January 2009 - Categories - categories.org.au

Research positions
by Maria Manuel Clementino 26 Feb '14

26 Feb '14

5-YEAR RESEARCH POSITIONS The Centre for Mathematics of the University of Coimbra (CMUC) invites applications for five 5-year research positions in all areas of Mathematics. Applicants should have a PhD in Mathematics and at least three years of post-doctoral experience, with an international-level publication record and demonstrated ability to perform independent research. Preference will be given to candidates working in one of the areas in which the members of CMUC are currently active. A very good command of English is required. The appointments will be made for three years, renewable for two more. Successful applicants are expected to develop research within the areas of interest of CMUC. They should also contribute to graduate studies, supervising students from the Department of Mathematics. The basic salary is equivalent to the index 195 of the Portuguese research career (in the order of 42 500 euros a year), in accordance with the Ciência 2008 guidelines http://alfa.fct.mctes.pt/apoios/contratacaodoutorados/edital2008 Benefits include private health insurance and social security. Applicants should send • cover sheet (available from www.mat.uc.pt/cmuc/coversheet.pdf) including names and contact information of three persons who can provide a letter of recommendation • curriculum vitae (publication list included) • a 5-year research proposal (2 pages max), emphasizing their own research goals as pdf files to cmuc(a)mat.uc.pt. The subject of the e-mail message must include the job reference C2008 FCTUC CMUC v15-v19. The deadline for applications is *September 10, 2008.* ------------------------------ More information can be found at www.mat.uc.pt

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Foundations?
by F W Lawvere 03 Sep '10

03 Sep '10

Down with "Foundations"! Up with algebra! Dear Friends, Presumably I am among those who are being "vilified" as "lovers of categories as foundation". By avoiding any precise definition, such a formulation might appeal to the widespread justified boredom induced by the past hundred years of "foundations as justification". Whenever I used the word "foundation" in my writings over the past forty years, I have explicitly rejected that reactionary use of the term and instead used the definition implicit in the work of my teachers Truesdell and Eilenberg. Namely, an important component of mathematical practice is the careful study of historical and contemporary analysis, geometry, etc. to extract the essential recurring concepts and constructions; making those concepts and constructions (such as homomorphism, functional, adjoint functor, etc.) explicit provides powerful guidance for further unified development of all mathematical subjects, old and new. What is the primary tool for such summing up of the essence of ongoing mathematics? Algebra! Nodal points in the progress of this kind of research occur when, as is the case with the finite number of axioms for the metacategory of categories, all that we know so far can be expressed in a single sort of algebra. I am proud to have participated with Eilenberg, Mac Lane, Freyd, and many others, in bringing about the contemporary awareness of Algebra as Category Theory Had it not been for the century of excessive attention given to the alleged possibility that mathematics is inconsistent, with the accompanying degradation of the F-word, we would still be using it in the sense known to the general public: the search for what is "basic". We, who supposedly know the explicit algebra of homomorphisms, functionals, etc. are long remiss in our duty to find ways to utilize those concepts also in guiding high school calculus. Best wishes, Bill Bibliography: - The Category of Categories as a Foundation for Mathematics, La Jolla conference 1965, Springer (1966) - Adjointness in Foundations, Dialectica, (1969), to be reprinted in TAC - Foundations and Applications: Axiomatization and Education, Bulletin of Symbolic Logic, (2003) vol 9, pp 213-224 - Sets for Mathematics, w/ Bob Rosebrugh, Cambridge Univ. Press, (2003) ************************************************************ F. William Lawvere Mathematics Department, State University of New York 244 Mathematics Building, Buffalo, N.Y. 14260-2900 USA Tel. 716-645-6284 HOMEPAGE: http://www.acsu.buffalo.edu/~wlawvere ************************************************************

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"Kantor dust"
by Galchin, Vasili 13 Feb '09

13 Feb '09

[Note from moderator: this may have been sent incorrectly earlier, apologies if you have received it twice.] Dear Category group, Here is a definition of Cantor dust .... http://en.wikipedia.org/wiki/Cantor_set. My question is from a constructivist viewpoint does this set really exist and if so, why? Very kind regards, Vasili

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It it a good idea to use the term 2-group outside of its use in group thoery?
by Ronnie Brown 01 Feb '09

