From MAILER-DAEMON Fri May 18 09:34:24 2007 Date: 18 May 2007 09:34:24 -0300 From: Mail System Internal Data Subject: DON'T DELETE THIS MESSAGE -- FOLDER INTERNAL DATA Message-ID: <1179491664@mta.ca> X-IMAP: 1170364124 0000000045 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 Thu Feb 1 16:48:29 2007 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 01 Feb 2007 16:48:29 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HCiiX-0001yT-Fz for categories-list@mta.ca; Thu, 01 Feb 2007 16:39:37 -0400 Date: Thu, 01 Feb 2007 10:44:38 +0000 From: Steve Vickers MIME-Version: 1.0 To: categories@mta.ca Subject: categories: Max Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: RO X-Status: X-Keywords: X-UID: 1 I only met Max a couple of times, but I vividly remember a particular phrase of his. He would ask, "What's the deal?", and that was a prelude to cutting right through to the mathematical essence of an argument. The phrase has stayed with me ever since. Steve Vickers. From rrosebru@mta.ca Thu Feb 1 16:48:29 2007 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 01 Feb 2007 16:48:29 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HCijE-00024N-RN for categories-list@mta.ca; Thu, 01 Feb 2007 16:40:20 -0400 Date: Thu, 01 Feb 2007 10:28:48 -0400 From: Dietmar Schumacher MIME-Version: 1.0 To: categories@mta.ca Subject: categories: Max Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: RO X-Status: X-Keywords: X-UID: 2 I heard Max once say, without bluster or false modesty, that he was just a competent mathematician. Setting the bar that high, he was an inspiration even to those (like me) who had little hope to clear it. D.Schumacher. From rrosebru@mta.ca Thu Feb 1 16:48:29 2007 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 01 Feb 2007 16:48:29 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HCikX-0002EP-1C for categories-list@mta.ca; Thu, 01 Feb 2007 16:41:41 -0400 Date: Thu, 01 Feb 2007 13:41:36 -0500 From: Walter Tholen MIME-Version: 1.0 To: categories@mta.ca Subject: categories: Summer School , Haute Bodeux June 2007 Content-Type: text/plain; charset=us-ascii; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: RO X-Status: X-Keywords: X-UID: 3 Dear categorists - A few additional spaces have become available for participation in the Summer School on Contemporary Categorical Methods in Algebra and Topology, to be held in Haute Bodeux (Belgium), 3-10 June 2007, and organized by Francis Borceux. All currently available information about the School, which entails four lecture series as well as contributed talks, can be obtained at http://www.math.yorku.ca/~tholen/hb072.htm Anybody interested in particpation who has not yet contacted me should do so as soon as possible. Notification to new applicats will be given in early March. Walter Tholen. From rrosebru@mta.ca Thu Feb 1 22:37:52 2007 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 01 Feb 2007 22:37:52 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HCoEB-0006uZ-P5 for categories-list@mta.ca; Thu, 01 Feb 2007 22:32:39 -0400 Date: Thu, 1 Feb 2007 22:57:12 +0100 Content-Type: text/plain; charset=US-ASCII; format=flowed Subject: categories: Max From: jean benabou To: Categories Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 4 So many persons have said so many nice things about Max, as a mathematician, with which of course I fully agree, that it would be vain for me to try to add anything on that subject. As a person, his kindness, his sense of humor will be missed by all of us, and as Eduardo said "category land" will be much different and a lot more dull. Jean Benabou From rrosebru@mta.ca Fri Feb 2 20:36:06 2007 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 02 Feb 2007 20:36:06 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HD8hx-00067G-DQ for categories-list@mta.ca; Fri, 02 Feb 2007 20:24:45 -0400 Date: Fri, 2 Feb 2007 09:39:50 +0100 (CET) Subject: categories: ALGEBRAIC AND TOPOLOGICAL METHODS IN NON-CLASSICAL LOGICS III From: ghilardi@dsi.unimi.it 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: RO X-Status: X-Keywords: X-UID: 5 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Preliminary Announcement and First Call for Papers ALGEBRAIC AND TOPOLOGICAL METHODS IN NON-CLASSICAL LOGICS III (TANCL'07) 5-9 August, 2007 St Anne's College (University of Oxford) Oxford, England This international conference is the third in the series Algebraic and Topological methods in Non-Classical Logics (TANCL). The first was held in 2003 in Tbilisi, Georgia: http://sierra.nmsu.edu/morandi/TbilisiConference/Home.html and the second in 2005 in Barcelona, Spain: http://www.mat.ub.es/~logica/meeting2005/ AIMS AND SCOPE The topics covered by TANCL'07 lie within a well-established and active area of mathematical logic. It is hoped to attract to the meeting established researchers and also postdoctoral and graduate students, from the UK and overseas. The objectives are (1) to provide a showcase for recent advances in the field; (2) to facilitate the exchange of ideas and expertise between mathematicians, logicians, and theoretical computer scientists working on many facets of non-classical logic; (3) to foster future collaborations. The programme will focus on three interconnecting mathematical themes central to the study of non-classical logics and their applications: algebraic, categorical, and topological methods. Three more specialized satellite workshops are planned (see below). INVITED SPEAKERS Samson Abramsky, University of Oxford, UK Wojciech Buszkowski, Adam Mickiewicz University, Poland Alexander Kurz, University of Leicester, UK Jean-Eric Pin, University of Paris, France Giovanni Sambin, University of Padova, Italy Yde Venema, University of Amsterdam, Netherlands Frank Wolter, University of Liverpool, UK PROGRAMME COMMITTEE Guram Bezhanishvili (Chair), New Mexico State University, USA Leo Esakia, Georgian Academy of Sciences, Georgia Mai Gehrke, New Mexico State University, USA Silvio Ghilardi, University of Milan , Italy Ramon Jansana, University of Barcelona , Spain Peter Jipsen, Chapman University, USA Hiroakira Ono, Japan Advanced Institute of Science and Technology, Japan Hilary Priestley, University of Oxford, UK Michael Zakharyaschev, Birkbeck, Universty of London, UK CONTRIBUTED PAPERS There will be an opportunity for participants to offer short talks, the selection to be made by the Programme Committee on the basis of submitted half-page abstracts. Details of the procedure will be on the conference homepage. SATELLITE WORKSHOPS It is planned to hold three specialized satellite workshops at Oxford University Computing Laboratory: Categorical Quantum Logic (convened by Bob Coecke) Coalgebraic Logic (convened by Alexander Kurz) Spatial and Spatio-temporal Logics (convened by Michael Zakharyaschev). CONFERENCE ORGANISERS Mai Gehrke and Hilary Priestley They can be contacted by email at tancl07@maths.ox.ac.uk KEY DATES Deadline for submission of abstracts: 1 May Acceptance notification: 15 May Deadline for registration and reservation of accommodation: 1 June VENUE The conference will be held at St Anne's College, Oxford [ http://www.st-annes.ox.ac.uk], one of the colleges of Oxford University. The college has excellent conference facilities and is within 10 minutes' walk of the centre of the city of Oxford. Accommodation of various types will be available. REGISTRATION Registration for the conference and reservation of accommodation will be through the conference homepage. FINANCIAL SUPPORT We hope to be able to provide financial support for a number of graduate students and perhaps for others who can make a strong case. FURTHER INFORMATION AND EXPRESSION OF INTEREST A conference homepage is being set up at http://www.maths.ox.ac.uk/notices/events/special/tancl07/ In the meantime, expression of interest by potential participants is welcomed; please email tancl07@maths.ox.ac.uk %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% From rrosebru@mta.ca Fri Feb 2 20:36:06 2007 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 02 Feb 2007 20:36:06 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HD8jj-0006Cc-Hb for categories-list@mta.ca; Fri, 02 Feb 2007 20:26:35 -0400 Mime-Version: 1.0 (Apple Message framework v752.3) Content-Type: text/plain; charset=ISO-8859-1; delsp=yes; format=flowed Content-Transfer-Encoding: quoted-printable From: Pierre-Louis Curien Subject: categories: 2 events related to JY Girard's 60th birthday Date: Fri, 2 Feb 2007 16:23:42 +0100 To: categories@mta.ca Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 6 We are pleased to announce two special events that will be held in =20 2007, in Italy and France respectively, in honour of Jean-Yves =20 Girard, who celebrates his 60th birthday this year: ************************* Workshop on Linear Logic, Ludics, Implicit Complexity and Operator Algebras. Dedicated to Jean-Yves Girard on his 60th birthday. University of Siena (Italy) at the Certosa di Pontignano, May 17-20, =20 2007. Organizing committee: Michele Abrusci (Roma III), Claudia Faggian =20 (CNRS - Paris 7), Simone Martini (Bologna), Simona Ronchi Della Rocca =20= (Torino), Aldo Ursini (Siena, chair) www.unisi.it/eventi/LOGIC ************************* and ************************* Journ=E9es Jean-Yves Girard Conference in honour of his 60th birthday Institut Henri Poincar=E9, Paris, September 10 and 11, 2007 Organizing committee: Michele Abrusci (Roma III) Pierre-Louis Curien =20 (CNRS - Paris 7, chair), Martin Hyland (Cambridge), Giuseppe Longo =20 (ENS, Paris), Mitsu Okada (Keio U., Tokyo), Phil Scott (Univ. of =20 Ottawa), Jacqueline Vauzeilles (Paris 13, co-chair) http://www-lipn.univ-paris13.fr/jyg60 ************************* Both events will be an occasion to celebrate Jean-Yves Girard's deep =20 achievements in Mathematics and in Computer Science, and the =20 pervasive influence of his ideas in those disciplines and beyond. The Siena workshop also celebrates the 20th anniversary of the =20 completion of his fundamental paper on Linear Logic. The aim is to gather people =20 working in the many research streams originating from Girard's main achievements of =20 the recent years. For each of the four main themes---Linear Logic =20 (specifically, Proof Nets and Geometry of Interaction), Ludics, =20 Implicit Complexity and Operator Algebras---there will be in-depth =20 lectures (3 to 4 hours), with emphasis on the state of the art and =20 prospects for future development. There will also be some time for 30-=20= minute contributed papers and for discussion of general perspectives =20 and philosophical foundations. This workshop has been organized to complement the celebration in =20 Paris, which will take place immediately after Jean-Yves' birthday. =20 Through our choice of invited speakers, we hope to illustrate the =20 wide range of scientific interests of Jean-Yves Girard over thirty-=20 five years, from the complexity of proofs to quantum mechanics, from =20= system F to the geometry of computation, from denotational semantics =20 to Von Neumann algebras. The two web sites will provide all details. Pierre-Louis Curien and Aldo Ursini= From rrosebru@mta.ca Fri Feb 2 20:36:06 2007 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 02 Feb 2007 20:36:06 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HD8j0-0006AY-6E for categories-list@mta.ca; Fri, 02 Feb 2007 20:25:50 -0400 Mime-Version: 1.0 (Apple Message framework v752.3) Content-Type: text/plain; charset=US-ASCII; format=flowed Content-Transfer-Encoding: 7bit From: Cristina Pedicchio Subject: categories: Max Date: Fri, 2 Feb 2007 13:51:47 +0100 To: Categories Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: RO X-Status: X-Keywords: X-UID: 7 We would like to add also our feelings of deep sadness at Max's death cristina e pierpaolo From rrosebru@mta.ca Sat Feb 3 10:26:17 2007 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 03 Feb 2007 10:26:17 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HDLk5-0003mI-UK for categories-list@mta.ca; Sat, 03 Feb 2007 10:19:50 -0400 Date: Fri, 2 Feb 2007 21:40:58 -0600 From: Peter May To: cat-dist@mta.ca Subject: categories: Max Kelly Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: RO X-Status: X-Keywords: X-UID: 8 Max visited Saunders Mac Lane in Chicago in 1970-71, and conversations with him then were both great fun and greatly influenced my work. To quote from the preface to ``The geometry of iterated loop spaces'', in which I introduced operads, ``The notion of `operad' defined in Section 1 arose simultaneously in Max Kelly's categorical work on coherence, and conversations with him led to the present definition''. It is a pity that, due to ill-advised suggestions by a referee a little later, his January, 1972, preprint ``On the operads of J.P. May'' was not published until 2006! It contains many often rediscovered insights. See http://www.tac.mta.ca/tac/reprints/articles/13/tr13abs.html. We