July 2008 - Categories - categories.org.au

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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Paper on slice stability in Locale Theory
by Townsend, Christopher 09 Aug '08

09 Aug '08

I was sorry not to be at the Calais meeting the other week and had hoped to have the paper Aspects of slice stability in Locale Theory http://www.christophertownsend.org/Documents/SliceStability_v30.pdf ready for it. This paper proves that a particular axiomatic approach to locale theory is slice stable and then uses this slice stability to prove some known locale theory/topos theory results. All the results are known (aside from a conjecture on localic subgroupoids) so it is really an investigation into this particular axiomatisation rather than a presentation of new results. It gives what I think is a novel proof of the well known slice stability result: Loc/Y = Loc_Sh(Y). Feedback is welcome. For example, I have always attributed the result Loc/Y = Loc_Sh(Y) to Joyal and Tierney. Am I right? Regards, Christopher

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Searching for Grothendieck
by Michael Barr 31 Jul '08

31 Jul '08

I would like to call the attention of the categorical community to the very interesting post http://www.fermentmagazine.org/Quest88.html It reports the successful quest in 1988 of Roy Lisker to meet Grothendieck. I first met Roy nearly 55 years ago when we were in a HS math club. I lost track of him for several decades and then met him again in Peter Freyd's office at Penn, probably in 1990. Since then I have had desultory e-contact with him (plus running into him once in person). I read this then, but he has now posted it online. Eventually, I will put a copy on my own ftp site. Michael

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two preprints
by Pedro Resende 31 Jul '08

31 Jul '08

I have placed in the arXiv the following two preprints that correspond to a part of my CT08 talk: • Groupoid actions as quantale modules, 14 pp.; http://arxiv.org/abs/arXiv:0807.3859 . • Groupoid sheaves as Hilbert modules, 27 pp.; http://arxiv.org/abs/arXiv:0807.4848 . Best, Pedro

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Two Category
by PETER EASTHOPE 30 Jul '08

30 Jul '08

Folk, Subsequent to my first attempt at illustrating the Two Category, Fred Linton added, "Is it worth noting, in this jpeg, that the arithmetical max(1-A, B) for B^A coincides here with the Boolean {not}A or B for the classical B => A?" Another insight for me. Thanks. I've made a fresh sketch including a table of notations. http://carnot.yi.org/TwoCategory.jpg Apologies for the very poor graphical quality. I am working on an SVG version. Further criticisms and suggestions are welcome of course. Thanks, ... Peter E. -- http://members.shaw.ca/peasthope/ http://carnot.yi.org/ = http://carnot.pathology.ubc.ca/

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Job at Macquarie
by Ross Street 29 Jul '08