01 Feb '09

I would like to raise an objection to using the term `2-group' as on nlab and elsehere since for the group theorists this has a specialised meaning: See the following wiki entry, especially the first 2 words: "In mathematics, given a prime number p, a p-group is a periodic group in which each element has a power of p as its order. That is, for each element g of the group, there exists a nonnegative integer n such that g to the power pn is equal to the identity element. Such groups are also called primary." I feel we should try to avoid and even to reduce confusion, especially as there are claims that crossed modules, for example, can be thought of as `2-dimensional groups' (I agree with this, of course!); there are nice crossed modules M \to P in which M and P are 2-groups in the group theoretic sense! My favourite example is \mu: Z_2 \times Z_2 \to Z_4 in which Z_4 acts by the twist (of order 2), and \mu maps each factor Z_2 injectively into Z_4. This crossed module has non trivial k-invariant. I think Johannes Huebschmann first observed this. So an example oriented approach to crossed modules could well need the term p-group in its standard group theoretic usage. Some examples of finite crossed modules are in R. Brown and C.D. Wensley, `Computation and homotopical applications of induced crossed modules', J. Symbolic Computation 35 (2003) 59-72. However I think one can be happy with the well established term 2-groupoid. I would just like this point to be discussed: terminology is important, and confusing an established use might raise hackles unnecessarily. Ronnie

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initial algebra question
by Paul Levy 31 Jan '09

31 Jan '09

Does anybody know a reference for the following (very easy) result? Let C and D be categories, and let F:C-->D and G:D-->C be functors. If (c,theta) is an initial algebra for GF, then (Fc, F theta) is an initial algebra for FG. thanks, Paul

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FMCS 2009
by John MacDonald 31 Jan '09

31 Jan '09

FMCS 2009 17th Workshop on Foundational Methods in Computer Science University of British Columbia, VANCOUVER, Canada MAY 28th - 31st, 2009 FIRST ANNOUNCEMENT * * * The Department of Mathematics at the University of British Columbia in cooperation with the Pacific Institute of Mathematical Sciences is hosting the Foundational Methods in Computer Science workshop on May 28th - 31st, 2009, on the University of British Columbia Campus in Vancouver, Canada The workshop is an annual informal meeting intended to bring together researchers in mathematics and computer science. There is a focus on the application of category theory in computer science. However, all those who are interested in category theory or computer science are welcome to attend. There will be a welcoming reception on the evening of Thursday May 28. The scientific program starts on May 29, and consists of a day of tutorials aimed at students and newcomers to category theory, as well as a day and a half of research talks. The meeting ends at mid-day on May 31. Research talks There will be some invited presentations, but the majority of the talks are solicited from the participants. If you wish to give a talk please send a title and abstract to johnm(a)math.ubc.ca. Time slots are limited, so please respond early if you would like to be considered for a talk. Graduate student participation is particularly encouraged at FMCS. Accommodations A block of rooms has been reserved for participants at Gage Towers on the UBC campus. Registration If you would like to come to the meeting or will come to the meeting please send a brief email to johnm(a)math.ubc.ca with the words "would like to attend" or "may attend" or "will attend". This is just so the local organizer and organizing committee wiil have a first estimate of how many people may show up. The Second Announcement will be out soon with links to the conference webpage, registration and accommodation. Previous meetings Previous FMCS meetings were held in Pullman (1992), Portland (1993), Vancouver (1994), Kananaskis (1995), Pullman (1996), Portland (1998), Kananaskis (1999), Vancouver (2000), Spokane (2001), Hamilton (2002), Ottawa (2003), Kananaskis (2004), Vancouver (2005), Kananaskis (2006), Hamilton (2007), and Halifax (2008). Organizing committee: Robin Cockett (Calgary) John MacDonald (UBC) Phil Mulry (Colgate) Peter Selinger (Dalhousie) Local Organizers: John MacDonald (UBC)

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Symmetric monoidal closed natural transformation?
by Mike Stay 31 Jan '09

31 Jan '09

A symmetric monoidal functor F:C->D is closed if the morphism c_D(Phi_{x -o y, x}^{-1} o F(c_C^{-1}(1_{x -o y}))):F(x -o y) -> F(x) -o F(y) is an isomorphism, where x,y in C, Phi_{x,y}:F(x) tensor F(y) -> F(x tensor y) and c_C and c_D are currying in C, D. Could someone give me the definition of a symmetric monoidal closed natural transformation? I thought it would be a simple commuting diagram like the one involving Phi, but one of the arrows goes the wrong way. -- Mike Stay - metaweta(a)gmail.com http://math.ucr.edu/~mike http://reperiendi.wordpress.com