also had many conversations about his upcoming role as chair in Sydney. In those days, before e-mail and even xerox, the problem of relative isolation down under was much on Max's mind, and he thought that this was one good reason for following his heart and working to make Sydney a home for the development of the then underappreciated area of category theory that he so much loved. We are all in his debt for the marvelous way that he succeeded. Peter May From rrosebru@mta.ca Sat Feb 3 13:05:53 2007 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 03 Feb 2007 13:05:53 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HDOGV-0005Gs-OS for categories-list@mta.ca; Sat, 03 Feb 2007 13:01:27 -0400 Date: Sat, 3 Feb 2007 11:43:38 -0400 (AST) From: Bob Rosebrugh To: categories Subject: categories: ACCAT workshop at ETAPS 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: 9 There is a workskop at ETAPS 2007 of interest to categories readers Applied and Computational Category Theory For information see: http://tfs.cs.tu-berlin.de/workshops/accat2007/ From rrosebru@mta.ca Sat Feb 3 13:05:53 2007 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 03 Feb 2007 13:05:53 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HDOHI-0005KK-Uc for categories-list@mta.ca; Sat, 03 Feb 2007 13:02:16 -0400 Date: Sat, 3 Feb 2007 16:51:41 +0100 (CET) From: "I. Moerdijk" Subject: categories: job opening To: categories@mta.ca 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 Dear colleagues, I'd like to draw your attention to an opening for a tenure (track) position at Utrecht, at the level of "universitair docent" (comparable to Lecturer in the UK, Assistant Professor in the US or Maitre de Conferences in France). The position is related to a large group grant in the area between (and including) geometry/topology and mathematical physics, which I'm sure will fit the interests of many readers of this list. For more information, see http://www.math.uu.nl/Positions/ With best regards, Ieke Moerdijk. From rrosebru@mta.ca Sun Feb 4 11:34:07 2007 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 04 Feb 2007 11:34:07 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HDjEj-000525-2h for categories-list@mta.ca; Sun, 04 Feb 2007 11:25:01 -0400 From: "RONALD BROWN" To: Subject: categories: email change Date: Sun, 4 Feb 2007 11:12:28 -0000 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: 11 I would like to notify friends that my home email is now=20 ronnie.profbrown@btinternet.com and prefer emails to come to this.=20 I still look at the bangor address r.brown@bangor.ac.uk Ronnie Brown From rrosebru@mta.ca Fri Feb 9 14:52:11 2007 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 09 Feb 2007 14:52:11 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HFahq-0002Ji-Bn for categories-list@mta.ca; Fri, 09 Feb 2007 14:42:46 -0400 From: fsen07@ipm.ir Subject: categories: Call for participation: FSEN07 + IFIP tutorial To: categories@mta.ca Date: Thu, 8 Feb 2007 11:16:44 +0330 Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 12 Our apologies if you have received multiple copies. ------------------------------------------------------------------------- FSEN07 Call for Participation International Symposium on Fundamentals of Software Engineering April 17-19 2007, Tehran, Iran http://cs.ipm.ac.ir/FSEN07 In Cooperation with ACM/SigSoft and IFIP/WG2.2 Registration deadline: February 23, 2007 Follow up event: IFIP WG 2.2 Tutorials April 20-21 2007 In the case a visa application by IPM is required February 15 is the deadline. Late Registration: with penalty, up to 5th April For more information check the symposium homepage. FSEN 2007 is an international workshop organized by the Institute for Studies in Theoretical Physics and Mathematics (IPM) in Iran (http://www.ipm.ac.ir). List of accepted papers are available at symposium homepage. Keynote Speakers ---------------- James C. Browne - University of Texas at Austin, USA Masahiro Fujita - University of Tokyo, Japan Davide Sangiorgi - University of Bologna, Italy Peter D. Mosses - Swansea University, UK IFIP WG 2.2 Tutorials ----------------------------------- Peter D. Mosses - Swansea University, UK An introduction to the semantics of programming languages: theory and practice Davide Sangiorgi - University of Bologna, Italy An introduction to the semantics of concurrency: behavioural equivalences and co-induction (more details on Homepage) Symposium goals ---------------- FSEN is an international symposium aiming to bring together researchers, engineers, developers and practitioners from universities and industry working in all the areas of formal methods. This symposium seeks to facilitate the transfer of experience, adaptation of methods, and where possible, collaboration between different groups. The topics may cover any aspect in formal methods, especially those related to advancing the application of formal methods in software industry and promoting their integration with practical engineering techniques. Following the success of the previous FSEN in 2005 a next symposium will be held in April 2007. Topics of Interest ------------------- The topics of this symposium include, but are not restricted to, the following: * Models of programs and systems * Software specification, validation and verification * Software architectures and their description languages * Object and multi-agent systems * Coordination and feature interaction * Integration of formal and informal methods * Integration of different formal methods * Component-based development * Service-oriented development * Model checking and theorem proving * Software and hardware verification * CASE tools and tool integration * Application to industrial cases Committees ----------- General Chairs: Ali Movaghar Sharif University of Technology, Iran IPM, Iran Jan Rutten Centre for Mathematics and Computer Science (CWI) Vrije Universiteit, The Netherlands PC Chairs: Farhad Arbab CWI, Netherlands Leiden University, Netherlands University of Waterloo, Canada Marjan Sirjani Tehran University, Iran IPM, Iran Local Arrangement Chair: Hamidreza Shahrabi IPM, Iran Program Committee ------------------ Gul Agha - University of Illinois at Urbana - Champaign, USA Farhad Arbab - CWI, Netherlands; Leiden University, Netherlands; University of Waterloo, Canada Mohammad Ardeshir - Sharif University of Technology, Iran Christel Baier - University of Bonn, Germany Frank de Boer - CWI, Netherlands; Leiden University, Netherlands Marcello Bonsangue - Leiden University, Netherlands Mario Bravetti - University of Bologna James C. Browne - University of Texas at Austin, USA Michael Butler - University of Southampton, UK Nancy Day - University of Waterloo, Canada Masahiro Fujita - University of Tokyo, Japan Maurizio Gabbrielli - University of Bologna, Italy Radu Grosu - State University of New York at Stony Brook, USA Jan Friso Groote - Technical University of Eindhoven, Netherlands Michael Huth - Imperial College of London, UK Joost Kok - Leiden University, Netherlands Mohammad Reza Meybodi - AmirKabir University of Technology, Iran Seyyed Hassan Mirian - Sharif University of Technology, Iran Marta Kwiatkowska - University of Birmingham, UK Ugo Montanari - University of Pisa, Italy Mohammad Reza Mousavi - Technical University of Eindhoven, Netherlands Ali Movaghar - IPM, Iran; Sharif University of Technology, Iran Andrea Omicini - University of Bologna, Italy George Papadopoulos - University of Cyprus, Cyprus Jan Rutten - CWI, Netherlands; Vrije University Amsterdam, Netherlands Sandeep Shukla - Virginia Tech, USA Marjan Sirjani - IPM, Iran; Tehran University, Iran Carolyn Talcott - SRI International, USA From rrosebru@mta.ca Mon Feb 12 07:59:58 2007 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 12 Feb 2007 07:59:58 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HGZij-0004St-Mp for categories-list@mta.ca; Mon, 12 Feb 2007 07:51:45 -0400 Date: Sun, 11 Feb 2007 19:46:05 -0800 From: John Baez To: categories Subject: categories: higher categories and their applications 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: 14 Dear Categorists - Here's a bit about a recent workshop on higher categories and their applications. The web version has a photo of Coxeter's piano. Best, jb ................................................................... Also available as http://math.ucr.edu/home/baez/week245.html February 11, 2007 This Week's Finds in Mathematical Physics (Week 245) John Baez The University of Toronto is an urban campus, rather grey and chilly at this time of year. Nestled amid other buildings at the southern edge of campus, the Fields Institute doesn't stand out. But inside, you'll find a spacious and peaceful atrium, with a fireplace to keep you cozy. A spiral staircase winds up three or four stories. Hanging from the ceiling far above is a 3d model of the "120-cell": a beautiful 4-dimensional solid with 120 regular dodecahedra as faces. This is a tribute to the great geometer H. S. M. Coxeter, master of polyhedra, who worked for 60 years at the University of Toronto after studying philosophy at Cambridge under Wittgenstein. You'll also find Coxeter's piano sitting at the base of the spiral staircase. It's out of tune, but resting on it there's a wonderful strange portrait of him playing the very same piano - at the age of three. He looks a bit like the child Mozart. And indeed, at the age of 12 Coxeter composed an opera! The Fields Institute specializes in having conferences, and it's a great place for that. A friendly and efficient staff, public workstations, wireless internet everywhere, a nice little cafe in the back, and the centerpiece: a large lecture room with 3 double blackboards. Unfortunately the middle blackboard doesn't stay up - it's needed that repair for years, old-timers say. But apart from that, everything is as close to mathematician's heaven as could be expected. Eugenia Cheng, Peter May and I ran a workshop at the Fields Institute from January 9th to 13th: 1) Higher Categories and Their Applications, http://math.ucr.edu/home/baez/fields/ You can see photos of people and abstracts of their talks at this site. You can also see PDF files of many of their talks - and even listen to talks! The first day, Tuesday, was all about 2-categories and 3-categories - "lower category theory", you might say. While some are eagerly sailing into the stratosphere of n-categories for general n, or even n = infinity, there's still a lot to understand for n = 2 and 3. For starters, Tom Leinster spoke about strict 2-categories versus weak ones (also known as bicategories). It's a famous fact - a generalization of Mac Lane's coherence theorem - that every weak 2-category C is equivalent to a strict one st(C). However, this is true *if* your notion of equivalence is suitably weak! In short, what we've got is an inclusion of weak 3-categories: i: Strict2Cat -> Weak2Cat where Strict2Cat = [strict 2-categories, strict 2-functors, strict natural transformations, modifications] and Weak2Cat = [weak 2-categories, weak 2-functors, weak natural transformations, modifications] Every object in Weak2Cat is equivalent to one in the image of this inclusion. But, the inclusion is not itself an equivalence! Steve Lack spoke about Gray-categories, also known as "semistrict" 3-categories - a convenient middle ground between the strict 3-categories and the weak ones (also known as tricategories). The idea here goes back to John Gray. In the usual Cartesian product of categories, whenever we have a morphism f: A -> B in the first category and a morphism f': A' -> B' in the second, we get a commuting square: (f,1) (A,A') -------> (B,A') | | (1,g)| |(1,g) | | v v (A,B') -------> (B,B') (f,1) in their Cartesian product. The same is true for the Cartesian product of 2-categories. But in the "Gray" tensor product of 2-categories, these squares commute only up to 2-isomorphism. And, we can use this weakening of the Cartesian product to weaken the concept of strict 3-category, and obtain the concept of "semistrict" 3-category, or "Gray-category". Here's how. A strict 3-category is a gizmo with: a) a bunch of objects, b) for any pair of objects x,y, a 2-category hom(x,y), and c) for any triple of objects x,y,z, a 2-functor o: hom(x,y) x hom(y,z) -> hom(x,z) such that d) associativity and the unit laws hold. A semistrict 3-category is a gizmo with: a) a bunch of objects, b) for any pair of objects x,y, a 2-category hom(x,y), and c) for any triple of objects x,y,z, a 2-functor o: hom(x,y) tensor hom(y,z) -> hom(x,z) where "tensor" is the Gray tensor product, such that d) associativity and the unit laws hold. The slight difference is very important. Not every weak 3-category is equivalent to a strict one. But, they're all equivalent to semistrict ones! There are, alas, some deficiencies in the semistrict world, which Steve Lack has recently noted: 2) Steve Lack, Bicat is not