29 Jul '08

Please note the job advertised on the Macquarie University Human =20 Relations page: = <http://macquarieuniversity.nga.net.au/bin/fnt_jobs_list.cfm?mode=3Ddef> Note that the Desirable Criteria include applied or analysis =20 specialties. We hope there will be a more senior position advertised =20 in a year or two aimed more at category theorists. =3D=3DRoss =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D Ref. 21439 Lecturer in Mathematics - Start New Application The Department of Mathematics is seeking to appoint a Lecturer in =20 Mathematics who will contribute significantly to its research and =20 teaching activities. The successful applicant will carry out =20 independent research in an area closely related to the Department=92s =20= current research strengths in applied mathematics, analysis, category =20= theory and number theory. Areas of applied mathematics and/or =20 analysis are strongly preferred. The appointee will teach a wide =20 range of mathematics courses and supervise research projects in the =20 Department=92s undergraduate and postgraduate programs. The Department =20= seeks applicants with proven research skills, a commitment to =20 teaching and developing courses of the highest standard and a =20 willingness to work with colleagues on new initiatives in the Faculty =20= and University. Essential Selection Criteria: PhD (or submitted); established =20 research record or evidence of outstanding research potential in =20 applied mathematics, analysis, category theory or number theory =20 (provided by one or two significant publications, evidence of =20 contributions to key research outcomes either individually or as a =20 member of a group, together with an outline of a coherent plan for =20 future research); interest in developing research links within, and =20 outside, the University (particular plans to develop cross-=20 disciplinary links within the University, research links with =20 external institutions or industry research collaborations should be =20 indicated); interest and ability to teach undergraduate mathematics =20 across the full range of service and specialised courses (as =20 demonstrated by documented experience in tutoring, lecturing or =20 workshop presentation); well-developed interpersonal, written =20 communication skills. Desirable Selection Criteria: Research background in applied =20 mathematics or analysis particularly in one of the following areas: =20 (i) analytical-numeral techniques in wave diffraction and/or interest =20= in applications to acoustic or electromagnetic waves, (ii) =20 applications of non-linear dynamical systems especially in electronic =20= and physical systems, (iii) harmonic analysis and partial =20 differential equations involving the theory of singular integrals or =20 related topics; experience in industry-collaborative research or =20 experience of active participation in an extensive national/=20 international research collaboration; established international =20 recognition (as demonstrated by publications, research grants, =20 citations or invited conference presentations); substantial =20 university-level teaching experience in mathematics across the full =20 range of service and specialised courses. Enquiries: Applicants are strongly encouraged to contact Professor =20 Paul Smith on +61-2-9850-8944 or e-mail pdsmith(a)maths.mq.edu.au Package: Lecturer (Level B) from $81,682 pa including base salary =20 $69,022 pa to $81,847 pa, annual leave loading and 17% employer=92s =20 superannuation. The position is available on a full-time (continuing) basis. =20 Probationary conditions may apply. Selection criteria must be =20 addressed in the application. The appointment is currently governed =20 by the terms of the Macquarie University Enterprise Agreement 2006-2009. Please visit www.jobs.mq.edu.au to apply online. Please note that =20 only those applications submitted via the Macquarie University Online =20= Recruitment System will be accepted. Closing Date: 30 August 2008 Macquarie University is an Equal Opportunity Employer with a =20 commitment to diversity and social inclusion. We encourage =20 applications from Indigenous Australians; people with a disability; =20 those from culturally and linguistically diverse backgrounds; and =20 women (particularly for senior and non-traditional vacancies). Please note that only those applications submitted via the Macquarie =20 University Online Recruitment System will be accepted. =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D Emeritus Professor Ross Street FAA Mathematics Department, Macquarie University, NSW 2109, Australia Web: www.math.mq.edu.au/~street/ Email: street(a)math.mq.edu.au

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Call for participation: ICGT 2008
by Reiko Heckel 27 Jul '08

27 Jul '08

4th International Conference on Graph Transformation Leicester (United Kingdom), September 7 - 13, 2008 http://www.cs.le.ac.uk/events/icgt2008/ The 4th Intl. Conference on Graph Transformation (ICGT 2008) will be held in Leicester (United Kingdom) in the second week of September 2008, along with a free Tutorial Introduction to Graph Transformation, a Doctoral Symposium, and workshops on * Natural Computing and Graph Transformation * Graph Computation Models * Petri Nets and Graph Transformation * Graph Transformation Tool Contest Information on the Program (including abstracts), Registration and Accommodation on-site is available at http://www.cs.le.ac.uk/events/icgt2008. Reduced rates are available for students and members of EATCS, EASST, and IFIP WG 1.3. UK PhD students funded by the EPSRC can take advantage of extra subsidies. Please note the Early Registration Deadline of 24 August. -- Prof Dr Reiko Heckel Chair of Software Engineering Department of Computer Science University of Leicester Leicester LE1 7RH United Kingdom Tel +44 (0)116 252 3406 Fax +44 (0)116 252 3915 http://www.cs.le.ac.uk/people/rh122

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Review of Symbolic Logic (RSL)
by Patrick Blackburn 26 Jul '08

26 Jul '08

The Association of Symbolic Logic (ASL) has just launched a new journal, the Review of Symbolic Logic (RSL). It is published by Cambridge University Press. The first issue has just appeared and you can see the table of contents and download articles from the journal's CUP homepage at: http://journals.cambridge.org/action/displayIssue?jid=RSL&volumeId=1&issueI… RSL is devoted to philosophical and non-classical logics and their applications, history and philosophy of logic, and philosophy and methodology of mathematics. Submissions are welcome.

