V, and B over (by) W. > [4] Strong functors and monoidal monads, Archiv der Math. 23 (1972), > 113-120. From rrosebru@mta.ca Wed Jul 18 10:58:22 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 18 Jul 2007 10:58:22 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1IB9vf-0002Qg-EE for categories-list@mta.ca; Wed, 18 Jul 2007 10:50:59 -0300 Mime-Version: 1.0 Date: Wed, 18 Jul 2007 10:52:50 +0200 To: categories@mta.ca From: Anders Kock Subject: categories: tensorial strength Content-Type: text/plain; charset="us-ascii" ; format="flowed" Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 21 In reply to Jeff Egger: Actions by monoidal categories were considered by Benabou in 1967 ("Intoduction to bicategories", Midwest Category Seminar I); strength of functors between categories on which a monoidal category acts were considered by H. Lindner, in some papers/preprints in the late 70s, and a summary is given in his "Enriched categories and enriched modules", Cahiers Vol 22 (1981), 161-174. This paper also contains several references. -Aspects of tensorial strength has been developed by several computer-science mathematicians later (starting with E. Moggi, I believe); I do not know much about their work, so my answer to Jeff's question may not be up to date. Anders Kock From rrosebru@mta.ca Wed Jul 18 14:29:07 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 18 Jul 2007 14:29:07 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1IBDJK-0001I5-4x for categories-list@mta.ca; Wed, 18 Jul 2007 14:27:38 -0300 Date: Wed, 18 Jul 2007 15:12:29 +0200 From: MIME-Version: 1.0 Subject: categories: MCU 2007: Call for Participation - Poster and Open Session Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit To: undisclosed-recipients:; Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 22 = = = = Apologies for multiple postings = = = = = PARTICIPATION POSTER OPEN SESSION ---------------------------------------------------------------------- International Conference M M CCC U U 22222 00000 00000 7777777 MM MM C C U U 2 2 0 0 0 0 7 M M M M C U U 2 2 0 0 0 0 7 M M M C U U 22 0 0 0 0 7 M M C U U 2 0 0 0 0 7 M M C C U U 22 0 0 0 0 77 M M CCC UUU 2222222 00000 00000 77 MACHINES, COMPUTATIONS AND UNIVERSALITY ORLEANS, FRANCE SEPTEMBER, 10-13, 2007 http://www.univ-orleans.fr/lifo/Manifestations/MCU07/ ----------------------------------------------------------------------- MCU takes place every 3 years since 1995. Its proceedings are in Springer's LNCS (from 2001). From the beginning they gave rise to special issues of first TCS then Fundamenta Informaticae. ----------------------------------------------------------------------- TOPICS: Digital computation (fundamental classical models): Turing machines, register machines, word processing (groups and monoids), other machines. Digital models of computation: cellular automata, other automata, tiling of the plane, polyominoes, snakes, neural networks, molecular computations, Analog and Hybrid Computations: BSS machines, infinite cellular automata, real machines, quantum computing In all these settings: frontiers between a decidable halting problem and an undecidable one in the various computational settings minimal universal codes: size of such a code, namely, for Turing machines, register machines, cellular automata, tilings, neural nets, Post systems, ... computation complexity of machines with a decidable halting problem as well as universal machines, connections between decidability under some complexity class and completeness according to this class, self-reproduction and other tasks, universality and decidability in the real field PROGRAM COMMITTEE: Erzsebet CSUHAJ-VARJU, Hungarian Academy of Sciences, Hungary Jerome DURAND-LOSE, University of Orleans, France, co-chair Angsheng LI, Institute of Software, Chinese Academy of Sciences, Beijing, China Maurice MARGENSTERN, LITA, University of Metz, France, co-chair Jean-Yves MARION, LORIA, Ecole des Mines de Nancy, France Gheorghe PAUN, Romanian Academy, Bucharest, Romania Yurii ROGOZHIN, Institute of Mathematics, Chisinau, Moldova Grzegorz ROZENBERG, University of Leiden, The Netherlands Jiri WIEDERMANN, Academy of Science, Czech Republic Damien WOODS, University College, Cork, Ireland INVITED SPEAKERS: Andrew ADAMATZKY, University of Bristol, UK Encapsulating Reaction-diffusion Computers Olivier BOURNEZ, LORIA, INRIA-Lorraine, France On the Computational Capabilities of Several Models Mark BURGIN, UCLA, Los Angeles, USA Universality, Reducibility, and Completeness Manuel CAMPAGNOLO, Lisbon University of Technology, Portugal Using Approximation to Relate Computational Classes over the Reals Joel David HAMKINS, CUNY, New-York, USA A Survey of Infinite Time Turing Machines Jarkko KARI, University of Turku, Finland The Tiling Problem Revisited Pascal KOIRAN, Ecole Normale Superieure de Lyon, France Decision versus Evaluation in Algebraic Complexity Kenichi MORITA, University of Hiroshima, Japan A Universal Reversible Turing Machine KG SUBRAMANIAN, Christian College of Chennai, India P Systems and Picture Languages Klaus SUTNER, Carnegie Mellon University, Pittsburgh, USA Information Hiding and Incompleteness POSTER / OPEN SESSION: We are planning to have a poster session and/or an open session. If you are interested in presenting some work in either form please contact one the PC chairs before July 31st at jerome.durand-lose@univ-orleans.fr margens@univ-metz.fr REGISTRATION: Registration is open on the web site: http://www.univ-orleans.fr/lifo/Manifestations/MCU07/ Category | Early registration | Late (after July, the 31st, 2007) ----------+--------------------+---------------------------------- Full | 300 | 350 Student | 200 | 250 ACCEPTED PAPERS: Artiom ALHAZOV, Rudolf FREUND, Marion OSWALD, Sergey VERLAN Partial Halting in P Systems Using Membrane Rules with Permitting Contexts Artiom ALHAZOV, Mario de Jesus PEREZ-JIMENEZ Uniform Solution of QSAT using Polarizationless Active Membranes Dorothea BAUMEISTER, Jorg ROTHE Satisfiability Parsimoniously Reduces to the Tantrix(TM) Rotation Puzzle Problem Tommaso BOLOGNESI Planar trivalent network computation Jurgen DASSOW, Bianca TRUTHE On the Power of Networks of Evolutionary Processors Liesbeth De MOL Study of Limits of Solvability in Tag Systems John FISHER, Marc BEZEM Query Completeness of Skolem Machine Computations Hermann GRUBER, Markus HOLZER, Martin KUTRIB More on the Size of Higman-Haines Sets: Effective Constructions Artiom MATVEEVICI, Yurii ROGOZHIN, Sergey VERLAN Insertion-Deletion Systems with One-Sided Contexts Victor MITRANA, Juan CASTELLANOS, Florin MANEA, Luis Fernando MINGO LOPEZ Accepting Networks of Splicing Processors With Filtered Connections Frantisek MRAZ, Martin PLATEK, Friedrich OTTO Hierarchical relaxations of the correctness preserving property for restarting automata Turlough NEARY, Damien WOODS Four small universal Turing machines Hidenosuke NISHIO Changing the Neighborhood of Cellular Automata Alexander OKHOTIN A simple P-complete problem and its representations by language equations Olivier TEYTAUD Slightly beyond Turing's computability for studying