triequivalent to Gray, available as math.CT/0612299. To understand this, you may need a little warmup. Given strict 2-categories B and C there's a strict 2-category hom(B,C) such that strict 2-functors A x B -> C are in natural 1-1 correspondence with strict 2-functors A -> hom(B,C) Here's what hom(B,C) is like: hom(B,C) has strict 2-functors from B to C as objects, strict natural transformations between these as morphisms, modifications between these as 2-morphisms. We can pose the same question with the Gray tensor product replacing the Cartesian product. Given 2-categories B and C there's a 2-category [B,C] such that strict 2-functors A tensor B -> C are in natural 1-1 correspondence with strict 2-functors A -> [B,C] Here's what [B,C] is like: [B,C] has strict 2-functors from B to C as objects, weak natural transformations between these as morphisms, modifications between these as 2-morphisms. This suggests that we consider a 3-category intermediate between Strict2Cat and Weak2Cat. It's called Gray, and it goes like this: Gray = [strict 2-categories, strict 2-functors, weak natural transformations, modifications] We have inclusions of weak 3-categories: Strict2Cat -> Gray -> Weak2Cat and Lack shows, not only that the second inclusion fails to be an equivalence, but that there's *no* equivalence between Gray and Weak2Cat. All this suggests that for some purposes we really need to face up to weak 2-categories: the strict and semistrict setups aren't flexible enough for every job. The same is undoubtedly true at the 3-category level - and that's where the next talk comes in! In the next talk, Nick Gurski spoke about weak 3-categories. He wrote his thesis about these, and I'm starting to really wish he'd put his thesis on the arXiv, so everyone can see how cool it is and learn more about 3-categories. But, I guess he wants to perfect it. In his talk, Nick not only explained the definition of weak 3-category, which is famously complicated - he did his best to convince us that we could reinvent this definition ourselves if we tried! Then he went ahead and discussed various proofs that every weak 3-category is equivalent to a semistrict one. An interesting theme of all three talks was the idea of treating the "strictification" functor implicit in Mac Lane's coherence theorem: st: Weak2Cat -> Strict2Cat as the left adjoint of the inclusion i: Strict2Cat -> Weak2Cat where now we think of both Strict2Cat and Weak2Cat as mere 1-categories. You can read more about this idea here: 3) Miles Gould, Coherence for categorified operadic theories, available as math.CT/0607423. On Tuesday night, Mike Shulman gave an introduction to model categories, which are a tool developed by Quillen in the late 1960s to unify homotopy theory and homological algebra. If you want to understand the basics of model categories, you should probably start by listening to his talk, and then read this: 4) W. G. Dwyer and J. Spalinski, Homotopy theories and model categories, available at http://hopf.math.purdue.edu/Dwyer-Spalinski/theories.pdf For more references, try "week170". Here's the rough idea: In homotopy theory we study topological spaces; in homological algebra we study chain complexes. But, in both cases we study them in a funny way. There's a category of topological spaces and continuous maps, and there's a category of chain complexes and chain maps, but these categories are not everything that counts. Normally, we say two objects in a category are "the same" if they're isomorphic. But in this case we often use a weaker concept of equivalence! In homotopy theory, we say a map between spaces f: X -> Y is a "weak homotopy equivalence" if it induces isomorphisms on homotopy groups: pi_n(f): pi_n(X) -> pi_n(Y) In homological algebra, we say a map between chain complexes f: X -> Y is a "quasi-isomorphism" if it induces isomorphisms on homology groups: H_n(f): H_n(X) -> H_n(Y) Model category theory formalizes this by speaking of a category C equipped with a classes of morphisms called "weak equivalences". We can formally invert these and get a new category Ho(C) where the weak equivalences are isomorphisms: this is called the "homotopy category" or "derived category" of our model category. But this loses information, so it's often good *not* to do this. In a model category, we also have a class of morphisms called "fibrations", which you should imagine as being like fiber bundles. Dually, we have a class of morphisms called "cofibrations", which you should imagine as well-behaved inclusions, like the inclusion of the closed unit interval in the real line - not the inclusion of the rationals into the real line. Finally, the weak equivalences, fibrations and cofibrations satisfy some axioms that make them interlock in a powerful way. These axioms are a bit mind-numbing at first glance, so I won't list them. But, they encapsulate a lot of wisdom about homotopy theory and homological algebra! On Wednesday the talks were about n-categories and homotopy theory. I kicked them off with a general introduction to the "Homotopy Hypothesis": Grothendieck's idea that homotopy theory was secretly about infinity-groupoids - that is, infinity-categories where all the j-morphisms have weak inverses. 5) John Baez, The homotopy hypothesis, http://math.ucr.edu/home/baez/homotopy/ Part of the idea is that if you hand me a space X, I can cook up an infinity-groupoid which has: points of X as objects, paths in X as morphisms, homotopies between paths in X as 2-morphisms, homotopies between homotopies between paths in X as 3-morphisms, etc.... This is called the "fundamental infinity-groupoid of X". But another part of the idea is that if you hand me a model category C, I can cook up an infinity-category which has: nice objects of C as objects, morphisms in C as morphisms, homotopies between morphisms in C as 2-morphisms, homotopies between homotopies between morphisms in C as 3-morphisms, etc.... The basic idea here is simple: we're studying homotopies between homotopies between... and so on. (But, there's a little technicality - this "nice object" business. An object of C is "fibrant" if its unique morphism from the initial object is a fibration, and "cofibrant" if its unique morphism to terminal object is a cofibration. Objects with both properties are what I'm calling "nice". For example, in the category of topological spaces, the "cell complexes" (made by gluing balls together) are nice. In the category of chain complexes, the "projective" chain complexes are nice. Only for these nice objects do homotopies work as well as you'd hope. Luckily, every object in C is weakly equivalent to one of these nice ones.) The interesting thing about the above infinity-category is that it's an "(infinity,1)-category", meaning that all its j-morphisms are weakly invertible for j > 1. For example, maps between spaces aren't necessarily invertible, even up to homotopy - but homotopies are always invertible. We can define "(infinity,k)-categories" for any k in the same way, and we see that (infinity,0)-categories are just infinity-groupoids. So, the Homotopy Hypothesis reveals the beginning of what might be a very nice pattern. Roughly: Topological spaces, as studied in homotopy theory, are secretly (infinity,0)-categories. Model categories, as studied in homotopy theory, are secretly (infinity,1)-categories. ????, as studied in homotopy theory (not yet?), are secretly (infinity,2)-categories. Etcetera.... Presumably the ???? should be filled in with something like "model 2-categories", with the primordial example being the 2-category of model categories, just as the primordial example of a model category is the category of spaces. But, there's only been a little study of this sort of "meta-homotopy theory" so far. For example: 6) Julie Bergner, Three models for the homotopy theory of homotopy theories, available as math.AT/0504334. After my talk, Simona Paoli spoke about her work on turning the homotopy hypothesis from a dream into a reality: 7) Simona Paoli, Semistrict models of connected 3-types and Tamsamani's weak 3-groupoids, available as math.AT/0607330. 8) Simona Paoli, Semistrict Tamsamani n-groupoids and connected n-types, available as math.AT/0701655. Eugenia Cheng then spent the afternoon leading us through another approach: 9) Clemens Berger, A cellular nerve for higher categories, available at http://citeseer.ist.psu.edu/383423.html 10) Denis-Charles Cisinski, Batanin higher groupoids and homotopy types, available as math.AT/0604442. I would love to explain this stuff, mainly as an excuse for learning it better! But alas, I'm getting a bit tired and we're only on the second day of the workshop... I must hurry on. On Wednesday evening, Peter May spoke about some applications of weak 2-categories that appear in his new book: 11) Peter May and J. Sigurdsson, Parametrized Homotopy Theory, American Mathematical Society, 2006. The rough idea is that we have a weak 2-category with: spaces as objects, spectra over X x Y as morphisms from X to Y, maps between spectra over X x Y as 2-morphisms. Lots of ideas from "parametrized" stable homotopy theory are neatly encoded as results about this 2-category. Thursday was all about (infinity,1)-categories. The first talk was by Mike Shulman, who gave a nice intuitive treatment of Andre Joyal's approach to (infinity,1)-categories. In 1957, Daniel Kan figured out a nice way to describe infinity-groupoids as simplicial sets with a certain property: now they're called "Kan complexes". They're very popular among homotopy theorists. You can read about them here: 12) Paul G. Goerss and J. F. Jardine, Simplicial Homotopy Theory, Birkhaeuser, Basel, 1999. Given this, it's not so surprising that we can describe (infinity,1)-categories as simplicial sets with some more general property. In fact this was done by Boardmann and Vogt back in 1973. In the last decade or so, Joyal has developed an enormous body of results about these (infinity,1)-categories, which he calls "quasicategories". He is writing a book on the subject, which is not quite done yet - but it's already enormously influenced the state of higher category theory, and I expect it will continue to do so. Next Julie Bergner compared different approaches to (infinity,1)- categories. I mentioned a while back that she's one of the few people who has worked hard on "meta-homotopy theory". That was very much in evidence in her talk. She began by describing a bunch of different definitions of (infinity,1)-category. But then she showed these definitions weren't really so different! For each definition, she constructed a model category of all (infinity,1)-categories of that type. And then, she sketched the proof that all these model categories were "Quillen equivalent". For details, listen to her talk or try this paper: 13) Julie Bergner, A survey of (infinity, 1)-categories, available as math.AT/0610239. In the afternoon, Andre Joyal spoke about quasicategories. I urge you to listen to his talk and also the minicourse he later gave on this subject: 14) Andre Joyal, Graduate course on basic aspects of quasicategories, http://www.fields.utoronto.ca/audio/#crs-quasibasic I can't possibly summarize this stuff! It basically amounts to taking the whole of category theory and extending it to quasicategories. (Well, I guess I just summarized it, but....) After Joyal's talk, Joshua Nichols-Barrer spoke about using quasicategories as an approach to understanding "stacks", which are like sheaves, only categorified. In the evening, Kathryn Hess spoke about some work she's doing with Steve Lack, on parallel transport in bundles of bicategories. Sounds like physics, but they came to the subject from a completely different motivation! Finally, Dorette Pronk spoke about weak 2-categories and weak 3-categories of fractions. The notion of a "calculus of fractions" goes back at least to the work of Gabriel and Zisman in 1967: 15) P. Gabriel and M. Zisman, Categories of Fractions and Homotopy Theory, Springer-Verlag, Berlin, 1967. Say you have a category and you want to throw in formal inverses to some morphisms. Well, you can do it! But in general, the morphisms in the resulting category will be arbitrarily long "zig-zag" diagrams in your original category, like this: X_1 ---> X_2 <--- X_3 ---> X_4 <--- X_5 ---> X_6 The arrows pointing backwards are the ones you threw in formal inverses for. This is a nuisance! But luckily, in nice cases, you only need to use zig-zags of length two. This is what a "calculus of fractions" achieves. A classic example is when you start with a model category C, and you throw in formal inverses for the weak equivalences to get the "homotopy category" Ho(C). Dorette Pronk has been looking at how all this generalizes when you have a weak 2-category or weak 3-category and you throw in *weak* inverses to some morphisms. This has some interesting applications to stacks: 16) Dorette A. Pronk, Etendues and stacks as bicategories