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Weak cubical categories
by Marco Grandis 26 Jul '08

26 Jul '08

The following preprint, exposed in my talk at CT2008, Calais, can be downloaded from my web page "The role of symmetries in cubical sets and cubical categories (On cubical categories, I)" (34 pages) http://www.dima.unige.it/~grandis/CCat.ps http://www.dima.unige.it/~grandis/CCat.pdf With best wishes Marco Grandis ______________ Abstract. Symmetric weak cubical categories were introduced in previous papers, as a basis for the study of cubical cospans in Algebraic Topology and higher cobordism. Such cubical structures are equipped with an action of the n-dimensional symmetric group on the n- dimensional component, which has been used to simplify the coherence conditions of the weak case. We give now a deeper study of the role of symmetries. The category of ordinary cubical sets has a Kan tensor product, which is non symmetric and biclosed, with left and right internal homs based on the right and left path functors. On the other hand, symmetric cubical sets have one path functor leading to one internal hom and a symmetric monoidal closed structure. Similar facts hold for cubical and symmetric cubical categories, and should play a relevant role in the sequel, the study of limits and adjunctions in these higher dimensional categories. Weak double categories, studied in four papers with R. Pare, are a cubical truncation of the present structures. While constructing examples of cubical categories, we also investigate a 'rewriting' procedure of reduction to canonical forms, which allows one to quotient a weak symmetric cubical category of cubical spans (resp. cospans), and obtain a strict symmetric cubical category of 'cubical relations' (resp. 'cubical profunctors'). ______________

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LATA 2009: call for papers
by carlos.martin＠urv.cat 24 Jul '08