genetic programming Hiroshi UMEO A Smallest Five-State Solution to the Firing Squad Synchronization Problem Damien WOODS, Turlough NEARY Small semi-weakly universal Turing machines Jean-Baptiste YUNES Simple New Algorithms which solve the Firing Squad Synchronization Problem: a 7-states 4n-steps solution From rrosebru@mta.ca Wed Jul 18 14:29:08 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 18 Jul 2007 14:29:08 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1IBDIQ-0001BL-9O for categories-list@mta.ca; Wed, 18 Jul 2007 14:26:42 -0300 Subject: categories: Re: tensorial strength To: categories@mta.ca Date: Wed, 18 Jul 2007 12:23:56 -0300 (ADT) MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit From: rjwood@mathstat.dal.ca (RJ Wood) Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 23 (I wrote this to Jeff and Anders a few minutes ago. Since Anders has replied to all I am circulating it more widely.) Dear Jeff and Anders In my thesis (supervised by Bob Pare at Dalhousie in 1976) I considered (for reasons I won't labour here) (V^op,set)-categories, for monoidal V. The monoidal structure I took on (V^op,set) was Brian Day's convolution. Necessarily, a (V^op,set)-category A gives rise to a functor P:A^op x V^op x A ---> set and this reveals that there are three special kinds of (V^op,set)-categories: 1) those for which P(-,v,b) is representable, for all v and b, by {v,b} say 2) those for which P(a,-,b) is representable, for all a and b, by [a,b] say 3) those for which P(a,v,-) is representable, for all a and v, by v@a say. Ordinary V-categories are given by 2). The others have been known by various names but they are best understood in terms of actions. Now suppose that F:A--->B is a (V^op,set)-functor where A is of type i) and B is of type j) as above. Each of the nine possibilities admits a simple encoding of the enrichment as displayed in the following table: i)\j) 1) 2) 3) 1) F{v,b}--->{v,Fb} v--->[F{v,b},Fb] v@F{v,b}--->Fb 2) Fa--->{[a,b],Fb} [a,b]--->[Fa,Fb] [a,b]@Fa--->Fb 3) Fa--->{v,F(v@a)} v--->[Fa,F(v@a)] v@Fa--->F(v@a) Susan Niefield, Robin Cockett, and I are writing a paper whose sequel will deal with later developments of this topic. Best to all, Richard > Dear all, > > Anders Kock's reply to Yemon Choi gives me a good opportunity to pose a > question which I have been meaning to ask the list for a while: > > > The V-enrichment ("strength") of an endofunctor T on V can be encoded > > without reference to the closed structure of V as a transformation > > T(A)@B-->T(A@B) ("tensorial strength", introduced in [4]). > > This notion of "tensorial strength" is just a special case of what > I would call "an action of a monoidal functor on a (mere) functor". > Specifically, it is a right-action of the identity monoidal functor > on the functor T. > > In general, given a monoidal functor M:V-->W and a functor T:V-->W, a > right-action of M on T should be a n.t. of the form T(A)@M(B)-->T(A@B) > satisfying the obvious associativity and unitality axioms. > > For instance, if we regard a G-graded algebra as a monoidal functor G-->Vec, > then a right-action of this on a mere functor G-->Vec is precisely the same > thing as a G-graded right-module. [Here the monoid G (G can also stand for > grading-object!) is considered as a discrete monoidal category.] > > I have always assumed that this concept is well-known, but I haven't > succeeded in finding a reference in the literature for it... perhaps > some of the more well-read readers of this list could help me out? > > Cheers, > Jeff. > > P.S. Upon reviewing [4], I see that there is a more general notion of > tensorial strength which can be applied to a functor A-->B whenever A > and B are tensored over some monoidal category V. There is a similar > adaptation of the notion of action of a monoidal functor V-->W to > functors A-->B whenever A is tensored over (or I would say, acted on by) > V, and B over (by) W. > > > [4] Strong functors and monoidal monads, Archiv der Math. 23 (1972), > > 113-120. From rrosebru@mta.ca Fri Jul 20 17:04:37 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 20 Jul 2007 17:04:37 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1IByZ6-0002pt-Ow for categories-list@mta.ca; Fri, 20 Jul 2007 16:55:04 -0300 Mime-Version: 1.0 (Apple Message framework v752.2) Content-Type: text/plain; charset=US-ASCII; format=flowed Content-Transfer-Encoding: 7bit From: Ross Street Subject: categories: Re: Actions of monoidal functors [was Re: Arens product] Date: Thu, 19 Jul 2007 14:46:41 +1000 To: Categories Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 24 Dear Jeff "Monoid" and "object on which a monoid acts" make sense in any multicategory. A monoidal functor is a monoid in the convolution multicategory [V,W] of functors from V to W. The T of which you speak is an object on which M acts in [V,W]. Regards, Ross On 18/07/2007, at 4:11 AM, Jeff Egger wrote: > In general, given a monoidal functor M:V-->W and a functor T:V-->W, a > right-action of M on T should be a n.t. of the form T(A)@M(B)-->T(A@B) > satisfying the obvious associativity and unitality axioms. > -------------------- > I have always assumed that this concept is well-known, but I haven't > succeeded in finding a reference in the literature for it... perhaps > some of the more well-read readers of this list could help me out? From rrosebru@mta.ca Fri Jul 20 17:04:37 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 20 Jul 2007 17:04:37 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1IByaD-0002tg-Sf for categories-list@mta.ca; Fri, 20 Jul 2007 16:56:13 -0300 Date: Thu, 19 Jul 2007 15:23:56 +0200 From: Francois Lamarche To: categories@mta.ca Subject: categories: PSSL86: The website is now open. Reply-To: lamarche@loria.fr MIME-Version: 1.0 (generated by SEMI 1.14.6 - "Maruoka") Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 25 Fellow Category Theorists, The website for PSSL86 is now open, including a list of suggested hotels and the registration page, in two languages. http://www.loria.fr/~lamarche/psslHomeEN.html http://www.loria.fr/~lamarche/psslHomeFR.html We are asking you to use the registration page to inform us of your intention to attend. The process is quite informal, but we need to keep track of how many people are coming, in order to prepare for the catering. There are no registration fees, but those who want to attend the Saturday banquet will be asked for a moderate sum. See you soon in Nancy, Fran=E7ois Lamarche http://www.loria.fr/~lamarche ****************************************************** PSSL86 IN NANCY The 86th edition of the Peripatetic Seminar on Sheaves and Logic will be held at the Institut =C9lie Cartan (IECN) on the Universit=E9 Henri Poincar=E9 campus in Nancy, France, on the weekend of September 8-9 2007. We intend to continue the PSSL tradition of informality, and to schedule talks pertaining to any aspect of category theory, with or without applications in natural science, logic, computer science, or other branches of mathematics. The schedule will be announced shortly before the event. From rrosebru@mta.ca Fri Jul 20 17:04:37 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 20 Jul 2007 17:04:37 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1IByam-0002vb-FY for categories-list@mta.ca; Fri, 20 Jul 2007 16:56:48 -0300 From: Aaron Lauda Date: Thu, 19 Jul 2007 14:05:46 -0400 To: categories@mta.ca Subject: categories: pivotal adjoints? 