of fractions, Compositio Mathematica, 102 (1996), 243-303. Also available at http://www.numdam.org/numdam-bin/recherche?h=nc&id=CM_1996__102_3_243_0 Dorette's talk ended at 9 pm, and everyone went home and collapsed after a hard day's work. Actually not: a bunch of us went out and partied! One of the great things about working on n-categories is the sense of camaraderie among the small crowd that does this. Friday's talks were about higher gauge theory. Since I've discussed this many times here, I'll be terse. Alissa Crans explained Lie 2-groups and Lie 2-algebras, and then Danny Stevenson explained his work on connections, 2-connections and Schreier theory (see "week223"). In the afternoon, Urs Schreiber described his ideas on higher-dimensional parallel transport and local trivializations, with a little help from Toby Bartels. Friday evening, we heard talks from Simon Willerton (on Hopf monads) and Igor Bakovic (on 2-bundles). Quite an evening! Bakovic is an impressive young Croatian fellow who seems to have taught himself n-categories. We were all horrified when it became clear he had over 30 pages of transparencies, but his talk was actually quite nice. And if you like higher-dimensional diagrams anywhere near as much as I do, you've got to take a look at Willerton's slides: 17) Simon Willerton, The diagrammatics of Hopf monads, http://math.ucr.edu/home/baez/fields/willerton/ Again the talks ended at 9 pm. Finally, on Saturday morning, spoke about Frobenius algebras and their relation to Khovanov homology: 18) Aaron Lauda, Frobenius algebras, quantum topology and higher categories, available at http://www.math.columbia.edu/~lauda/talks/Fields/ Urs Schreiber then wrapped things up with a talk about the quantization of strings from a higher category viewpoint. You can get a good feeling for this from his blog entries at the n-Category Cafe, which are all listed on my webpage for this workshop - the first webpage mentioned this Week. From rrosebru@mta.ca Mon Feb 12 20:34:43 2007 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 12 Feb 2007 20:34:43 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HGlX0-0001gg-K6 for categories-list@mta.ca; Mon, 12 Feb 2007 20:28:26 -0400 Date: Mon, 12 Feb 2007 16:22:03 GMT From: Oege.de.Moor@comlab.ox.ac.uk To: Subject: categories: Positions at Oxford: refactoring tools Content-Type: text Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 15 Programming Tools Group University of Oxford, UK http://progtools.comlab.ox.ac.uk http://aspectbench.org >> fully funded 3-year PhD studentship << >> numerous paid 2-months internships << Applications from category theorists (or their students) would be particularly welcome! 1. PROJECT SUMMARY: ASPECT REFACTORING TOOLS Software systems are rarely written from scratch: they evolve over long periods of time. When a change is made, this often affects many different locations in a system, and it is hard to make a change consistently. For that reason, automated tools to help the process of software change are desirable. "Refactoring" refers to the process of restructuring an existing piece of software, often prior to introducing new functionality, or to take advantage of a new technology. Refactoring must preserve the behaviour of existing code, and tools that help in refactoring both assist in the restructuring process and in checking that the behaviour has not changed. Unfortunately today's refactoring tools are very hard to construct, they are still quite limited in functionality, and they often contain bugs. This project aims to construct a framework for better refactoring tools. In particular, the work is driven by refactorings for a new set of language features, called `aspect-oriented programming' that have recently been added to Java. Our framework will be based on developments in three separate areas of computer science: * `strategies' to control the process of rewriting program code, from the `term rewriting' community * `reference attributed grammars' to specify the conditions that guarantee behaviour is preserved, from the `compilers' community * `incremental evaluation' of declarative rules, from the `functional and logic programming' community. The quality of our framework will be assessed by coding selected case studies using alternative methods. In particular, we shall implement several refactorings directly in Eclipse, the leading development environment for writing aspect-oriented programs in industry. The project is funded by the EPSRC (UK equivalent of NSF). 2. REQUIREMENTS The PhD student will be concerned with the theoretical foundations of the refactoring framework, for instance proofs of correctness for refactorings, and also for the incremental evaluation mechanism. We are thus looking for someone with good mathematical skills, in particular regarding formal properties of type systems and program analyses. Candidates must have an outstanding undergraduate or master's degree in computer science. Funding is provided to pay for university fees at EU level (overseas candidates need supplementary funding), plus subsistence, travel, equipment etc. The 2-months positions are intended to assist with implementation work. We are thus looking for highly skilled Java programmers; familiarity with program analysis, formal type systems and so on will be an advantage. These internships are in fact short-term appointments as research assistants at the University of Oxford, and so the holders will be paid a salary. Interns can be outstanding undergraduate students who wish to gain research experience. 3. HOW TO APPLY The deadline for applications is March 20, 2007. * For the PhD studentship, follow the instructions on http://web.comlab.ox.ac.uk/oucl/prospective/dphil/ Clearly mark your application "Aspect Refactoring Tools project". Also send a full electronic copy of your application to oege@comlab.ox.ac.uk, by March 20, 2007. * For the 2-months positions, send a letter explaining your interest in the project, plus a full cv and the names of 3 referees to oege@comlab.ox.ac.uk. 4. FURTHER INFORMATION We are happy to discuss any of the above informally with prospective candidates. Just email one or all of the project leaders: Oege de Moor (oege@comlab.ox.ac.uk) Torbjorn Ekman (torbjorn@comlab.ox.ac.uk) Mathieu Verbaere (matv@comlab.ox.ac.uk) From rrosebru@mta.ca Mon Feb 12 20:41:40 2007 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 12 Feb 2007 20:41:40 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HGlii-0002cg-9s for categories-list@mta.ca; Mon, 12 Feb 2007 20:40:32 -0400 Date: Tue, 13 Feb 2007 00:46:51 +0100 (CET) To: categories@mta.ca Subject: categories: PSSL 85 - Call for participation From: Eugenia.CHENG@unice.fr MIME-Version: 1.0 Content-Type: TEXT/PLAIN; CHARSET=3DISO-8859-1; FORMAT=3Dflowed Content-Transfer-Encoding: 8BIT Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 16 [Note from moderator: apologies for repeated postings of this item - by inadvertence the From: field did not appear in the earlier postings, regards to all, Bob] PSSL 85 - Second announcement Dear All, This is the second announcement and call for participation for the 85th Peripatetic Seminar on Sheaves and Logic. The conference will be held on the weekend of 24th and 25th March in Nice, France, and should finish at lunchtime on Sunday. The conference will take place at the Laboratoire J.A. Dieudonne, Universite de Nice Sophia-Antipolis. If you would like to attend the PSSL please send an e-mail to Eugenia Cheng (eugenia@math.unice.fr), using the form attached below, indicating if you would like to give a talk. COST We will be booking participants into the Hotel Mirabeau, where the University rate is 45.70 Euros per night, for bed and breakfast, subject to availability. In addition, for Saturday evening we have organised a large group booking at a restaurant in central Nice.=A0The cost for the dinner will be 25 Euros, or 35 Euros for guests. Please indicate if you would like to join us. Payment will be by cash on the first morning of the conference. There is no registration fee. Lunch on Saturday will be provided. DEADLINES There is no deadline for registration. However if you would like us to book your hotel accommodation for you, please register by *Thursday February 22nd*. After this date you can still get University rates subject to availability, but you will need to contact the hotel yourself. See the PSSL85 website for details. FUNDING There is still some financial support available for students. If you are interested please write to Eugenia Cheng. This and further information can be found at the PSSL85 website: http://math.unice.fr/~eugenia/pssl85 . Here you can also find information about travel to Nice. A list of participants and schedule will be posted in due course. We look forward to seeing you in March. With best regards, The organiser, Eugenia Cheng ----------------------------------------------------------------------- REGISTRATION FORM I, __________________________________________, would like to attend the 85th PSSL. I will not be giving a talk / I would like to give a talk entitled ________________________________________________________________________ My affiliation is _____________________________________ (University etc) I will not require accommodation / I would like accommodation at the Hotel Mirabeau for the nights of _____________ March * if replying by 22nd Feb I will not be attending the dinner on Saturday / I would like to attend the dinner on Saturday for 25 Euros. I will be bringing ____ guest(s) to dinner on Saturday for 35 Euros each. I/we have the following special dietary requirements: ____________________________________________________________________ From rrosebru@mta.ca Tue Feb 13 14:37:25 2007 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 13 Feb 2007 14:37:25 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HH2LO-00045v-NK for categories-list@mta.ca; Tue, 13 Feb 2007 14:25:34 -0400 Date: Tue, 13 Feb 2007 08:24:30 +0000 From: Alexander Kurz MIME-Version: 1.0 To: categories@mta.ca Subject: categories: PhD in Theoretical Computer Science Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 17 ----------------------------------------- PhD Position in Leicester, UK ----------------------------------------- The Department of Computer Science of the University of Leicester offers three PhD studentships (GTA). The GTA scheme involves some teaching and runs for 4 years. Unfortunately, the university waives the fees only for EU nationals. One of the positions will be in the area of Theoretical Computer Science under the supervision of Alexander Kurz. Colleagues in Leicester working on related topics include Nick Bezhanishvili, Roy Crole, Reiko Heckel, Vincent Schmitt, Emilio Tuosto, and Fer-Jan de Vries. Moreover, there will be close collaboration with the logic groups at the University of Amsterdam (in particular with the VICI-project directed by Yde Venema at ILLC) and at the University of Oxford (Hilary Priestley, Alexandru Baltag). For more information email to: kurz@mcs.le.ac.uk The official announcement and application form is available at (Ref S3149) http://www.le.ac.uk/personnel/supportjobs/index.html The applications should be submitted no later than 23 February 2007. From rrosebru@mta.ca Tue Feb 13 16:32:56 2007 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 13 Feb 2007 16:32:56 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HH4Fc-0003m5-AM for categories-list@mta.ca; Tue, 13 Feb 2007 16:27:44 -0400 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: Michael Mislove Subject: categories: MFPS 23 Registration Now Open Date: Tue, 13 Feb 2007 13:30:55 -0600 To: mfpsmail@linus.math.tulane.edu, categories@mta.ca Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 18 Dear Colleagues, Registration is now open for MFPS 23. The meeting will be held on the campus of Tulane University in New Orleans, LA from April 11 through April 14, 2007. The program features five plenary lectures and four special sessions on topics ranging from security to systems biology to physics, information and computation. A list of the accepted papers and of the invited speakers is linked to the MFPS 23 home page http://www.math.tulane.edu/~mfps/mfps23.htm There is also a link on the home page that leads to a registration form for the meeting. In addition to the usual MFPS program, we will also hold a Tutorial Day on April 10. The topic this year is domain theory, and there will be lectures by Andrej Bauer, Achim Jung, Giuseppe Rosolini and Alex Simpson. There is no charge to attend the Tutorial Day, and graduate students are especially encouraged to attend. Best regards, Mike Mislove From rrosebru@mta.ca Wed Feb 14 20:23:48 2007 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 14 Feb 2007 20:23:48 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HHUGb-0001ZT-Tv for categories-list@mta.ca; Wed, 14 Feb 2007 20:14:29 -0400 