May 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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Famous unsolved problems in ordinary category theory
by Hasse Riemann 11 Jun '09

11 Jun '09

Hi all categorists Here are other questions i think about and need your help with. 4> Are there any famous unsolved problems in category theory not related to higher dimensional category theory (but monoidal categories are ok as categories)? Best regards Rafael Borowiecki

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patenting colimits?
by Ronnie Brown 02 Jun '09

02 Jun '09

Larry Lambe passed on the following url to me for comment and I thought it would be of interest to others on the category theory list, with more expertise than I. I have not had time to study it, but on the face of it, it seems like patenting mathematics, and to be deplored intensely. Am I wrong? http://www.freepatentsonline.com/6964037.html Title: Method and apparatus for determining colimits of hereditary diagrams Document Type and Number: United States Patent 6964037 A computer-implemented method and system for determining colimits of hereditary diagrams. A user specifies a diagram of diagram and specifies performance of a colimit operation. Once the colimit is performed, the name of the colimit is added to the hereditary diagram. The described embodiment supports diagrams of diagrams, also called hierarchical diagrams. Ronnie http://www.freepatentsonline.com/6964037.html

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postdoc position in Paris
by Paul-Andre Mellies 31 May '09

31 May '09

====================================================== Postdoctoral position in PPS (CNRS & University Paris 7) Curry-Howard and Concurrency Theory ====================================================== A 12-month postdoctoral position is available within the Laboratory PPS (Preuves Programmes Systemes) located at University Paris 7 Denis Diderot: http://www.pps.jussieu.fr/ The position is supported by the research project Curry-Howard and Concurrency Theory (CHOCO) funded by the French national research agency ANR. http://choco.pps.jussieu.fr/ Important dates: - deadline for application: May 31st 2009 - notification: June 15th 2009 - suggested starting date: September 1st 2009 Application procedure. Full application should be sent before May 31st 2009 including a resume, a short research project (1 page) and two names of possible references. This should be preferably done by email or at the postal address below. For all correspondance use the contact addresses: postdoc-choco(a)pps.jussieu.fr Paul-Andre Mellies Laboratoire PPS Universite Paris 7 - Denis Diderot Case 7014 75205 Paris Cedex 13 FRANCE The net salary will be around 2000 euro/month before income tax. The starting date for the postdoctoral position is September 2009 although later dates may be also considered. Description The general purpose of the project CHOCO is to investigate the syntactic, semantic and algebraic aspects of proof theory in order to integrate concurrency theory in the Curry-Howard correspondence between proofs and programs. The interdisciplinary nature of the project between proof theory and concurrency theory means that candidates from various scientific horizons are welcome to apply. On the other hand, we will consider with special interest applications by candidates with background in one or several of the fields: - linear logic (proof nets, geometry of interaction) - semantics (game semantics, vectorial semantics) - concurrency theory (process calculi, presheaf semantics) - type theory (realizability, types for process calculi) - rewriting theory (lambda-calculus, diagrammatic rewriting) - category theory (categorical algebra, topos theory) The applicant should hold a PhD or be about to defend his/her PhD thesis by December 2009. The postdoc researcher will work within the laboratory PPS (Preuves, Programmes, Systemes) http://www.pps.jussieu.fr which is internationally recognized as one of the leading research laboratories in mathematics and computer science, with its distinctive proof-theoretic culture. The laboratory PPS is located in Chevaleret, the largest research community of mathematicians in France. The laboratory PPS is also part of the Fondation Sciences Mathematiques de Paris. http://www.sciencesmath-paris.fr Strong interaction of the postdoc researcher with the partner sites of the CHOCO project is also expected: - Laboratoire d'Informatique de Paris Nord. - Laboratoire d'Informatique du Parallelisme, Lyon, - Laboratoire de Mathematiques de l'Universite de Savoie, Chambery - Institut de Mathematiques de Luminy, Marseille, - Laboratoire d'Informatique Fondamentale de Marseille, Further information will possibly be made available from the web page of the project indicated above.