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Second CfP: "Structures and Deduction", Bordeaux, July 20-24, 2009
by Lutz Strassburger 30 Jan '09

30 Jan '09

******************************************************************* SECOND CALL FOR PAPERS International Workshop "Structures and Deduction" (SD09) <http://www.lix.polytechnique.fr/~lutz/orgs/SD09.html> July 20 - 24, 2009 organized as part of the European Summer School on Logic, Language and Information ESSLLI 2009 <http://esslli2009.labri.fr/> July 20 - 31, 2009 in Bordeaux ******************************************************************* ORGANIZERS: Michel Parigot (CNRS, Univ. Paris 7, France) Lutz Strassburger (INRIA Saclay-IdF, France) DESCRIPTION OF THE WORKSHOP: The topic of this workshop is the application of algebraic, geometric, and combinatorial methods in proof theory. In recent years many researchers have proposed approaches to understand and reduce "syntactic bureaucracy" in the presentation of proofs. Examples are proof nets, atomic flows, new deductive systems based on deep inference, and new algebraic semantics for proofs. These efforts have also led to new methods of proof normalisation and new results in proof complexity. The workshop is relevant to a wide range of people. The list of topics includes among others: algebraic semantics of proofs, game semantics, proof nets, deep inference, tableaux systems, category theory, deduction modulo, cut elimination, complexity theory, etc. The goal of the workshop is twofold: first, to bring together researchers from various fields who share the interest of understanding and dealing with structural properties of proofs and second, to provide an opportunity for PhD students and researchers to present and discuss their work with colleagues who work in the broad subject areas that are represented at ESSLLI. The workshop is intended to be a sequel of the ICALP-workshop SD05 in Lisbon 2005 <http://www.cs.bath.ac.uk/ag/w/sd05>. SUBMISSION DETAILS: Contributions can be regular papers, but also work in progress, programmatic/position papers or tutorials. Submissions should be formatted with the LNCS LaTeX style, take between two and fifteen pages and allow the committee to assess their merits with reasonable effort. The length limit can be relaxed for the versions that will be presented at the workshop, depending on the total bulk of the accepted contributions. Please use the SD'09 submission page <http://www.easychair.org/conferences/?conf=sd09> handled by the EasyChair conference system, to submit papers. The accepted papers will appear in the workshop proceedings published by ESSLLI. One author of each accepted paper must attend the workshop in order to present the paper. WORKSHOP FORMAT: The workshop is part of ESSLLI and is open to all ESSLLI participants. It will consist of five 90-minute sessions held over five consecutive days in the first week of ESSLLI. There will be 2 or 3 slots for paper presentation and discussion per session. On the first day the workshop organizers will give an introduction to the topic. INVITED SPEAKER: François Lamarche (LORIA, Nancy) PROGRAM COMMITTEE: Lev Beklemishev (Moscow) Stefano Berardi (Torino) Agata Ciabattoni (Vienna) Alessio Guglielmi (Bath/Nancy) Martin Hyland (Cambridge) Grigori Mints (Stanford) Michel Parigot (Paris) Lutz Strassburger (Palaiseau) Kazushige Terui (Kyoto) IMPORTANT DATES: Deadline for submissions: February 15, 2009 Notification of acceptance: April 15, 2009 Deadline for final versions: May 11, 2009 Workshop dates: July 20 - 24, 2009 LOCAL ARRANGEMENTS: All workshop participants including the presenters will be required to register for ESSLLI. The registration fee for authors presenting a paper will correspond to the early student/workshop speaker registration fee. Moreover, a number of additional fee waiver grants will be made available by the ESSLLI local organizing committee on a competitive basis and workshop participants are eligible to apply for those. There will be no reimbursement for travel costs and accommodation. Workshop speakers who have difficulty in finding funding should contact the local organizing committee to ask for the possibilities for a grant. FURTHER INFORMATION: About the workshop: <http://www.lix.polytechnique.fr/~lutz/orgs/SD09.html> About ESSLLI: <http://esslli2009.labri.fr/>

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New York City Category Seminar
by Noson 30 Jan '09