Mime-Version: 1.0 (Apple Message framework v752.2) To: Categories Subject: categories: A web page for Max From: Ross Street Date: Wed, 14 Feb 2007 21:03:57 +1100 Content-Transfer-Encoding: 7bit Content-Type: text/plain;charset=US-ASCII;delsp=yes;format=flowed Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: RO X-Status: X-Keywords: X-UID: 19 Dear Category People Max's son Simon has set up a web page that you might like to see: www.maxkelly.com.au I would also like to mention that I have been asked to write Max's obituary for the Sydney Morning Herald, the Gazette of the Australian Math Society, and the Australian Academy of Science. I am very grateful for the many messages you have sent in the last couple of weeks. I would also be grateful for any material that you think would be helpful to me in writing these documents. Ross From rrosebru@mta.ca Wed Feb 14 20:23:48 2007 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 14 Feb 2007 20:23:48 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HHUEs-0001Qn-7U for categories-list@mta.ca; Wed, 14 Feb 2007 20:12:42 -0400 From: Rob van Glabbeek and Matthew Hennessy To: categories@mta.ca Date: Wed, 14 Feb 2007 23:34:25 +1100 Subject: categories: SOS 2007 - Call for Papers Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 20 Structural Operational Semantics 2007 An Affiliated Workshop of LICS 2007 and ICALP 2007 July 9, 2007, Wroclaw, Poland http://www.cse.unsw.edu.au/~rvg/SOS2007 Aim: Structural operational semantics (SOS) provides a framework for giving operational semantics to programming and specification languages. A growing number of programming languages from commercial and academic spheres have been given usable semantic descriptions by means of structural operational semantics. Because of its intuitive appeal and flexibility, structural operational semantics has found considerable application in the study of the semantics of concurrent processes. Moreover, it is becoming a viable alternative to denotational semantics in the static analysis of programs, and in proving compiler correctness. Recently, structural operational semantics has been successfully applied as a formal tool to establish results that hold for classes of process description languages. This has allowed for the generalisation of well-known results in the field of process algebra, and for the development of a meta-theory for process calculi based on the realization that many of the results in this field only depend upon general semantic properties of language constructs. This workshop aims at being a forum for researchers, students and practitioners interested in new developments, and directions for future investigation, in the field of structural operational semantics. One of the specific goals of the workshop is to establish synergies between the concurrency and programming language communities working on the theory and practice of SOS. Moreover, it aims at widening the knowledge of SOS among postgraduate students and young researchers worldwide. Specific topics of interest include (but are not limited to): * programming languages * process algebras * higher-order formalisms * rule formats for operational specifications * meaning of operational specifications * comparisons between denotational, axiomatic and SOS * compositionality of modal logics with respect to operational specifications * congruence with respect to behavioural equivalences * conservative extensions * derivation of proof rules from operational specifications * software tools that automate, or are based on, SOS. Papers reporting on applications of SOS to software engineering and other areas of computer science are welcome. History: The first SOS Workshop took place on the 30th of August 2004 in London as one of the satellite workshops of CONCUR 2004. Subsequently, SOS 2005 occurred on the 10th of July 2005 in Lisbon as a satellite workshop of ICALP 2005, and SOS 2006 on the 26th of August 2006 in Bonn as a satellite workshop of CONCUR 2006. A special issue of the Journal of Logic and Algebraic Programming on Structural Operational Semantics appeared in 2004; a special issue of Theoretical Computer Science dedicated to SOS 2005 is in press, and a special issue of Information & Computation on Structural Operational Semantics inspired by SOS 2006 is in preparation. INVITED SPEAKER: Pawel Sobocinski (Cambridge, UK) PAPER SUBMISSION: We solicit unpublished papers reporting on original research on the general theme of SOS. Prospective authors should register their intention to submit a paper by uploading a title and abstract via the workshop web page by: *** Friday 6 April 2007. *** Papers should take the form of a pdf file in ENTCS format [http://www.entcs.org/], whose length should not exceed 15 pages (not including an optional "Appendix for referees" containing proofs that will not be included in the final paper). We will also consider 5-page papers describing tools to be demonstrated at the workshop. Proceedings: Preliminary proceedings will be available at the meeting. The final proceedings of the workshop will appear as a volume in the ENTCS series. We may decide to arrange a special issue of an archival journal devoted to full versions of selected papers from the workshop. IMPORTANT DATES: * Submission of abstract: Friday 6 April 2007 * Submission: Sunday 15 April 2007 * Notification: Wednesday 9 May 2007 * Final version: Friday 25 May 2007 * Workshop: Monday 9 July 2007 * Final ENTCS version: Friday 10 August 2007. PROGRAMME COMMITTEE Luca Aceto (Aalborg, DK; Reykjavik, IS) Rocco De Nicola (Florence, IT) Rob van Glabbeek (NICTA, AU, co-chair) Reiko Heckel (Leicester, UK) Matthew Hennessy (Sussex, UK, co-chair) Bartek Klin (Warsaw, PL) Ugo Montanari (Pisa, IT) MohammadReza Mousavi (Eindhoven, NL; Reykjavik, IS) Prakash Panangaden (Montreal, CA) Grigore Rosu (Urbana-Champaign, IL, USA) Simone Tini (Insubria, I) Shoji Yuen (Nagoya, JP) CONTACT: sos2007@cs.stanford.edu WORKSHOP ORGANISERS: Rob van Glabbeek National ICT Australia Locked Bag 6016 University of New South Wales Sydney, NSW 1466 Australia Matthew Hennessy Department of Informatics University of Sussex Falmer, Brighton, BN1 9QN United Kingdom From rrosebru@mta.ca Wed Feb 14 20:23:49 2007 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 14 Feb 2007 20:23:49 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HHUDU-0001KQ-P7 for categories-list@mta.ca; Wed, 14 Feb 2007 20:11:16 -0400 Mime-Version: 1.0 (Apple Message framework v752.3) Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: quoted-printable From: ICLP07 publicity Subject: categories: Second CFP: 23rd International Conference on Logic Programming (ICLP 2007) Date: Wed, 14 Feb 2007 09:37:38 +0000 To: ICLP07 publicity Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 21 (apologies for cross-posting) Second Call for Papers 23rd International Conference on Logic Programming ICLP 2007 Porto, Portugal, September 8-13, 2007 http://www.dcc.fc.up.pt/iclp07/ Conference Scope Since the first conference held in Marseilles in 1982, ICLP has been the premier international conference for presenting research in logic programming. Contributions (papers and posters) are sought in all areas of logic programming including but not restricted to: - Theory: Semantic Foundations, Formalisms, Nonmonotonic Reasoning, Knowledge Representation. - Implementation: Compilation, Memory Management, Virtual Machines, Parallelism. - Environments: Program Analysis, Program Transformation, Validation and Verification, Debugging, Profiling. - Language Issues: Concurrency, Objects, Coordination, Mobility, Higher Order, Types, Modes, Programming Techniques. - Alternative Paradigms: Abductive Logic Programming, Answer Set Programming, Constraint Logic Programming, Inductive Logic Programming, Alternative Inference Engines and Mechanisms. - Applications: Deductive Databases, Data Integration, Software Engineering, Natural Language, Web Tools, Internet Agents, Artificial Intelligence, Bioinformatics. The three broad categories for submissions are: (1) technical papers, where specific attention will be given to work providing novel integrations of the areas listed above, (2) application papers, where the emphasis will be on their impact on the application domain as opposed to the advancement of the the state-of-the-art of logic programming, and (3) posters, ideal for presenting and discussing current work not yet ready for publication, for PhD thesis summaries and research project overviews. In addition to papers and posters, the technical program will include invited talks, tutorials, a Doctoral Consortium, and workshops. Papers and Posters Papers and posters must describe original, previously unpublished research, and must not simultaneously be submitted for publication elsewhere. They must be written in English. Technical and application papers must not exceed 15 pages in the Springer LNCS format. The limit for posters is 2 pages in the same format. The primary means of submission is electronic. Papers and posters must be submitted at http://www.easychair.org/ICLP2007/. Publication It is expected that the proceedings will be published by Springer-Verlag in the LNCS series. All accepted papers and abstracts of accepted posters will be included in the proceedings. Important Dates Paper registration deadline: March 2, 2007 Submission deadline: March 9, 2007 Notification of authors: May 4, 2007 Camera-ready copy due: June 8, 2007 ICLP 2007 Organization Program Chairs: Ver=F3nica Dahl and Ilkka Niemel=E4 General Chair: Fernando Silva Local Chair: Ricardo Rocha Publicity Chair: Salvador Abreu Workshops Chair: Agostino Dovier Doctoral Consortium Chairs: Enrico Pontelli and In=EAs Dutra Prolog Programming Contest: Bart Demoen Contact Address: iclp07@dcc.fc.up.pt Program Committee: Maurice Bruynooghe Keith Clark Ver=F3nica Dahl (Co-chair) Marina De Vos Yannis Dimopoulos In=EAs Dutra Esra Erdem Maurizio Gabbrielli Patricia M Hill Katsumi Inoue Tomi Janhunen Tony Kusalik Nicola Leone Vladimir Lifschitz Ilkka Niemel=E4 (Co-chair) Lu=EDs Moniz Pereira German Puebla Francesca Rossi Kostis Sagonas Peter Schachte Torsten Schaub Fernando Silva Guillermo R. Simari Tran Cao Son Paul Tarau Francesca Toni Eric Villemonte de la Clergerie David S. Warren Stefan Woltran Workshops The ICLP'07 program will include several workshops. They are perhaps the best place for the presentation of preliminary work, novel ideas, and new open problems to a wide and interested audience. Workshops also provide a venue for presenting specialized topics and opportunities for intensive discussions and project collaboration in any areas related to logic programming, including cross-disciplinary areas. You can find the call for proposals in http://www.dimi.uniud.it/dovier/WICLP07/. Workshop proposal submission deadline: February 14, 2007. Doctoral Consortium The Doctoral Consortium (DC) on Logic Programming is the third doctoral consortium to be offered as part of ICLP conference series. The DC builds on the experience of the previous successful consortiums (held in Sitges, Spain and in Seattle, WA) during ICLP-05 and ICLP-06. The DC is designed for doctoral students working in areas related to logic and constraint programming, who are planning to pursue a career in academia. The DC also considers applications from Master's students pursuing projects in logic programming and interested in entering a doctoral program. The Doctoral Consortium aims to provide students with an opportunity to present and discuss their research directions and to obtain feedbacks from peers as well as world-renown experts in the field. The Doctoral Consortium will also offer invited speakers and panels discussions. More information can be found at http://www.cs.nmsu.edu/~epontell/DC2007/. Conference Venue ICLP 2007 will be held in the city of Porto, second largest in Portugal. Porto is located by the Douro river and the Atlantic, has a truly unique appearance with many striking bridges, a historic center classified by UNESCO as a World Heritage site, a new House of Music by Rem Koolhaas and a nice Museum of Modern Art (Museu de Serralves). Porto is also well known for the much celebrated Port wine grown in the Douro valley. The conference will feature a cruise in the Douro river along with other optional tours. The Conference will take place in the Hotel "Le Meridien Park Atlantic Porto". From rrosebru@mta.ca Wed Feb 14 20:23:49 2007 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 14 Feb 2007 20:23:49 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HHUFL-0001TC-40 for categories-list@mta.ca; Wed, 14 Feb 2007 20:13:11 -0400 Date: Wed, 14 Feb 2007 22:13:59 +0000 From: "Jamie Vicary" To: categories@mta.ca Subject: categories: Equalisers and coequalisers in categories with a \dag-involution 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: 22 Dear all, Consider the following straightforward coequaliser (e,E) formed by f,g:A-->B and e:B-->E, with e.f=e.g. I am working in a category with biproducts, and with a contravariant involutive endofunctor (--)^\dag on the category which is compatible with the biproducts; i.e. (projection)^\dag = injection for all projections and injections making up a part of a biproduct. In such a category, it is natural to consider the coequaliser object E to be the subspace of B on which the morphisms f and g agree. It is therefore natural to require e.