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: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 26 Dear category theorists, Suppose we have chosen left and right adjoints for F:A->B and G:A->B F-| F* -| F and G-| G*-|G i_F: 1_B =3D> FF* i_G: 1_B =3D> GG* e_F: F*F =3D> 1_A e_G: G*G =3D> 1_A j_F: 1_A =3D> F*F j_G: 1_A =3D> G*G k_F: FF* =3D> 1_B k_G: GG* =3D> 1_B Then given any 2-morphism a:F=3D>G there are two obvious duals (mates =20 under adjunction) for the 2-morphsism a a+ :G*=3D>F* :=3D (e_G F*).(G*aF*).(G* i_F) +a :G*=3D>F* :=3D (F* k_G).(F*aG*).(j_F G*) or for those who like pictures: +a a+ __ __ / \ | | / \ | | | | | | | a | | a | | | | | | | | \__/ \__/ | | | In general a+ is not equal to +a because if is was we could always twist one of the units and counits so that it does not hold. Has the condition =20 that a+ =3D +a been investigated in the literature anywhere? In =20 particular, if a 2-category is such that all 1-morphisms F have a =20 simultaneous left and right adjoint then has anyone studied the =20 context where the adjoints are such that a+ =3D +a is always =20 satisfied? Perhaps, this notion has been studied in the language of =20 duals for 1-morphisms? The above condition appears to be related to the notion of pivotal =20 category when we look at Hom(A,A) for any object A. Thanks, Aaron Lauda From rrosebru@mta.ca Sat Jul 21 11:05:50 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 21 Jul 2007 11:05:50 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1ICFVz-0001pj-VW for categories-list@mta.ca; Sat, 21 Jul 2007 11:01:00 -0300 Date: Sat, 21 Jul 2007 00:36:32 +0100 From: Reiko Heckel MIME-Version: 1.0 To: categories@mta.ca Subject: categories: Graduate Teaching Assistant in Computer Science, University of Leicester Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 27 Dear all the department of CS at Leicester is advertising a position for Graduate Teaching Assistant, a PhD grant with teaching duties, for a period of four years. The topic is open, but will normally match some aspects of the research profile of the department. Candidates are expected to submit a short outline proposal with their application. Please don't hesitate to contact any member of staff if you would like to discuss possible topics and supervisors. http://www.cs.le.ac.uk/people/ The closing date is 10th of August, see http://www.le.ac.uk/personnel/supportjobs/s3366a.html for further details. Best wishes Reiko -- Dr Reiko Heckel Professor in Software Engineering Department of Computer Science University of Leicester Leicester LE1 7RH United Kingdom Tel +44 (0)116 252 3406 Fax +44 (0)116 252 3915 http://www.cs.le.ac.uk/people/rh122 From rrosebru@mta.ca Sun Jul 22 11:39:53 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 22 Jul 2007 11:39:53 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1ICcSc-0006dv-EJ for categories-list@mta.ca; Sun, 22 Jul 2007 11:31:02 -0300 From: Prof. Dr. Pumpluen To: Subject: categories: Re: Maps of monads - references Date: Sun, 22 Jul 2007 11:14:07 +0200 MIME-Version: 1.0 Content-Type: text/plain;charset="iso-8859-1" Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: RO X-Status: X-Keywords: X-UID: 28 There is still another, very detailed reference (probably earlier) to this topic in my paper "Eine Bemerkung ueber Monaden und adjungierte Funktoren", Math. Ann.185, 329-337 (1970). Best regards Nico Pumpluen. On Jul 10, 2007, at 9:25 AM, Steven R. Costenoble wrote: > In Toposes, Triples, and Theories, Barr and Wells define a morphism > of triples (which, being a student of Peter May, I will call a map of > monads) in the context of two monads on a given category C. I have a > situation where I have two categories C and D, a monad S on C, a > monad T on D, and a functor F: C -> D. There is a fairly obvious > generalization of the TTT definition, to say that a map from S to T > is a natural transformation FS -> TF making certain diagrams commute. > My guess is that someone else noticed this long ago, so I'm looking > for references to where this has appeared in the literature. I'm > particularly interested in references that include the fact (at > least, I'm pretty sure it's a fact) that such maps are in one-to-one > correspondence with extensions of F to a functor between the > respective Kleisli categories of S and T. > > Thanks in advance. > > --Steve Costenoble > > > From rrosebru@mta.ca Tue Jul 24 12:14:27 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 24 Jul 2007 12:14:27 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1IDLyB-0006J0-EV for categories-list@mta.ca; Tue, 24 Jul 2007 12:06:39 -0300 From: "Michael Ignaz Schumacher - CM at ACM SAC08" To: "Michael Ignaz Schumacher - CM at ACM SAC08" Subject: categories: 2nd CFP: ACM SAC Special Track on Coordination Models, Languages and Architectures Date: Tue, 24 Jul 2007 15:54:21 +0200 MIME-Version: 1.0 Content-Type: text/plain;charset="us-ascii" Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 29 [Apologies if you receive multiple copies] 2nd CFP: ACM SAC Special Track on Coordination Models, Languages and Architectures ----------------------------------------------------------------------- CALL FOR PAPERS ----------------------------------------------------------------------- Coordination Models, Languages and Applications Special Track of the 23rd ACM Symposium on Applied Computing (SAC08) March 16 - 20, 2008, Fortaleza, Brazil http://ii.hevs.ch/sac2008 ----------------------------------------------------------------------- IMPORTANT DATES * Submission deadline: 7 September 2007 * Author notification: 15 October 2007 * Camera ready: 30 October 2007 ----------------------------------------------------------------------- AIMS & SCOPE Building on the success of the nine previous editions (1998-2007), a special track on coordination models, languages and applications will be held at SAC 2008. Over the last decade, we have witnessed the emergence of models, formalisms and mechanisms to describe concurrent and distributed computations and systems based on the concept of coordination. The purpose of a coordination model is to enable the integration of a number of, possibly heterogeneous, components (processes, objects, agents) in such a way that the resulting ensemble can execute as a whole, forming a software system with desired characteristics and functionalities which possibly takes advantage of parallel and distributed systems. The coordination paradigm is closely related to other contemporary software engineering approaches such as multi-agent systems, service-oriented architectures, component-based systems and related middleware platforms. Furthermore, the concept of coordination exists in many other Computer Science areas such as workflow systems, cooperative information