30 Jan '09

We would like to announce the formation of a Category Theory Seminar to be held at the Graduate Center of the City University of New York. We anticipate talks in applied and pure category theory. We also encourage students to make presentations on their work. New York City is central enough that someone prominent is always passing through. When: Commencing Spring 2009, weekly, Monday evenings 6:00 - 7:00 PM. Where: Room 4421 The Graduate Center, The City University of New York, 365 Fifth Avenue (at 34th street. Diagonally across from the Empire State Building) New York, NY 10016-4309 Web: <http://www.sci.brooklyn.cuny.edu/~noson/CTseminar.html> http://www.sci.brooklyn.cuny.edu/~noson/CTseminar.html Please forward this e-mail on to anyone who might be interested. If you are interested in receiving announcements about the seminar, or know someone who would be or are interested in giving a talk, please drop me a line. All the best, Noson Yanofsky

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[Calco'09] cfp: deadline is approaching
by calco09 28 Jan '09

28 Jan '09

***---------- Deadline is approaching -------- *** *------------------------------------------------------------------* * Call for Papers * * * * CALCO 2009 * * * * 3rd Conference on Algebra and Coalgebra in Computer Science * * CALCO Tools Day * * CALCO-jnr * * * September 6-10 2009, Udine, Italy * * * *------------------------------------------------------------------* * Abstract submission: February 2, 2009 * * Technical paper submission: February 7, 2009 * * Tools Day submission: February 24, 2009 * * Author notification: April 22, 2009 * *------------------------------------------------------------------* * http://www.dimi.uniud.it/calco09/ * *------------------------------------------------------------------* CALCO brings together researchers and practitioners to exchange new results about both traditional and emerging uses of algebras and =20 coalgebras in computer science. This is a high-level, bi-annual conference formed by joining the forces and reputations of CMCS (the International Workshop on Coalgebraic =20 Methods in Computer Science), and WADT (the Workshop on Algebraic Development Techniques). The first and second CALCO conferences took place 2005 in Swansea, Wales (http://www.cs.swan.ac.uk/calco/index.php) and 2007 in Bergen, Norway (http://www.ii.uib.no/calco07/) The second event will take place September 2009 in Udine, Italy. CALCO 2009 will be preceded by two events on September 6, 2009. * CALCO-jnr - a CALCO Young Researchers Workshop dedicated to presentations by PhD students and by those who completed their doctoral studies within the past few years. * CALCO Tools Day - providing the opportunity to give system demonstrations. See below for more information. There are separate submission procedures for the CALCO main conference, CALCO-jnr and CALCO Tools Day, respectively. Invited Speakers ------------------ Mai Gehrke (Nijmegen, NL) Conor McBride (Strathclyde, UK) Prakash Panangaden (McGill, Canada) Gordon Plotkin (Edinburgh, UK) Topics of Interest ------------------ We invite submissions of technical papers that report results of theoretical work on the mathematics of algebras and coalgebras, the way these results can support methods and techniques for software development, as well as experience with the transfer of resulting technologies into industrial practice. We encourage submissions in topics included or related to those in the lists below. * Abstract models and logics - Automata and languages, - Categorical semantics, - Modal logics, - Relational systems, - Graph transformation, - Term rewriting, - Adhesive categories * Specialised models and calculi - Hybrid, probabilistic, and timed systems, - Calculi and models of concurrent, distributed, mobile, and context-aware computing, - General systems theory and computational models (chemical, biological, etc) * Algebraic and coalgebraic semantics - Abstract data types, - Inductive and coinductive methods, - Re-engineering techniques (program transformation), - Semantics of conceptual modelling methods and techniques, - Semantics of programming languages * System specification and verification - Algebraic and coalgebraic specification, - Formal testing and quality assurance, - Validation and verification, - Generative programming and model-driven development, - Models, correctness and (re)configuration of hardware/middleware/architectures, - Process algebra Submission Guidelines --------------------- Prospective authors are invited to submit full papers in English presenting original research. Submitted papers must be unpublished and not submitted for publication elsewhere. Experience papers are welcome, but they must clearly present general lessons learned that would be of interest and benefit to a broad audience of both researchers and practitioners. As in 2005 and 2007, it is planned