(e^\dag) = id_E; this sort of condition is similar to the sorts of conditions that form part of the definition of the biproduct. I'm asking whether there exists a natural framework generalising the theory of biproducts, which is analagous to the way that (co)limits generalise (co)products, within which I can safely assume that e.(e^\dag) = id_E. Biproducts seem quite different from products and coproducts, though, so I don't know how it would work. Jamie Vicary. From rrosebru@mta.ca Thu Feb 15 21:59:03 2007 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 15 Feb 2007 21:59:03 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HHsC0-0004DU-IW for categories-list@mta.ca; Thu, 15 Feb 2007 21:47:20 -0400 Mime-Version: 1.0 (Apple Message framework v752.2) Content-Type: text/plain; charset=US-ASCII; delsp=yes; format=flowed To: categories@mta.ca Subject: categories: Lectureship in Foundations at Sussex Date: Thu, 15 Feb 2007 17:12:57 +0000 From: Bernhard Reus Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 23 The Department of Informatics at the University of Sussex is seeking to appoint a Lecturer in Software Systems or _Foundations_ . Closing date is March 5th. Note that this post is for Software Systems OR Foundations, so strong candidates with interests in Categorical Logic or/and Semantics (Domain Theory) are very welcome to apply. More info at http://www.sussex.ac.uk/Units/staffing/personnl/vacs/ vac667_668.shtml . Best, Bernhard --- Dr B Reus Dept. of Informatics, School of Science & Technology, University of Sussex From rrosebru@mta.ca Fri Feb 16 12:25:31 2007 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 16 Feb 2007 12:25:31 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HI5nj-00039Q-BM for categories-list@mta.ca; Fri, 16 Feb 2007 12:19:11 -0400 Subject: categories: Re: Equalisers and coequalisers in categories with a \dag-involution Date: Fri, 16 Feb 2007 02:39:44 -0400 (AST) To: categories@mta.ca MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit From: selinger@mathstat.dal.ca (Peter Selinger) Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 24 Jamie Vicary wrote: > > Dear all, > > Consider the following straightforward coequaliser (e,E) formed by > f,g:A-->B and e:B-->E, with e.f=e.g. I am working in a category with > biproducts, and with a contravariant involutive endofunctor (--)^\dag > on the category which is compatible with the biproducts; i.e. > (projection)^\dag = injection > for all projections and injections making up a part of a biproduct. In > such a category, it is natural to consider the coequaliser object E to > be the subspace of B on which the morphisms f and g agree. It is > therefore natural to require e.(e^\dag) = id_E; this sort of condition > is similar to the sorts of conditions that form part of the definition > of the biproduct. > > I'm asking whether there exists a natural framework generalising > the theory of biproducts, which is analagous to the way that > (co)limits generalise (co)products, within which I can safely assume > that e.(e^\dag) = id_E. Biproducts seem quite different from products > and coproducts, though, so I don't know how it would work. > > Jamie Vicary. Dear Jamie, your equation e.(e^\dag) = id_E only makes sense if your functor (--)^\dag is the identity on objects. In this case, you are dealing with a dagger category in the sense of [1]. Dagger categories are important in quantum physics; an important example is the category Hilb of Hilbert spaces and linear operators, with dagger being the adjoint of an operator. I will dualize your question to make it a question about equalizers, or more generally, monomorphisms. Monomorphisms with the property (e^\dag).e = id_E are investigated in [2], where they are called dagger-subobjects. (Both papers also deal with biproducts of the kind you asked about). Your question raises a basic problem, which is that it is not well-defined. Specifically, while equalizers are only defined "up to isomorphism", the property (e^\dag).e = id_E (*) is not invariant under isomorphisms of E. As a simple example, the two morphisms f,g: C -> C^2 in Hilb, defined by f(x) = (x,0) and g(x) = (2x,0), define isomorphic subobjects, yet f satisfies (*), whereas g does not. Therefore one cannot ask whether "the" equalizer of two maps satisfies (*). The fundamental issue is that in a dagger-category, there is a distinguished subclass of isomorphisms: the unitary ones. An isomorphism f: E -> E' is called unitary if f^\dag = f^{-1}. And although the property (*) is not invariant under arbitrary isomorphisms, it is invariant under unitary isomorphisms. To many category theorists, it may seem strange that some important categorical property is not invariant under isomorphism. But actually, this is quite natural. With every notion of structure comes a notion of structure-preserving isomorphism, and one expects properties related to the structure to be preserved only by the structure-preserving isomorphisms, not by arbitrary isomorphisms. Dagger is such a structure, whose structure-preserving morphisms are exactly the unitary ones. Now to get back to your question: Consider equalizers (or more generally, subobjects) in a dagger category. Of the many maps e: E -> A representing a given subobject (or equalizing a given pair of arrows), some may not be unitarily isomorphic to some others, so they fall into equivalence classes modulo unitary isomophism. One may ask whether any of these equivalence classes is distinguished, i.e., whether one of them deserves to be called "the" equalizer or "the" subobject, and would be unique up to unitary isomorphism. It turns out that, provided it exists at all, there is indeed a distinguished choice of such a subobject, and it is the one satisfying (*). So we can call a monomorphism satisfying (*) a "dagger-subobject", and an equalizer satisfying (*) a "dagger-equalizer", and so forth. (In the literature, particularly on Hilbert spaces, a morphism satisfying (*) is also called an "isometry"). Fortunately, if any representative of a subobject satisfies (*), then that representative is unique up to unitary isomorphism. So it really makes sense to speak of "the" dagger-subobject etc. While uniqueness is easy, existence is a tricky matter. There certainly are examples of subobjects that are not isomorphic to any dagger-subobject. One such example is in the category of integer matrices (objects are arities, composition is matrix multiplication, and dagger is transpose). The morphism (2) (as a 1x1-matrix) is monic, but not isomorphic (as a subobject) to any isometries. However, it is also not an equalizer. To get an example with equalizers, consider the two morphisms f = (1,0) and g = (0,1) (as 1x2-matrices). Their equalizer is the 2x1-matrix e = (1,1)^\dag. However, this is not isomorphic to any isometry, and hence not to any dagger-equalizer. So in general, dagger-equalizers don't exist even if equalizers do. (For this example, it is important that the scalars are integers. If real numbers were allowed, then e/sqrt{2} would be the dagger-equalizer.) On the other hand, it is proved in [2] (Proposition 5.6) that under some relatively mild condition, every subobject is isomorphic to a dagger-subobject. I hope this answers part of your question! Let me close with some speculation: if e : E -> A is a monomorphism such that (e^\dag).e is invertible, then it is probably relatively easy to add a representative e' : E' -> A freely, and fully faithfully, to the category such that e,e' are isomorphic (as subobjects) and e' satisfies (*). [Clearly if (e^\dag).e is not invertible, then this is never possible]. On the other hand, it is not clear whether (e^\dag).e is invertible in general, or whether at least this is the case when e is an equalizer. -- Peter [1] P. Selinger. Dagger compact closed categories and completely positive maps. To appear in Proceedings of the 3rd International Workshop on Quantum Programming Languages, Chicago, June 30 - July 1, 2005. ENTCS, 23 pages. http://www.mathstat.dal.ca/~selinger/papers.html#dagger [2] P. Selinger. Idempotents in dagger categories. To appear in Proceedings of the 4th International Workshop on Quantum Programming Languages, Oxford, July 17-19, 2006. ENTCS, 15 pages. http://www.mathstat.dal.ca/~selinger/papers.html#idem From rrosebru@mta.ca Fri Feb 16 12:25:31 2007 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 16 Feb 2007 12:25:31 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HI5p9-0003I9-DJ for categories-list@mta.ca; Fri, 16 Feb 2007 12:20:39 -0400 Message-ID: <131dedfb0702160214u62adb9fva396dab7be1678b7@mail.gmail.com> Date: Fri, 16 Feb 2007 10:14:46 +0000 From: "Jamie Vicary" Subject: categories: Re: Equalisers and coequalisers in categories with a \dag-involution To: categories@mta.ca 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 Status: O X-Status: X-Keywords: X-UID: 25 Peter, Thank you for that detailed response! So it seems that if these dagger-subobjects do exist, then then will have good properties. But existence is tricky; in particular, there does not seem to be an elegant property (analagous to having finite limits and colimits) that will guarantee that all of this works. Could we make the following definition: a dagger-category has 'finite bilimits' if any finite diagram D in the category has an 'isometric cone', a cone for which all the associated morphisms to the objects of D are isometries, along with some sort of condition that the isometries are orthogonal in the correct way. It is interesting to consider this in the case of products and equalisers: for products AxB, so it seems, the isometries to A and B will generally be _projectors_, but for equalisers E-e->A=f,g=>B, the isometry e will generally be an _injector_! So we cannot ask for the cone morphisms to be isometric projectors, or isometric injectors. But perhaps this is OK, and we can just require them to be isometries. This definition of bilimit has the 'local flavour' of the definition of biproducts, but cooking up a generally-applicable orthogonality condition on the isometries seems tricky. Of course, in the light of http://www.arxiv.org/abs/math.CT/0604542 , perhaps we only need require that our dagger-category has products and equalizers in order for it to have 'finite bilimits'! In remark 2.6 of [2] cited in your email below, you write that if a dagger-category has products then it must of course have coproducts, but it need not have biproducts. Presumably, math.CT/0604542 proves you wrong here? Jamie. From rrosebru@mta.ca Sat Feb 17 09:51:35 2007 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 17 Feb 2007 09:51:35 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HIPo1-0001bG-He for categories-list@mta.ca; Sat, 17 Feb 2007 09:40:49 -0400 Date: Fri, 16 Feb 2007 19:49:16 +0100 (CET) From: Peter Schuster To: Categories Subject: categories: [3WFTop]: Third Workshop on Formal Topology, Second Announcement 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: 26 3WFTop Second Announcement THIRD WORKSHOP ON FORMAL TOPOLOGY (3WFTop) Padua (Italy) 7-8 May 2007 tutorials (Dept. of Math.) 9-12 May 2007 workshop (Accademia Galileiana) 13 May 2007 social excursion (for those who stay) See the web site http://www.3wftop.math.unipd.it/ for news on: - submission of papers (deadline March 15) - registration (early registration before March 31; note that there are some grants for students and young researchers) - program (preliminary version) - accommodation - social program (see also a photographic tour of Padua) A copy of the the first announcement follows: This is the third of a series of successful meetings on the development of Formal Topology and its connections with related approaches. The first two have been held in Padua, 1997, and Venice, 2002. For more information on 3WFTop see http://www.3wftop.math.unipd.it/ What is formal topology When topology is developed in a strictly constructive way, for instance over Martin-Loef's type theory, points cannot be given primitively and the pointfree approach is fundamental. This is the reason why it is called formal. Formal topology has now become an important tool in constructive mathematics. More on formal topology: http://www.3wftop.math.unipd.it/formal-topology.html Invited speakers Invited speakers include Andre' Joyal, Per Martin-Loef and many other prominent scholars: http://www.3wftop.math.unipd.it/invited-speakers.html Tutorials Before the workshop, two days of extensive