systems, distributed artificial intelligence, and internet technologies. After more than a decade of research, the coordination paradigm is gaining increased momentum in state-of-the-art engineering paradigms such as multi-agent systems and service-oriented architectures: in the first case, coordination abstractions are perceived as essential to design and support the working activities of agent societies; in the latter case, service coordination, orchestration, and choreography are going to be essential aspects of the next generations of systems based on Web services. The Special Track on Coordination Models, Languages and Applications takes a deliberately a broad view of what constitutes coordination. Accordingly, major topics of interest this year will include: - Novel models, languages, programming and implementation techniques - Applications of coordination technologies - Industrial points of view: experiences, applications, open issues - Internet- and Web-based coordinated systems - Coordination of multi-agent systems, including mobile agents, intelligent agents, and agent-based simulations - Coordination in Service-oriented architectures and Web Services - Languages for service description and composition - Models, frameworks and tools for Group Decision Making - Modern Workflow Management Systems and Case-Handling - Coordination in Computer Supported Cooperative Work - Software architectures and software engineering techniques - Configuration and Architecture Description Languages - Coordination Middleware and Infrastructures - Coordination in GRID systems - Emergent Coordination: Swam based, Stigmergy - Coordination technologies, systems and infrastructures - Relationship with other computational models such as object oriented, declarative (functional, logic, constraint), programming or their extensions with coordination capabilities - Formal aspects (semantics, reasoning, verification) ----------------------------------------------------------------------- PROCEEDINGS AND POST-PROCEEDINGS Papers accepted for the Special Track on Coordination Models, Languages and Applications will be published by ACM both in the SAC 2008 proceedings and in the Digital Library. Selected papers will be published in a Journal's special issue. ----------------------------------------------------------------------- PAPER SUBMISSION Original papers from the above-mentioned or other related areas will be considered. This includes three categories of submissions: 1) original and unpublished research; 2) reports of innovative computing applications in the arts, sciences, engineering, business, government, education and industry; and 3) reports of successful technology transfer to new problem domains. Each submitted paper will be fully refereed and undergo a blind review process by at least three referees. The accepted papers in all categories will be published in the ACM SAC 2008 proceedings. Format: Submit your paper electronically in either PDF or postscript format. Please note: neither hardcopy nor fax submissions will be accepted. Submissions should be printable on a standard printer on common paper formats such as letter and DIN A4. Please use a Postscript previewer such as Ghostview to check the portability of Postscript documents. The author(s) name(s) and address(es) must not appear in the body of the paper, and self reference should be in the third person. This is to facilitate blind review. The body of the paper should not exceed 4,000 words. Accepted full papers should not exceed 5 pages in a double column format (with the option, at additional expense, to add three more pages). Accepted poster papers will be published as extended 2-page abstracts in the symposium proceedings. All submissions must be received by 7 September 2007 SUBMISSION PROCEDURE Submission is entirely automated by an eCMS paper management tool, which is available from the main SAC Web Site: http://www.acm.org/conferences/sac/sac2008/. Authors must first register their own account by obtaining a password, and then follow the instructions. ----------------------------------------------------------------------- PROGRAM CHAIRMEN Michael Ignaz Schumacher, Swiss Federal Institute of Technology Lausanne (EPFL) & University of Applied Sciences Western Switzerland Alan Wood, University of York, UK Email contact : cm.sac2008@gmail.com ----------------------------------------------------------------------- PROGRAM COMMITTEE Arbab Farhad, CWI & Leiden University, Netherlands Bonsangue Marcello, Leiden University, Netherlands Bortenschlager Manfred, Salzburg Research, Austria Chaudron Michel, Technical University of Eindhoven, Netherlands de Nicola Rocco, University of Florence, Italy Ferrari Gianluigi, University of Pisa, Italy Fiadeiro Jose, University of Leicester, UK Harrison-Broninski Keith, Role Modellers Ltd, UK Jacob Jeremy, University of York, UK Lichtner Kurt, University of Waterloo, Canada Muccini Henry, University of l'Aquila, Italy Murphy Amy, University of Lugano, Switzerland Norton Barry, University of Sheffield, UK Omicini Andrea, University of Bologna, Italy Oriol Manuel, ETH Zurich, Switzerland Pallota Vincenzo, University of Fribourg, Switzerland Petta Paolo, Medical University of Vienna, Austria Picco Gian Pietro, University of Trento, Italy Razvan Popescu, University of Pisa, Italy Andries Stam, Leiden University, Netherlands Porto Antonio, New University of Lisbon, Portugal Pugliese, Rosario, University of Florence, Italy Rossi Davide, Scienze dell'Informazione, Bologna, Italy Tahara Yasuyuki, National Institute of Informatics, Japan Talcott Carolyn, SRI International, USA Wells George, Rhodes University, South Africa Wiklicky Herbert, Imperial College London, UK Wojciechowski Pawel T., Poznan University of Technology, Poland Zambonelli Franco, University of Modena-Reggio Emilia, Italy From rrosebru@mta.ca Tue Jul 24 12:14:27 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 24 Jul 2007 12:14:27 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1IDLxG-0006Cv-VG for categories-list@mta.ca; Tue, 24 Jul 2007 12:05:43 -0300 From: Thomas Streicher Subject: categories: generic families of finite sets in toposes with nno ? To: categories@mta.ca Date: Tue, 24 Jul 2007 15:25:26 +0200 (CEST) MIME-Version: 1.0 Content-Transfer-Encoding: 7bit Content-Type: text/plain; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 30 I have the following question about finite objects in toposes with nno where with ``finite'' I mean K-finite and with decidable equality. It is well known that in every topos EE with nno N there exists a family k : K -> N of finite sets such that for every family a : A -> I of finite sets there exists an epi e : I ->> J and a map f : J -> N such that e^*a \cong f^*k. Such a map k one may call a ``weakly generic family of finite sets''. I would like to know whether there always exists a family \pi : E -> U of finite sets which is "generic" in the sense that for every family a : A -> I of finite sets there exists an f : I -> U with f^*k' \cong a. Already for Psh(G) with G a nontrivial finite group one cannot take the usual weakly