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Tutorial: Categories for the practicing physicist
by Bob Coecke 28 May '09

28 May '09

We have put a tutorial on symmetric monoidal categories on the arXiv: http://arxiv.org/abs/0905.3010 Categories for the practising physicist (104 pages) Bob Coecke and Eric Oliver Paquette It is directed to physicists who unlike mathematical physicists, do not have a strong background in pure maths. The target audience are researchers in quantum foundations and quantum infomation. The main goal is to show that monoidal categories are a natural starting point to craft theories of physics, and that they are closely related to something physicists are very used to, namely Dirac notation. Some effort is made to unpack the definition of a symmetric monoidal category which given its `size', is just too much to grasp at once. On the other hand, there is a very clear physical intuition to monoidal categories which can be easily grasped by physicists or any other operational scientist. This tutorial starts from this operational intuition and gradually converts it on mathematical substance. As a consequence, the attempt to convey a story is more prominent than mathematical rigor. In our interaction with quantum foundationalists and quantum informaticians we noticed a great need for a tutorial of this nature. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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ICE09: LAST CALL FOR PAPERS
by fibonchi＠di.unipi.it 27 May '09

27 May '09

2nd Interaction and Concurrency Experience (ICE'09) Structured Interactions Satellite workshop of CONCUR 2009 31st of August 2009 Bologna, Italy Homepage: http://ice09.dimi.uniud.it/ -- Invited Speakers -- - Farhad Arbab (CWI) - Doron Peled (Bar Ilan University) Interaction and Concurrency Experiences (ICEs) is intended as a series of international scientific meetings oriented to researchers in various fields of theoretical computer science. The timeliness and novelty of these events relies both on the variety of the topics that will be treated on each event and on the adopted paper selection mechanism. Every experience will focus on a different specific topic which affects several areas of computer science. A thorough scientific debate among PC and authors of submitted papers will parallel the reviewing process. After the paper selection phase, papers will be published on the web and the discussion will be extended to perspective participants. -- Scope of ICE'09 -- The general scope is to include theoretical and applied aspects of interactions and the synchronization mechanisms used among actors of concurrent/distributed systems. The workshop intends to attract researchers interested in models, verification, tools, and programming primitives concerning such structured interactions. The theme of ICE09 will be structured interactions by which we mean the class of synchronisations that go beyond the "simple" point-to-point synchronisations. A few examples of such structured interactions are: multicast or broadcast synchronisations, even-notification based interactions, time dependent interactions, distributed transactions, stateless/statefull interactions. Not only structured interactions have been studied "in isolation", but researchers have also considered mutual relations and theoretical frameworks featuring uniform representations and/or co-existence of different structured interactions. As a matter of fact, different structured interactions are typically required when specifying views of a distributed system or when considering it at different levels of abstraction. For instance, multicast or broadcast interactions (desirable at a high level of abstraction) have to be mapped on more basic kind of interactions like point-to-point asynchronous synchronisations. The interest in such interactions is growing due to the recent trend in providing abstractions that allow one to master the complexity of distributed systems. Remarkable research lines in this area are the use of types or behavioural equivalences to guarantee properties of concurrent/distributed systems (eg., progress properties) or the use of model-driven approaches in order to achieve correctness "by construction" (eg., graceful termination), or else the relations among interactions, mobility and spatial aspects (eg., bigraphs). -- Topics -- Topics of interest include, but shall not be limited to: - models, logic and types for structured interactions; - expressiveness results; - timed and hybrid interactions; - verification, analysis and tools; - programming primitives for structured interactions; - structured interactions as coordination mechanisms; - structured interactions inspired by emerging computational models (systems biology, quantum computing, etc.). -- Selection Procedure -- The workshop proposes an innovative paper selection mechanism based on an interactive discussion amongst authors and PC members. As shown by the past edition of ICE, this considerably improves the quality of the papers, the reviews and the discussion during the workshop. We continue by detailing the selection procedure. After the submission deadline expires, each PC member selects a number of suitable papers to review before the start of the discussion phase. At the beginning of the discussion, each submitted paper is published on a Wiki and associated with a discussion forum whose access will be restricted to the authors and to all the PC members. The latter will be able to post comments/questions which the authors will reply to (authors will obviously have access only to forums associated with their own papers). Thus, the discussion on forums (and hence the reviewing process of papers) may be enhanced by the additional comments of interested PC members. -- The Public Wiki -- After the notification, the accepted papers will be published on a public forum, the rationale being to initiate public discussions that will trigger and stimulate the scientific debate of the workshop. We argue that this will drive the workshop discussions and let perspective participants to interact with each other well in advance with respect to the modus operandi of more traditional events. -- Submission Guidelines -- Papers must report previously unpublished work and not be submitted to another conference/workshops with refereed proceedings. Programme Committee members, barring the co-chairs, may (and indeed are encouraged) to contribute. Accepted papers must be presented at the workshop by one of the authors. There is no specific page limit, but authors should strive for brevity. Details of the submission mechanism will follow in due course. -- Dissemination -- The ICE09 post-proceeding will be published in a novel series: Electronic Proceedings in Theoretical Computer Science. -- Important Dates -- - Abstract submission: 29 May 2009 - Submission deadline: 5 June 2009 - Reviews due: 26 June 2009 - Discussion: from 29 June to 11 July 2009 - Notification to authors: 13 July 2009 - Workshop: 31 August 2009 -- Program Committee -- * Simon Bliudze (CEA LIST, France) * Eduardo Bonelli (LIFIA, University of LaPlata, Argentina) * Andrea Bracciali (University of Pisa, Italy) * Roberto Bruni (University of Pisa, Italy) * Marco Carbone (IT University of Copenhagen, Denmark) * Bob Coecke (Oxford University, UK) * Vincent Danos (University of Edinburgh, UK) * Erik de Vink (Technische Universiteit Eindhoven) * Georgios Fainekos (NEC Laboratories, USA) * Goran Frehse (Universite Joseph Fourier Grenoble 1 - Verimag,France) * Carlo A. Furia (ETH Zuerich, Switzerland) * Fabio Gadducci (University of Pisa, Italy) * Ichiro Hasuo (Kyoto University, Japan) * Thomas Hildebrandt (IT University of Copenhagen, Denmark) * Daniel Hirschkoff (ENS, Lyon, France) * Barbara Koenig (University of Duisburg-Essen, Germany) * Ivan Lanese (University of Bologna, Italy) * Hernan Melgratti (Universidad de Buenos Aires, Argentina) * Dimitris Mostrous (Imperial College, London, UK) * Madhavan Mukund (Chennai mathematical Institute, India) * Dejan Nickovic (EPFL Lausanne, Switzerland) * Ana Sokolova (University of Salzburg, Austria) * Hugo Torres Vieira (New University of Lisbon, Portugal) * Angelo Troina (University of Torino, Italy) * Nobuko Yoshida (Imperial College, London, UK) * Herbert Wiklicky (Imperial College, London, UK) -- ICEcreamers -- - Filippo Bonchi (CWI) - Davide Grohmann (Universita' di Udine) - Paola Spoletini (Politecnico di Milano) - Emilio Tuosto (University of Leicester) ---------------------------------------------------------------- This message was sent using IMP, the Internet Messaging Program. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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FMCS 2009 SCHEDULE
by John MacDonald 27 May '09