and coordinated tutorials are planned, given by Bernhard Banaschewski and other pioneers: http://www.3wftop.math.unipd.it/tutorials.html Contacts If you wish to be kept updated with information about 3WFTop, please send an e-mail to: fortop@math.lmu.de with KEEP ME UPDATED in the subject. The Scientific Committee Thierry Coquand Giovanni Sambin Peter Schuster From rrosebru@mta.ca Sat Feb 17 09:56:37 2007 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 17 Feb 2007 09:56:37 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HIQ26-00026M-AN for categories-list@mta.ca; Sat, 17 Feb 2007 09:55:22 -0400 Subject: categories: Re: Equalisers and coequalisers in categories with a \dag-involution Date: Fri, 16 Feb 2007 17:08:06 -0400 (AST) To: categories@mta.ca MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit From: selinger@mathstat.dal.ca (Peter Selinger) Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 27 Jamie Vicary wrote: > > Of course, in the light of > http://www.arxiv.org/abs/math.CT/0604542 , > perhaps we only need require that our dagger-category has products and > equalizers in order for it to have 'finite bilimits'! In remark 2.6 of > [2] cited in your email below, you write that if a dagger-category has > products then it must of course have coproducts, but it need not have > biproducts. Presumably, math.CT/0604542 proves you wrong here? You are referring to the paper "Finite Products are Biproducts in a Compact Closed Category" by Robin Houston. It does not prove me wrong. Robin's construction only applies to compact closed categories. In general, a dagger category doesn't need to be compact closed. Actually, there is a counterexample to support my remark 2.6. It is due to Robin Houston and myself (any typos or mistakes are mine). (1) There exists a category C with finite products and coproducts, with a zero object, and such that for all A,B, A+B is isomorphic to AxB (not naturally), but for some A,B, the canonical map f:A+B -> AxB is not an isomorphism. Proof: Let C be the category of sets of cardinality 0 or aleph_0, with partial functions as the morphisms. Then the empty set is initial and terminal. We have AxB = A \union (A*B) \union B, where "x" denotes categorical product, and "*" denotes cartesian product of sets. Further A+B = A \union B. By inspecting cardinalities, we find that AxB and A+B have equal cardinality, for all A, B, and hence they are (not naturally) isomorphic. However, the canonical map f:A+B -> AxB satisfying p_i.f.q_j = \delta_{ij} maps everything to the first and third components of AxB = A \union (A*B) \union B, hence is not onto when A,B are non-empty. (2) Corollary: C does not have biproducts. (3) Corollary: There exists a category C with finite products and coproducts, and such that A+B = AxB for all A,B, but which does not have biproducts. Proof: choose a skeleton of the category in (1). (4) There exists a dagger category with finite products, but which does not have biproducts. Proof: Take C as in (3), and consider D = C x C^op. Then D has products and coproducts as inherited componentwise from C and C^op. Also, it satisfies X+Y = XxY. Further, D has no biproducts, or else the forgetful functor to C would preserve them. Now consider D', the full subcategory of D consisting of objects of the form (A,A). This has products and coproducts, and they are not biproducts. Further, D' is a dagger category with (f,g)^{\dag} = (g,f). Another related remark is that even *if* a dagger category has biproducts, then they need not be dagger-biproducts. Here is a counterexample. Consider the category of matrices with rational entries. Objects are arities, and composition is standard matrix multiplication, but define the following non-standard dagger: if A is an mxn-matrix, then let A^\dag = A^{transpose} * 3^(n-m). This is indeed an involutive, identity-on-objects functor. As a category, it is equivalent to finite-dimensional Q-vector spaces, so it has biproducts, and it is also compact closed. However, there are no isometries e : Q -> Q^2 (and hence, no dagger-biproducts). If such an isometry existed, say with matrix (a, b)^{transpose}, then we would have e^\dag.e = (a^2 + b^2)/3 = 1. However, the equation a^2 + b^2 = 3 has no solution in the rational numbers. (In Z/9Z, any sum of two squares that is divisible by 3 is also divisible by 9; therefore the same holds in the integers. The claim about the rational numbers follows by taking a sufficiently large square common denominator). I do not know whether Robin Houston's construction, when applied to a dagger compact closed category, yields dagger-biproducts. Note that the previous counterexample is not dagger-compact closed (dagger does not preserve tensor). It therefore doesn't answer this last question. Best, -- Peter From rrosebru@mta.ca Sun Feb 18 10:33:40 2007 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 18 Feb 2007 10:33:40 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HImvQ-0003DH-Bg for categories-list@mta.ca; Sun, 18 Feb 2007 10:22:00 -0400 Date: Sat, 17 Feb 2007 17:39:16 +0000 From: "Jamie Vicary" To: categories@mta.ca Subject: categories: Re: Equalisers and coequalisers in categories with a \dag-involution 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: 28 > Could we make the following definition: a dagger-category has > 'finite bilimits' if any finite diagram D in the category has an > 'isometric cone', a cone for which all the associated morphisms to the > objects of D are isometries, along with some sort of condition that > the isometries are orthogonal in the correct way. It is interesting to > consider this in the case of products and equalisers: for products > AxB, so it seems, the isometries to A and B will generally be > _projectors_, but for equalisers E-e->A=f,g=>B, the isometry e will > generally be an _injector_! So we cannot ask for the cone morphisms to > be isometric projectors, or isometric injectors. But perhaps this is > OK, and we can just require them to be isometries. This definition of > bilimit has the 'local flavour' of the definition of biproducts, but > cooking up a generally-applicable orthogonality condition on the > isometries seems tricky. Fred Linton has pointed out to me that my terminology here is not standard. By "isometric injector", I mean a morphism which is unitary on its range, i.e., one-to-one and norm-preserving in the case of Hilbert spaces; I believe this is usually simply referred to as an isometry. By "isometric projector", I mean a morphism which is unitary on the complement of its kernel; some people prefer to call this a "partial isometry". I was then using the terms "isometric" and "isometry" to mean "isometric projector or isometric injector". Anyway, the simple prescription I give for a bilimit cannot work, as it is easy to find diagrams in the category of finite-dimensional Hilbert spaces, our canonical example of a strongly compact-closed category with biproducts, for which the colimit and limit are not isomorphic. A diagram f:A-->B for non-iso A and B is the simplest example. However, if we restrict to diagrams F:D-->FdHilb such that D admits a dagger-operation compatible with the dagger on FdHilb, then I believe the conjecture becomes plausible. Regards, Jamie Vicary. From rrosebru@mta.ca Tue Feb 20 10:21:57 2007 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 20 Feb 2007 10:21:57 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HJViE-0006Ln-Fu for categories-list@mta.ca; Tue, 20 Feb 2007 10:11:22 -0400 From: "Jonathon Funk" To: Subject: categories: job opening Date: Mon, 19 Feb 2007 09:14:50 -0400 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: O X-Status: X-Keywords: X-UID: 29 Job opening at Cave Hill, Barbados. Please see http://www.jobs.ac.uk/jobfiles/TL649.html Note the phrases ``Outstanding candidates in any area of Mathematics will be considered.'' and ``....able to teach a wide range of both introductory and upper level undergraduate courses in Mathematics, especially including Optimization Theory and Numerical Analysis.'' Try to emphasize this aspect if you can, because the successful applicant will teach optimization and numerical analysis. Jonathon Funk From rrosebru@mta.ca Tue Feb 20 10:21:58 2007 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 20 Feb 2007 10:21:58 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HJVig-0006OB-TC for categories-list@mta.ca; Tue, 20 Feb 2007 10:11:51 -0400 Subject: categories: New Journal: Algebra and Number Theory From: Tom Leinster To: categories@mta.ca Content-Type: text/plain Date: Mon, 19 Feb 2007 17:13:42 +0000 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: 30 Algebraically-inclined readers may be interested in the following new journal, which embodies all the virtues discussed in the recent thread on publishing as well as boasting an impeccably eminent editorial board. -------- Forwarded Message -------- From: David Eisenbud Subject: [Eager-gen] New Journal: Algebra and Number Theory Date: Sat, 17 Feb 2007 17:54:02 -0800 Dear number theorists, algebraists, and algebraic geometers, We are thrilled to announce the launch of a new journal: Algebra & Number Theory http://jant.org The purpose of the journal is to provide an alternative to the current range of commercial specialty journals in these fields - an alternative of higher quality and much lower cost. The policies of Algebra & Number Theory are set by the editorial board, a group of working mathematicians, rather than by a profit-oriented company, so they will remain friendly to mathematicians' interests. In particular, they will promote broad dissemination, easy electronic access, and permissive use of content to the greatest extent compatible with survival of the journal. The journal is published by Mathematical Sciences Publishers, using the efficient model that has proved successful for its other journals, such as Geometry & Topology. Please encourage your library to subscribe! And submit your high-quality original articles to us! For more information, see http://jant.org Best, -- David Eisenbud, chair of the editorial board Bjorn Poonen, managing editor on behalf of the editorial board: Georgia Benkart, Dave Benson, Richard E. Borcherds, John H. Coates, Jean-Louis Colliot-Th\'el\`ene, Brian D. Conrad, H\'el\`ene Esnault, Hubert Flenner, Andrew Granville, Joseph Gubeladze, Ehud Hrushovski, Craig Huneke, Mikhail Kapranov, Yujiro Kawamata, J\'anos Koll\'ar, Hendrik W. Lenstra, Yuri Manin, Barry Mazur, Susan Montgomery, Shigefumi Mori, Andrei Okounkov, Raman Parimala, Victor Reiner, Karl Rubin, Peter Sarnak, Michael Singer, Ronald Solomon, Vasudevan Srinivas, J. Tobias Stafford, Richard Stanley, Bernd Sturmfels, Richard Taylor, Ravi Vakil, Michel van den Bergh, Marie-France Vign \'eras, Kei-Ichi Watanabe, Andrei Zelevinsky, and Efim Zelmanov --- David Eisenbud Director, MSRI www.msri.org tel: 510-642-0143 fax: 510-642-8609 _______________________________________________ Eager-gen mailing list Eager-gen@euclid.mathematik.uni-kl.de http://www-euclid.mathematik.uni-kl.de/mailman/listinfo/eager-gen -- Tom Leinster From rrosebru@mta.ca Fri Feb 23 00:17:03 2007 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 23 Feb 2007 00:17:03 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HKRh1-0003rb-3W for categories-list@mta.ca; Fri, 23 Feb 2007 00:05:59 -0400 Date: Thu, 22 Feb 2007 12:56:43 +0000 From: Robin Houston To: categories@mta.ca Subject: categories: A dagger compact closed category with biproducts, but without dagger biproducts (was: categories: Re: Equalisers and coequalisers in categories with a \dag-involution) Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Disposition: inline Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: RO X-Status: X-Keywords: X-UID: 31 On Fri, Feb 16, 2007 at 05:08:06PM -0400, Peter Selinger wrote: > I do not know whether Robin Houston's construction, when applied to a > dagger compact closed category, yields dagger-biproducts. The answer is no (unless I have overlooked something below, which is all too easy to do when cooking up pathological counterexamples). We're looking for a category that: - has a dagger compact-closed structure, - has biproducts - does *not* have dagger-biproducts. I've tried to keep the description quite concrete, perhaps too much so for the taste of some readers of this list. 1. Let A be the category with: - the set of objects is the set of integers; - an arrow is a rational number: A(n,n) = Q, and A(m,n) = {0}, for m != n; - composition is multiplication; - the following compact closed structure: [ The symbol @ denotes tensor below] m @ n := m + n for objects m, n q @ r := q x r for arrows q, r, The tensor unit is the object 0, n* := -n; - the obvious preadditive structure: addition within a hom set is just addition of rational numbers; - the trivial dagger: q^\dagger := q for each arrow q. Note that A is a (preadditive) dagger compact closed category. 