generic map k = \succ \circ \add : N x N -> N because the representable object G = y(*) is finite but not isomorphic to n^*k for some n : 1 -> N. However, for arbitrary small cats C such a map \pi : E -> U exist: take for U(I) the set of presheaves on C/I valued in FinSet_iso and where u operates by precomposing with (C/u)^\op. E(I) consists of pairs (F,x) where F is in U(I) and x \in F(\id_I). (This is a variation of a construction in my paper "Universes in Toposes" pp.9-10 albeit with FinSet instead of a Groth.universe). However, it is not clear to me for the case of sheaf toposes. In realizability toposes I think the usual k = \succ \circ \add : N x N -> N does work. Anyway, I would like to know if anyone has considered the problem and whether there is a "logical" (i.e. in the internal language) construction of a generic family family \pi : E -> U for every topos with nno. Thomas Streicher From rrosebru@mta.ca Tue Jul 24 19:24:49 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 24 Jul 2007 19:24:49 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1IDSjE-0007Bn-47 for categories-list@mta.ca; Tue, 24 Jul 2007 19:19:40 -0300 Content-Type: text/plain; charset=US-ASCII; delsp=yes; format=flowed Content-Transfer-Encoding: 7bit From: Steve Vickers Subject: categories: Bicomma objects Date: Tue, 24 Jul 2007 17:02:49 +0100 To: categories@mta.ca Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 31 What is the difference between a bicomma object and a comma object (a.k.a. lax pullback)? Steve. From rrosebru@mta.ca Tue Jul 24 19:24:49 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 24 Jul 2007 19:24:49 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1IDSmx-0007U7-6m for categories-list@mta.ca; Tue, 24 Jul 2007 19:23:31 -0300 From: "Categorical Methods" To: Subject: categories: Workshop in honour of J Adamek and W Tholen Date: Tue, 24 Jul 2007 20:00:57 +0100 MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: RO X-Status: X-Keywords: X-UID: 32 REGISTRATION for the Workshop Categorical Methods in Algebra, Topology and Computer Science, in honour of Jiri Adamek and Walter Tholen, to be held in Coimbra, in October 26-28, 2007, is now OPEN, at the web page http://www.mat.uc.pt/~cmatcs/ If you plan to participate, please register as soon as possible. The number of rooms in the hotels indicated in the web page is limited, = so early reservations are recommended. From rrosebru@mta.ca Wed Jul 25 09:38:28 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 25 Jul 2007 09:38:28 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1IDg2v-0004c8-DT for categories-list@mta.ca; Wed, 25 Jul 2007 09:32:53 -0300 MIME-Version: 1.0 Content-Type: text/plain;charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Subject: categories: Re: Bicomma objects Date: Wed, 25 Jul 2007 09:54:22 +1000 From: "Stephen Lack" To: Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 33 Dear Steve, A bicomma object is a bicategorical limit, so determined only up to equivalence. A comma object is a strict limit, so determined up to isomorphism.=20 In the case of Cat, comma objects are just the usual comma categories (strictly speaking, anything isomorphic to the comma category), while anything equivalent to the comma category will be a bicomma object. So any comma object is also a bicomma object, but the converse is false. Moreover, there are 2-categories in which bicomma objects exist but comma objects do not. The situation with pullbacks, by the way, is slightly different. It is not the case that every pullback is a bipullback (but there is a paper=20 of Joyal and Street giving a sufficient condition for a pullback to be a bipullback). Steve. -----Original Message----- From: cat-dist@mta.ca on behalf of Steve Vickers Sent: Wed 25/07/2007 2:02 AM To: categories@mta.ca Subject: categories: Bicomma objects =20 What is the difference between a bicomma object and a comma object (a.k.a. lax pullback)? Steve. From rrosebru@mta.ca Wed Jul 25 09:38:28 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 25 Jul 2007 09:38:28 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1IDg42-0004jW-Ra for categories-list@mta.ca; Wed, 25 Jul 2007 09:34:02 -0300 Date: Wed, 25 Jul 2007 04:45:16 -0700 From: John Baez To: categories Subject: categories: pivotal adjoints? Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Disposition: inline Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 34 Aaron Lauda writes: >Suppose we have chosen left and right adjoints for F:A->B and G:A->B > >Then given any 2-morphism a:F=>G there are two obvious duals (mates >under adjunction) for the 2-morphism a: > > a+ :G*=>F* := (e_G F*).(G*aF*).(G* i_F) > +a :G*=>F* := (F* k_G).(F*aG*).(j_F G*) > >or for those who like pictures: > > +a a+ > __ __ > / \ | | / \ > | | | | | | > | a | | a | > | | | | | | > | \__/ \__/ | > | | > > In general a+ is not equal to +a because if is was we could always twist one > of the units and counits so that it does not hold. Has the condition > that a+ = +a been investigated in the literature anywhere? In > particular, if a 2-category is such that all 1-morphisms F have a > simultaneous left and right adjoint then has anyone studied the > context where the adjoints are such that a+ = +a is always > satisfied? Perhaps, this notion has been studied in the language of > duals for 1-morphisms? I'd be curious to know what if any replies you received. As you already hinted, the special case of a monoidal category with this property has been studied: it's called "pivotal". Strict pivotal categories were studied here: P.J. Freyd and D.N. Yetter, Braided compact closed categories with applications to low dimensional topology, Adv. Math. 77 (1989), 156--182 and there's more discussion here: John W. Barrett and Bruce W. Westbury, Spherical Categories, Adv. Math. 143 (1999) 357-375. http://arxiv.org/abs/hep-th/9310164 I don't know who has studied more general (strict or weak) 2-categories with this pivotal property, though it's a natural generalization. Street should have bumped into it in his work on 2-categorical string diagrams. I've written about "2-categories with duals" in my work on the Tangle Hypothesis. These are pivotal, but they also have more structure, which you may not want. (You may want it if you're studying things like tangles!) Perhaps it would be good to pose a specific question. What would you like to know about pivotal 2-categories? Or are you mainly just looking for references? Best, jb From rrosebru@mta.ca Wed Jul 25 14:22:23 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 25 Jul 2007 14:22:23 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1IDkQi-000383-7H for categories-list@mta.ca; Wed, 25 Jul 2007 14:13:44 -0300 Date: Wed, 25 Jul 2007 07:55:50 +1200 (NZST) From: Markus Kirchberg To: categories@mta.ca Subject: categories: CFP: FoIKS 2008 MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 35 C A L L F O R P A P E R S --------------------------------- Fifth International Symposium on Foundations of Information and Knowledge Systems (FoIKS 2008) February 11-15, 2008 -- Pisa, Italy http://2008.foiks.org/ The FoIKS