to =20 publish the proceedings in the Springer LNCS series. Final papers will be no more than 15 pages long in the format specified by Springer. It is recommended that submissions adhere to that format and length (see http://www.springer.de/comp/lncs/authors.html) Submissions that are clearly too long may be rejected immediately. Proofs omitted due to space limitations may be included in a clearly marked appendix. Both an abstract and the full paper must be submitted by their =20 respective submission deadlines. A special issue of the new high-quality open access journal Logical Methods in Computer Science (http://www.lmcs-online.org) consisting of extended versions of selected papers will be produced after the =20 conference if there are enough good papers that can be extended and revised to the standards of this journal. Important Dates (all in 2009) ----------------------------- February 2 Abstract submission due February 7 Technical paper submission due February 24 Submissions to CALCO Tools Day, see below April 22 Author notification May 22 Camera ready due ----------------------------- September 6 CALCO-jnr and CALCO Tools Day September 6-10 CALCO technical programme Programme Committee ------------------- Luca Aceto, Reykjavik University, IS Stephen Bloom, Stevens Institute of Technology, Hoboken, USA Marcello Bonsangue, Leiden University, NL Corina Cirstea, University of Southampton, UK Andrea Corradini, University of Pisa, I Jos=E9 Fiaderio, University of Leicester, UK Rolf Hennicker, University of Munich, D Furio Honsell, University of Udine, I Bart Jacobs, University of Nijmegen, NL Bartek Klin, University of Warsaw, PL Alexander Kurz, University of Leicester, UK (co-chair) Stefan Milius, University of Braunschweig, D Ugo Montanari, University of Pisa, I Larry Moss, Indiana University, Bloomington, USA Till Mossakowski, DFKI Lab Bremen and University of Bremen, D Dirk Pattinson, Imperial College London, UK Dusko Pavlovic, Kestrel Institute, USA Jean-Eric Pin, CNRS-LIAFA Paris, F John Power, University of Bath, UK Grigore Rosu, University of Illinois, Urbana, USA Jan Rutten, CWI and Free University, Amsterdam, NL Davide Sangiorgi, University of Bologna, I Lutz Schr=F6der, DFKI Lab Bremen and University of Bremen, D Eugene Stark, State University of New York, USA Andrzej Tarlecki, Warsaw University, PL (co-chair) Yde Venema, University of Amsterdam, NL James Worrell, University of Oxford, UK Steering Committee ------------------ Jiri Adamek, Michel Bidoit, Corina Cirstea, Jose Fiadeiro (co-chair, http://www.cs.le.ac.uk/people/jfiadeiro/) H.Peter Gumm, Magne Haveraaen, Bart Jacobs, Hans-Joerg Kreowski, Alexander Kurz, Marina Lenisa, Ugo Montanari, Larry Moss, Till Mossakowski, Peter Mosses, Fernando Orejas, Francesco Parisi-Presicce, John Power, Horst Reichel, Markus Roggenbach, Jan Rutten (co-chair, http://homepages.cwi.nl/=20 ~janr/), Andrzej Tarlecki Organising Committee -------------------- Fabio Alessi, Alberto Ciaffaglione, Pietro Di Gianantonio, Davide =20 Grohmann, Furio Honsell, Marina Lenisa (chair, http://www.dimi.uniud.it/~lenisa) Marino Miculan, Ivan Scagnetto, University of Udine, Italy Location ------------------------- The conference will be held in the city of Udine, the capital of the =20 historical region of Friuli, Italy. Located between the Adriatic sea and the =20 Alps, close to Venice, Austria and Slovenia, Udine is a city of Roman origins, funded =20= by Emperor Otto in 983. Rich of historical sites, Udine is also famous =20 for its outstanding wine and culinary traditions. CALCO Tools Day --------------- A special day at CALCO'09 is dedicated to tools based on algebraic and coalgebraic principles. These include systems/prototypes/tools developed specifically for design, checking, execution, and verification of (co)algebraic specifications, but also tools targeting different application domains but making core or interesting use of (co)algebraic techniques. Tool submissions should be no longer than 5 pages in the LNCS format; the accepted tool papers will be included in the final LNCS proceedings of the conference. The tools should be available on the web for download and evaluation. Each submission will be evaluated by at least three reviewers; one or more of the reviewers will be asked to download and run the tool. At least one of the authors of each tool paper must attend the conference to demo the tool. Submissions by e-mail to grosu(a)cs.uiuc.edu. Important Dates (all in 2009) February 24 Tools software and paper submissions due March 28 Author notification May 16 Camera ready due September 6 CALCO Tools Day Program Committee Luigi Liquori, INRIA, Sophia Antipolis, France http://www-sop.inria.fr/members/Luigi.Liquori/ Grigore Rosu, University of Illinois, Urbana, USA http://fsl.cs.uiuc.edu/index.php/Grigore_Rosu http://www.dimi.uniud.it/calco09/

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