2. Let B be the category of matrices over A, i.e. the result of freely adding finite biproducts to A. Concretely, an object of B is a finite tuple of integers (n_i | i (n_j | j (n_j | j A* @ A. Define eta'_A to be the product of eta_A with the scalar 2 ^ -max(A). By the restriction of (3), we know that max (A* @ A) = 2 max(A), hence (eta'_A)^\dagger = (2 ^ max(A)) x epsilon_A where epsilon_A is the standard counit. Thus the additional scalar factor in (eta'_A)^\dagger is the reciprocal of that in eta'_A, so they cancel out as required. Finally, to see that C does not have dagger biproducts, consider the objects (0) and (-1,1). The injection i: (0) --> (0,-1,1) is a matrix [ q ] for some rational q. Then i^\dagger = [ 2q 0 0 ], [ 0 ] [ 0 ] so i^\dagger . i : (0) -> (0) is the 1x1 matrix [ 2q^2 ]. For this to be the identity, we would need to have 2q^2 = 1, but that equation famously has no solution in the rationals! Can anyone see any errors in the above, or think of a simpler example? Robin From rrosebru@mta.ca Fri Feb 23 00:17:03 2007 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 23 Feb 2007 00:17:03 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HKRhj-0003vr-W9 for categories-list@mta.ca; Fri, 23 Feb 2007 00:06:44 -0400 Date: Thu, 22 Feb 2007 20:56:38 +0000 To: categories@mta.ca From: Category Theory 2007 Subject: categories: CT2007: Important dates 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: 32 ==================== CT2007 ==================== International Category Theory Conference Hotel Tivoli Almansor Carvoeiro, Portugal June 17-23, 2007 Deadlines: Accommodation: March 1, 2007 Registration: March 1, 2007 Abstract submission: May 1, 2007 For more information, please consult the web site http://www.mat.uc.pt/~categ/ct2007 The Organizing Committee. From rrosebru@mta.ca Mon Feb 26 09:33:05 2007 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 26 Feb 2007 09:33:05 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HLfpB-0005Xc-2F for categories-list@mta.ca; Mon, 26 Feb 2007 09:23:29 -0400 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: Marco Grandis Subject: categories: terminology: dagger and involution Date: Mon, 26 Feb 2007 09:23:20 +0100 To: Peter Selinger Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 33 Dear Peter, what you are calling a "dagger-category", i.e. a category equipped with a contravariant involutive endofunctor, which is the identity on objects, has been called "a category with involution", at least from Burgin 1969 to Lambek 2001. "Involutive category" has also been used, if less. (The main object of these papers, or most of them, is: categories of relations.) I think it would be better to come back to the old term, which is meaningful, translatable, and old. With best regards Marco From rrosebru@mta.ca Mon Feb 26 19:57:13 2007 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 26 Feb 2007 19:57:13 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HLpdQ-0002Pu-OH for categories-list@mta.ca; Mon, 26 Feb 2007 19:52:01 -0400 From: "Imogen Kelly" To: categories@mta.ca Subject: categories: Thanks from Imogen Date: Mon, 26 Feb 2007 21:14:36 +1100 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: RO X-Status: X-Keywords: X-UID: 34 My family and I sincerely thank all the members of the Category Theory community who, when Max died, sent messages of condolence to us through Ross. It has been a great comfort to us that so many mathematicians have commented on the contribution Max made to your area of mathematics. Many of you, too, made mention of the help and friendship he freely offered. Warm regards to you all, Imogen From rrosebru@mta.ca Tue Feb 27 21:54:14 2007 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 27 Feb 2007 21:54:14 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HMDsV-0001zm-Cu for categories-list@mta.ca; Tue, 27 Feb 2007 21:45:11 -0400 Date: Mon, 26 Feb 2007 17:22:37 +0100 To: categories@mta.ca From: Anders Kock Subject: categories: preprints available 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 Dear all, This is to announce the availability of two preprints. 1) "Group valued differential forms revisited" We study the relationship between combinatorial group valued differential forms and classical differential forms with values in the corresponding Lie algebra. In particular, we compare simplicial coboundary and exterior derivative. The results represent strengthening of results I obtained in 1982. This preprint can be downloaded from http://www.imf.au.dk/publs?id=636 or from my home page http://home.imf.au.dk/kock/ 2) "Some matrices with nilpotent entries, and their determinants" We study algebraic properties of matrices whose rows are mutual neighbours, and are also neigbours of 0 (neighbour in the sense of a certain nilpotency condition). The intended application is in synthetic differential geometry. For a square matrix of this kind, the product of the diagonal entries equals the determinant, modulo a factor n! This preprint can be downloaded from http://arxiv.org/abs/math.RA/0612435 or from my home page (address as above). Yours Anders From rrosebru@mta.ca Tue Feb 27 21:54:14 2007 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 27 Feb 2007 21:54:14 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HMDrk-0001vq-Ll for categories-list@mta.ca; Tue, 27 Feb 2007 21:44:24 -0400 Date: Mon, 26 Feb 2007 08:22:21 -0800 From: John Baez To: categories Subject: categories: terminology: dagger and involution 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: 36 Marco wrote: >what you are calling a "dagger-category", i.e. > > a category equipped with a contravariant involutive > endofunctor, which is the identity on objects, > >has been called "a category with involution", at least from Burgin >1969 to Lambek 2001. "Involutive category" has also been used, if >less. > >I think it would be better to come back to the old term, which is >meaningful, translatable, and old. There's also a body of work, mainly from mathematical physics, that calls these categories "star-categories". But, by now there's enough literature using the term "dagger-categories" that the genie is out of the bottle. Best, jb From rrosebru@mta.ca Wed Feb 28 18:56:14 2007 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 28 Feb 2007 18:56:14 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HMXbq-0005FL-9u for categories-list@mta.ca; Wed, 28 Feb 2007 18:49:18 -0400 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: Marco Grandis Subject: categories: Re: terminology: dagger and involution Date: Wed, 28 Feb 2007 09:19:58 +0100 To: categories@mta.ca Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 37 Dear John, Sooner or later somebody will call them "sharp" categories, or "tilde" categories... What you are saying is a good argument in favour of a sensible, well established name. Also, on a more general ground, should we have a different terminology in, say: - category theory, - category theory applied to computer science, - category theory applied to physics? Funny names, like quark, can be good and typographical names can be useful, when there is no better substitute. Eg, I do not know of any good substitute for "comma category". But I see no reason to replace a sensible name with a meaningless one; or, even worse, many meaningless ones. --------- Dear Jeff, The problem you are mentioning is essentially based on terminology for different dualities in higher categories. I do not think there is a way of finding a coherent terminology for them, which would not clash with some well established, quite sensible use, already existing in some particular case. Therefore, I would not be surprised if the contravariancy of an involution should assume different meanings in different contexts. --------- All the best Marco From rrosebru@mta.ca Wed Feb 28 18:56:14 2007 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 28 Feb 2007 18:56:14 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HMXej-0005XG-69 for categories-list@mta.ca; Wed, 28 Feb 2007 18:52:17 -0400 Date: Wed, 28 Feb 2007 19:52:53 +0300 From: Maxim Vsemirnov To: categories@mta.ca Subject: categories: Yuri Matiyasevich - 60! Call for papers. Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 38 Sorry for possible cross-posting Dear Academic Community, In March 2007 Yuri Matiyasevich will be 60. In addition to his outstanding scientific achievements, Yuri Matiyasevich was the editor of several issues of the journal "Zapiski Nauchnykh Seminarov POMI" ("Notes of Mathematical Seminars of St.Petersburg Department of V.A.Steklov Institute of Mathematics"). He remains an active author of our journal until now. We decided to devote the next issue of the journal to Yuri Matiyasevich. Please find the call for papers below. We will be grateful if you distribute this call for papers among your colleagues. The deadline is set to May 10, 2007. ****** If you are unable to meet the deadline ****** but strongly wish to contribute, please communicate a more appropriate date and an abstract to any of the editors at the addresses listed below. We have a tight schedule for the publication process (see below). Faithfully yours, Anatol Slissenko and Maxim Vsemirnov %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% CALL FOR PAPERS Notes of Mathematical Seminars of St.Petersburg Department of V.A.Steklov Institute of Mathematics http://www.pdmi.ras.ru/znsl/index.html Subseries: Studies in Constructive Mathematics and Mathematical Logic. Issue XI TOPICS. Papers (either describing an original research or surveying a topic) are solicited in all areas related to the interests of Yuri Matiyasevich. They include (but not limited to) all aspects of the mathematical logic, Diophantine equations and discrete mathematics. LANGUAGES. Submissions can be made either in English or in Russian. TRANSLATION AND PUBLICATION. The issue containing the original papers will appear in the printed form as well as on the Web. English translations (or original papers, for papers submitted in English) will later appear in Journal of Mathematical Sciences published by Springer. SUBMISSION and other contacts. Please send your Postscript or PDF file to either of the editors: Anatol Slissenko slissenko@univ-paris12.fr Maxim Vsemirnov vsemir@pdmi.ras.ru IMPORTANT DATES. Submission: by May 10, 2007. First referee reports: July-August 2007. Revised (final) version if needed: August-September 2007. Final decision: October 2007. Publication: November 2007. From rrosebru@mta.ca Wed Feb 28 18:56:14 2007 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 28 Feb 2007 18:56:14 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HMXdA-0005O4-0e for categories-list@mta.ca; Wed, 28 Feb 2007 18:50:40 -0400 Date: Wed, 28 Feb 2007 10:55:36 +0100 From: Jerome Scherer Subject: categories: SECA4 To: categories@mta.ca MIME-version: 1.0 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: 39 Second announcement SECA4, "SEminar on Category theory and Applications" Barcelona (CRM): June 6 - 9, 2007. This is the fourth of a series of meetings devoted to category theory and applications. It is intended as meeting point for specialists in category theory and related areas as homological algebra, representation theory, or homotopy theory. Plenary speakers: Denis-Charles Cisinski, Universit=E9 Paris 13 Jos=E9 L. Garc=EDa Hern=E1ndez, Universidad de Murcia Ken Goodearl, University of California at Santa Barbara Joachim Kock, Universitat Aut=F2noma de Barcelona Henning Krause, Universit=E4t Paderborn Tom Leinster, University of Glasgow Javier Majadas, Universidade de Santiago de Compostela Ieke Moerdijk, Universiteit Utrecht Antonio Viruel, Universidad de M=E1laga At the request of the organizing committee, the following have accepted to give survey talks, that are specially addressed to the young participants: Ronnie Brown, University of Wales Carles Casacuberta, Universitat de Barcelona Marco Grandis, Universit=E0 di Genova You will find more information on the following webpage http://mat.uab.es/~seca4/ Some financial support is available for young participants. The deadline to apply for it is March 27. The registration fee is 125 Eur= os, but there is a reduced registration fee of 100 Euros for those registrating before April 27. If you have specific questions, please send an email to: seca4@mat.uab.es Organizing committee: Pere Ara, Universitat Autonoma de Barcelona Carles Broto, Universitat Autonoma de Barcelona (coordinator) Jose Manuel Casas, Universidad de Vigo Luis Javier Hernandez, Universidad de La Rioja Manuel Ladra, Universidad de Santiago de Compostela Albert Ruiz, Universitat Autonoma de Barcelona Jerome Scherer, Universitat Autonoma de Barcelona Scientific committee: Ronnie Brown, University of Wales Carles Casacuberta, Universitat de Barcelona Jose Luis Gomez Pardo, Universidad de Santiago de Compostela Marco Grandis, Universita di Genova Lionel Schwartz, Universite Paris 13