symposia provide a biennial forum for presenting and discussing theoretical and applied research on information and knowledge systems. The goal is to bring together researchers with an interest in this subject, share research experiences, promote collaboration and identify new issues and directions for future research. FoIKS 2008 solicits original contributions dealing with any foundational aspect of information and knowledge systems, including submissions from researchers working in fields such as discrete mathematics, logic and algebra, model theory, information theory, complexity theory, algorithmics and computation, statistics and optimisation who are interested in applying their ideas, theories and methods to research on information and knowledge systems. Previous FoIKS symposia were held in Budapest (Hungary) in 2006, Vienna (Austria) in 2004, Schloss Salzau near Kiel (Germany) in 2002, and Burg/Spreewald near Berlin (Germany) in 2000. FoIKS took up the tradition of the conference series Mathematical Fundamentals of Database Systems (MFDBS), which initiated East-West collaboration in the field of database theory. Former MFDBS conferences were held in Rostock (Germany) in 1991, Visegrad (Hungary) in 1989, and Dresden (Germany) in 1987. The FoIKS symposia are a forum for intensive discussions. Speakers are given sufficient time to present their results, expound relevant background information and put their research into context. Furthermore, participants are asked in advance to prepare as correspondents to a contribution of another author. Suggested topics include, but are not limited to: * Database Design: formal models, dependency theory, schema translations, desirable properties; * Dynamics of Information and Knowledge Systems: models of transactions, models of interaction, updates, consistency preservation, concurrency control; * Information Integration: heterogeneous data, views, schema dominance and equivalence; * Integrity and Constraint Management: verification, validation, and enforcement of consistency, triggers; * Intelligent Agents: multi-agent systems, autonomous agents, foundations of software agents, cooperative agents; * Knowledge Discovery and Information Retrieval: machine learning, data mining, text mining, information extraction; * Knowledge Representation: planning, reasoning techniques, description logics, knowledge and belief, belief revision and update, non-monotonic formalisms, uncertainty; * Logics in Databases and AI: non-classical logics, spatial and temporal logics, probabilistic logics, deontic logic, logic programming; * Mathematical Foundations: discrete structures and algorithms, graphs, grammars, automata, abstract machines, finite model theory, information theory; * Security and Risk Management in Information and Knowledge Systems: privacy, trust, cryptography, steganography, information hiding; * Semi-Structured Data and XML: data modelling, data processing, data compression, data exchange; * Social and Collaborative Computing: symbiotic intelligence, self-organisation, knowledge flow, decision making; * The Semantic Web and Knowledge Management: languages, ontologies, agents, adaption, intelligent algorithms; and * The WWW: models of Web databases, Web dynamics, Web services, Web transactions and negotiations. SUBMISSION OF PAPERS -------------------- Papers must be typeset using the Springer-Verlag LaTeX2e style llncs for Lecture Notes in Computer Science (refer http://2008.foiks.org/). The suggested number of pages is 16, and the maximum number of pages is 18. Submissions which deviate substantially from these guidelines may be rejected without review. Initial submissions must be in PDF format, but authors should keep in mind that the LaTeX2e source must be submitted for the final versions of accepted papers. Submissions in alternate formats, such as Microsoft Word, cannot be accepted for either initial or final versions. The submissions will be judged for scientific quality and for suitability as a basis for broader discussion. The proceedings will be published by Springer-Verlag in the Lecture Notes in Computer Science series and will be available at the symposium. After the symposium authors of selected papers will be asked to prepare extended versions of their papers for publication in a special issue of the journal Annals of Mathematics and Artificial Intelligence. Electronic Submission --------------------- Submission to FoIKS 2008 will be electronically only. Authors are asked to create a submission system account first. Subsequently, this account can be used to submit one or more abstracts and upload corresponding papers. The online submission system will be available from late-July 2007. IMPORTANT DATES --------------- Abstract submission deadline: August 15, 2007 (extended) Paper submission deadline: August 22, 2007 (extended) Author notification: October 15, 2007 Camera ready paper due: November 12, 2007 Early registration due: January 31, 2008 Late registration: from February 01, 2008 Symposium in Pisa, Italy: February, 11-15 2008 CONFERENCE CHAIRS ----------------- Program Committee Co-Chairs --------------------------- Sven Hartmann Massey University, New Zealand Gabriele Kern-Isberner University of Dortmund, Germany Local Arrangements Chair ------------------------ Carlo Meghini Istituto di Scienza e Tecnologie dell'Informazione, Italy Publicity Chair --------------- Markus Kirchberg Massey University, New Zealand PROGRAM COMMITTEE ----------------- Rudolf Ahlswede, University of Bielefeld, Germany Catriel Beeri, The Hebrew University of Jerusalem, Israel Leopoldo Bertossi, Carleton University, Canada Joachim Biskup, University of Dortmund, Germany Stefan Brass, University of Halle, Germany Cristian S. Calude, University of Auckland, New Zealand John Cantwell, Royal Institute of Technology, Sweden Samir Chopra, City University of New York, USA James P. Delgrande, Simon Fraser University, Canada Juergen Dix, Clausthal University of Technology, Germany Rod Downey, Victoria University of Wellington, New Zealand Thomas Eiter, Vienna University of Technology, Austria Lluis Godo Lacasa, Institut d'Investigacioen Intel.ligencia Artificial, Spain Stephen J. Hegner, Umea University, Sweden Anthony Hunter, University College London, UK Hyunchul Kang, Chung-Ang University Seoul, Korea Odej Kao, Berlin University of Technology, Germany Gyula O. H. Katona, Hungarian Academy of Sciences, Hungary Hans-Joachim Klein, University of Kiel, Germany Dexter Kozen, Cornell University, USA Jerome Lang, Institut de Recherche en Informatique de Toulouse, France Uwe Leck, University of Wisconsin, USA Mark Levene, Birbeck University of London, UK Sebastian Link, Massey University, New Zealand Yue Lu, East China Normal University Shanghai, China Thomas Lukasiewicz, Universita di Roma "La Sapienza", Italy Carlo Meghini, Istituto di Scienza e Tecnologie dell'Informazione, Italy Peter Mika, Yahoo! Research Barcelona, Spain Wilfred S. H. Ng, Hong Kong University of Science and Technology, China Beng Chin Ooi, National University of Singapore Jeff B. Paris, University of Manchester, UK Henri