24 Jul '08

Apologies for multiple posting! Please, forward the announcement to whoever may be interested in it. Thanks. ********************************************************************* Call for Papers 3rd INTERNATIONAL CONFERENCE ON LANGUAGE AND AUTOMATA THEORY AND APPLICATIONS (LATA 2009) Tarragona, Spain, April 2-8, 2009 http://grammars.grlmc.com/LATA2009/ ********************************************************************* AIMS: LATA is a yearly conference in theoretical computer science and its applications. As linked to the International PhD School in Formal Languages and Applications that was developed at the host institute in the period 2002-2006, LATA 2009 will reserve significant room for young scholars at the beginning of their career. It will aim at attracting contributions from both classical theory fields and application areas (bioinformatics, systems biology, language technology, artificial intelligence, etc.). SCOPE: Topics of either theoretical or applied interest include, but are not limited to: - algebraic language theory - algorithms on automata and words - automata and logic - automata for system analysis and programme verification - automata, concurrency and Petri nets - biomolecular nanotechnology - cellular automata - circuits and networks - combinatorics on words - computability - computational, descriptional, communication and parameterized complexity - data and image compression - decidability questions on words and languages - digital libraries - DNA and other models of bio-inspired computing - document engineering - extended automata - foundations of finite state technology - fuzzy and rough languages - grammars (Chomsky hierarchy, contextual, multidimensional, unification, categorial, etc.) - grammars and automata architectures - grammatical inference and algorithmic learning - graphs and graph transformation - language varieties and semigroups - language-based cryptography - language-theoretic foundations of natural language processing, artificial intelligence and artificial life - mathematical evolutionary genomics - parsing - patterns and codes - power series - quantum, chemical and optical computing - regulated rewriting - string and combinatorial issues in computational biology and bioinformatics - symbolic dynamics - symbolic neural networks - term rewriting - text algorithms - text retrieval, pattern matching and pattern recognition - transducers - trees, tree languages and tree machines - weighted machines STRUCTURE: LATA 2009 will consist of: - 3 invited talks (to be announced in the second call for papers) - 2 invited tutorials (to be announced in the second call for papers) - refereed contributions - open sessions for discussion in specific subfields or on professional issues (if requested by the participants) PROGRAMME COMMITTEE: Parosh Abdulla (Uppsala) Stefania Bandini (Milano) Stephen Bloom (Hoboken) John Brzozowski (Waterloo) Maxime Crochemore (London) Juergen Dassow (Magdeburg) Michael Domaratzki (Winnipeg) Henning Fernau (Trier) Rusins Freivalds (Riga) Vesa Halava (Turku) Juraj Hromkovic (Zurich) Lucian Ilie (London, Canada) Kazuo Iwama (Kyoto) Aravind Joshi (Philadelphia) Juhani Karhumaki (Turku) Jarkko Kari (Turku) Claude Kirchner (Bordeaux) Maciej Koutny (Newcastle) Kamala Krithivasan (Chennai) Martin Kutrib (Giessen) Andrzej Lingas (Lund) Aldo de Luca (Napoli) Rupak Majumdar (Los Angeles) Carlos Martin-Vide (Tarragona & Brussels, chair) Joachim Niehren (Villeneuve d'Ascq) Antonio Restivo (Palermo) Joerg Rothe (Duesseldorf) Wojciech Rytter (Warsaw) Philippe Schnoebelen (Cachan) Thomas Schwentick (Dortmund) Helmut Seidl (Muenchen) Alan Selman (Buffalo) Jeffrey Shallit (Waterloo) Frank Stephan (Singapore) ORGANIZING COMMITTEE: Madalina Barbaiani Gemma Bel-Enguix Cristina Bibire Adrian-Horia Dediu Szilard-Zsolt Fazekas Alexander Krassovitskiy Guangwu Liu Carlos Martin-Vide (chair) Robert Mercas Catalin-Ionut Tirnauca Bianca Truthe Sherzod Turaev Florentina-Lilica Voicu SUBMISSIONS: Authors are invited to submit papers presenting original and unpublished research. Papers should not exceed 12 single-spaced pages and should be formatted according to the standard format for Springer Verlag's LNCS series (see http://www.springer.com/computer/lncs/lncs+authors?SGWID=0-40209-0-0-0) Submissions have to be uploaded at: http://www.easychair.org/conferences/?conf=lata2009 PUBLICATION: A volume of proceedings published by Springer in the LNCS series will be available by the time of the conference. A refereed volume of extended versions of selected papers will be published after it as a special issue of a major journal. (This was Information and Computation for LATA 2007 and LATA 2008.) REGISTRATION: The period for registration will be open since September 1, 2008 to April 2, 2009. The registration form can be found at the website of the conference: http://grammars.grlmc.com/LATA2009/ Early registration fees: 450 euros Early registration fees (PhD students): 225 euros Registration fees: 540 euros Registration fees (PhD students): 270 euros At least one author per paper should register. Papers that do not have a registered author by December 31, 2008 will be excluded from the proceedings. Fees comprise free access to all sessions, one copy of the proceedings volume, and coffee breaks. For the participation in the full-day excursion and conference lunch on Sunday April 5, the amount of 70 euros is to be added to the fees above: accompanying persons are welcome at the same rate. PAYMENT: Early registration fees must be paid by bank transfer before December 31, 2008 to the conference account at Open Bank (Plaza Manuel Gomez Moreno 2, 28020 Madrid, Spain): IBAN: ES1300730100510403506598 - Swift code: OPENESMMXXX (account holder: LATA 2009 – Carlos Martin-Vide). (Non-early) registration fees can be paid either by bank transfer to the same account or in cash on site. Besides paying the registration fees, it is required to fill in the registration form at the website of the conference. A receipt for the payment will be provided on site. FUNDING: Up to 20 grants covering partial-board accommodation will be available for nonlocal PhD students. To apply, candidates must e-mail their CV together with a copy of the document proving their present status as a PhD student. IMPORTANT DATES: Paper submission: October 22, 2008 Notification of paper acceptance or rejection: December 10, 2008 Application for funding (PhD students): December 15, 2008 Notification of funding acceptance or rejection: December 19, 2008 Final version of the paper for the proceedings: December 24, 2008 Early registration: December 31, 2008 Starting of the conference: April 2, 2009 Submission to the journal special issue: June 22, 2009 FURTHER INFORMATION: carlos.martin(a)urv.cat ADDRESS: LATA 2009 Research Group on Mathematical Linguistics Rovira i Virgili University Plaza Imperial Tarraco, 1 43005 Tarragona, Spain Phone: +34-977-559543 Fax: +34-977-559597

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