Prade, Universite Paul Sabatier, France Attila Sali, Hungarian Academy of Sciences, Hungary Vladimir Sazonov, University of Liverpool, UK Klaus-Dieter Schewe, Massey University, New Zealand Karl Schlechta, Universite de Provence, France Dietmar Seipel, University of Wuerzburg, Germany Guillermo R. Simari, Universidad Nacional del Sur, Argentina Nicolas Spyratos, University of Paris-South, France Ernest Teniente, Universitat Politecnica de Catalunya, Spain Bernhard Thalheim, University of Kiel, Germany Yannis Theodoridis, University of Piraeus, Greece Miroslav Truszczynski, University of Kentucky, USA Jose Maria Turull-Torres, Massey University Wellington, New Zealand Dirk Van Gucht, Indiana University, USA Marina de Vos, University of Bath, UK Jef Wijsen, University of Mons-Hainaut, Belgium Ian H. Witten, University of Waikato, New Zealand Jeffrey Xu Yu, Chinese University of Hong Kong, China FURTHER INFORMATION ------------------- For further information refer to the FoIKS 2008 Web-site at http://2008.foiks.org/ From rrosebru@mta.ca Wed Jul 25 14:22:23 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 25 Jul 2007 14:22:23 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1IDkSx-0003PI-Hr for categories-list@mta.ca; Wed, 25 Jul 2007 14:16:03 -0300 From: Aaron Lauda Date: Wed, 25 Jul 2007 09:27:11 -0400 To: categories Subject: categories: Re: pivotal adjoints? 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: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 36 I would like to thank all those that I replied so far. Quoting John Baez : > Perhaps it would be good to pose a specific question. What would > you like to know about pivotal 2-categories? Or are you mainly > just looking for references? To answer John, I would like to know what condition is required on =20 left and right adjoints in a 2-category K to ensure that a string =20 diagram representing a 2-morphism in K is invariant under topological =20 deformation restricting to the identity on the boundary. I prefer not =20 to use monoidal 2-categories, just ordinary 2-categories/bicategories. If I take a monoidal bicategory with duals and forget the monoidal =20 structure will this be what I am after? 2-tangles clearly have the =20 property I am looking for, but what if we adjoin some new 2-morphism A =20 to 2-tangles. What condition would I need in order to ensure that any =20 string diagram with the new morphism A was invariant under topological =20 deformation? > I'd be curious to know what if any replies you received. Aside from the replies that have been posted, I have also received a =20 pointer to the paper "Introduction to linear bicategories" by Cockett, =20 Koslowski, and Seely. The condition that *a=3Da* is studied in the =20 context of linear bicategories and what are called cyclic adjoints. =20 In particular, the discussion of cyclic mates seems to especially =20 relevant. But I have not finished reading the paper and am still =20 trying to understand what implications the `linear' in linear =20 bicatgories will have on the ordinary bicategory case. Regards, Aaron From rrosebru@mta.ca Wed Jul 25 17:24:00 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 25 Jul 2007 17:24:00 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1IDnKS-0004sP-Gb for categories-list@mta.ca; Wed, 25 Jul 2007 17:19:28 -0300 Date: Wed, 25 Jul 2007 15:32:41 -0300 From: Joachim Kock Subject: categories: CRM 2007/2008: Homotopy Theory and Higher Categories To: categories@mta.ca MIME-version: 1.0 Content-type: text/plain; charset=iso-8859-1 Content-transfer-encoding: 7BIT Content-disposition: inline Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 37 CRM 2007/2008: Homotopy Theory and Higher Categories This is to announce that a research programme on homotopy theory and higher categories, in a broad sense, will take place at the CRM in Barcelona during the academic year 2007-2008. The scientific organisers are Carles Casacuberta (Barcelona), Andre Joyal (Montreal), Joachim Kock (Barcelona), Amnon Neeman (Canberra), and Frank Neumann (Leicester). In addition to a weekly seminar throughout the year, the following events are scheduled: - November 5 to 14, 2007: Workshop on Derived Categories - February 4 to 14, 2008: Advanced Course on Simplicial Methods in Higher Categories - February 18 to 22, 2008: Workshop on Algebra and Geometry of Groups and Classifying Spaces - April 1 to 5, 2008: Workshop on Topological and Differentiable Stacks - June 16 to 20, 2008: Workshop on Categorical Groups - June 30 to July 5, 2008: HOCAT 2008, a conference on Homotopy Structures in Geometry and Algebra; Derived Categories, Higher Categories Participants are welcome to any of these activities. Longer-term visits are partially constrained by office space availability at the CRM. Please contact the coordinators of each activity or the CRM Secretariat if you need more information. Updated details about activities and visitors can be found on the website http://www.crm.cat/HOCAT/. With best regards, The Scientific Organisers From rrosebru@mta.ca Thu Jul 26 14:16:13 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 26 Jul 2007 14:16:13 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1IE6pX-0003Xn-RC for categories-list@mta.ca; Thu, 26 Jul 2007 14:08:51 -0300 From: Thomas Streicher Subject: categories: answer by Blass: generic family To: categories@mta.ca Date: Thu, 26 Jul 2007 12:29:39 +0200 (CEST) MIME-Version: 1.0 Content-Transfer-Encoding: 7bit Content-Type: text/plain; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: RO X-Status: X-Keywords: X-UID: 38 A very satisfying answer to my recent question on this list has been given to me by Andreas Blass. Since \Delta : Set -> Psh(G) is logical there is no way of defining a generic family of finite objects in the language of higher order arithmetic since every such family would be of the form \Delta(u). That such a family can't be generic is shown already by the argument in my mail. Moreover, as he pointed out and I also observed, although A -> I is a family of finite sets iff \forall i:I.\exists! n:N. A_i \cong K_n there will in general be no external choice function providing such an n:N for i:I although internally by AUC there exists a unique such choice function. After all this is no suprise since the representable object of Psh(G) has global support but no global element (unless G is trivial). Thomas From rrosebru@mta.ca Fri Jul 27 12:34:29 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 27 Jul 2007 12:34:29 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1IERhp-0000TX-4B for categories-list@mta.ca; Fri, 27 Jul 2007 12:26:17 -0300 From: Thomas Streicher Subject: categories: correction w.r.t. generic finite family of finite objects To: categories@mta.ca Date: Fri, 27 Jul 2007 17:14:15 +0200 (CEST) MIME-Version: 1.0 Content-Transfer-Encoding: 7bit Content-Type: text/plain; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 39 Andreas Blass has pointed out to me that that there was a mistake in my recent mail. There does exist a global element n : 1 -> N such that G \cong K_n (n is the order of the group G) BUT the statement G \cong K_n contains a hidden existential quantifier over Iso(G,K_n) and this latter one is not witnessed by a global section of Iso(G,K_n). Thomas Streicher From rrosebru@mta.ca Mon Jul 30 10:53:32 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 30 Jul 2007 10:53:32 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1IFVYC-0003Lg-6m for categories-list@mta.ca; Mon, 30 Jul 2007 10:44:44 -0300 Date: Mon, 30 Jul 2007 08:24:46 +0200 (CEST) To: categories@mta.ca Subject: categories: definition of parsimony From: Axel Rossberg Mime-Version: 1.0 Content-Type: Text/Plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 40 Dear List Members, I am looking for a formal definition of parsimony for fundamental scientific theories. From the tiny bit I understood of category theory, I had the impression it might provide the right framework for such a definition. The problem of motivating and defining parsimony is being discussed in analytic philosophy. An overview over the discussion can be found at http://plato.stanford.edu/entries/simplicity/ , which starts off with the sentences Most philosophers believe that, other things being equal, simpler theories are better. But what exactly does theoretical simplicity amount to? Syntactic simplicity, or elegance, measures the number and conciseness of the theories basic principles. Ontological simplicity, or parsimony, measures the number of kinds of entities postulated by the theory. One issue concerns how these two forms of simplicity relate to one another. I am interested in the "ontological simplicity, or parsimony". However, if one understands modern physics as describing essentially only one thing, the wave-function of the universe, then even the idea of defining parsimony in terms of numbers of kinds of things seems to be a bit odd. Yet, I think the idea is intuitively clear. The minimum requirement for a formal definition of parsimony is perhaps that it should identify theories such as the dynamics of Newtonian point-particles or the current "standard model" of particle physics as parsimonious, while the same theories with some oddities added, which do not themselves affect the "real" physics, should be identifiable as non-parsimonious. Beyond this, such a definition should presuppose as little as possible about the nature of the theories it applies to. Does somebody know about applications of category theory to this problem, or have an idea for who to do it? Cheers, Axel Rossberg --- Evolution and Ecology Program International Institute for Applied Systems Analysis Schlossplatz 1 A-2361 Laxenburg AUSTRIA ++++++++++++++++++++++++ reprints http://axel.rossberg.net/paper and more http://axel.rossberg.net From rrosebru@mta.ca Mon Jul 30 20:33:52 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 30 Jul 2007 20:33:52 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1IFeeN-0004xz-JD for categories-list@mta.ca; Mon, 30 Jul 2007 20:27:43 -0300 Date: Mon, 30 Jul 2007 09:30:12 -0700 From: Vaughan Pratt MIME-Version: 1.0 To: categories@mta.ca Subject: categories: Re: definition of parsimony Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 41 Without going into its relevance to category theory, I would put the SEP article on parsimony that Axel Rossberg pointed to alongside the Wikipedia article on spice (the vegetative substance described at http://en.wikipedia.org/wiki/Spice, not the rock group). On the one hand spices, as the latter article points out, "have been prominent in human history virtually since their inception. Spices were among the most valuable items of trade in the ancient and medieval world." On the other hand what restaurant serves only spices on its menu? Cuisine is a complex art for which spices are merely a valuable adjunct that can make a big difference in a catalytic kind of way. Parsimony is the catalytic converter of mathematics. It is not the main engine, but can be helpful in cleaning up the noxious byproducts of inefficient thinking. Too much however can be a bad thing: overdoing parsimony undermines its efficacy for mathematics while adding to the cost, just as overdoing spices does for food and platinum for catalytic converters. Rossberg's suggestion that modern physics describes only the wave function of the universe illustrates this nicely. If this were really true, physics would not be a degree major, let alone a career option, but merely a module of a course in some other major. In any event it is contradicted by the standard model Rossberg refers to in the next paragraph. Explaining the standard model by a suitably parsimonious Theory of Everything is a nice thought, like an antigravity belt when you're stuck in traffic, but the standard model is a complex and evolving account of how the huge zoo of particles fits together. "Parsimony" in any account of the standard model today is only accomplished by leaving things out. The Particle Physics Booklet (formerly the Particle Properties Data Booklet) is some 200 pages of densely packed information about uncountably many particles parametrized by nearly a score of fundamental physical constants each determined by careful measurement. (The number of particles is uncountable because many are merely conjectured to exist, although billions of dollars are being spent today in the expectation of confirming at least some of those conjectures. If only the Riemann Hypothesis were so well-endowed!) Some idea of the parsimony achieved by the PPB can be had from its expansion as the Review of Particle Physics, the PPB's 1100-page big brother. Ironically the parsimony article is considerably less parsimonious than the spice article. As a talisman against the off-topic rule, I should relay here an unverified report from the fourth millennium to the effect that "categories were prominent in human mathematics virtually since their inception, and were among the most heavily trafficked items of metamathematical discourse during the third millennium." They're a good investment, I have some in my own kitchen but many on this list who take their cooking more seriously have invested much more heavily. Vaughan Pratt From rrosebru@mta.ca Wed Aug 1 16:48:23 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 01 Aug 2007 16:48:23 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1IGK0N-0002yU-3z for categories-list@mta.ca; Wed, 01 Aug 2007 16:37:11 -0300 Date: Tue, 31 Jul 2007 10:10:25 -0700 From: Vaughan Pratt MIME-Version: 1.0 To: categories@mta.ca Subject: categories: Re: definition of parsimony Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 42 (Out of fairness to *the* standard model, the Higgs boson is its only remaining unobserved particle. The other particles being sought at Fermilab and CERN belong to supersymmetric (SUSY) extensions of the standard model. Ironically such an extension while having more particles could nevertheless claim to be more parsimonious than the current standard model as measured by the number of its free parameters, in particular fewer Yukawa constants. Disclaimer: if you knew SUSY like I know SUSY no physics lab would even think of hiring you.)