27 May '09

FMCS 2009 17th Workshop on Foundational Methods in Computer Science University of British Columbia, VANCOUVER, Canada MAY 28th - 31st, 2009 FINAL ANNOUNCEMENT * * * Last minute registration is possible. Registration forms are available from the conference webpage http://www.pims.math.ca/scientific/general-event/foundational-methods-compu… Accommodations may also be reserved from the same page. FMCS 2009 SCHEDULE Thursday, May 28, 2009 3:00p.m. Gage residence rooms available for check-in 6:00p.m. Welcome Reception - Ruth Blair AB - Gage Residence Friday, May 29, 2009 Tutorial Sessions - WMAX 240 - 1933 West Mall 9:00-10:30a.m. Ernie Manes - Equationally definable full subcategories of spaces. 10:30-11:00a.m. Break 11:00-12:30p.m. Vaughan Pratt - Axiomatizing affine and Euclidean space. 12:30-2:30p.m. Lunch 2:30-4:00p.m. Pieter Hofstra - Types, groupoids and homotopy. 4:00-4:30p.m. Break 4:30-5:30p.m. Dorette Pronk - The left and right adjoints of Span. Saturday, May 30, 2009 Research talks - WMAX 240 - 1933 West Mall 9:00-9:50a.m. Mehrnoosh Sadrzadeh - What is the vector space content of what we say? A compact categorical approach to distributed meaning. 9:50-10:30a.m. Robert Seely - The basics of Cartesian differential restriction categories. 10:30-11:00a.m. Break 11:00-12:00 Michael Johnson - Monadicity, descent, and classical database view updating. 12:00-12:30p.m. Art Stone - What might Counter-bi-algebras be? 12:30-2:00p.m. Lunch 2:00-2:40p.m. Robin Cockett - Cartesian differential restriction categories. 2:40-3:05p.m. Brian Redmond - TBA 3:05-3:40p.m. Shusaku Tsumoto - Medical data mining. 3:40-4:10p.m. Break 4:10-4:35p.m. Brett Giles - Reversible computation and Frobenius algebras. 4:35-5:00p.m. Aaron Hunter - Algebraic considerations on the dynamics of belief. 6:00p.m. Banquet - Cedar Room in the Ponderosa Building Sunday, May 31, 2005 Sunday talks will be in WMAX 240 - 1933 West Mall 9:00- 9:50a.m. Bob Rosebrugh - EASIK: Database design and manipulation implemented categorically. 9:50-10:20a.m. Sean Nichols - On strong reduction in combinatory logic. 10:20-11:00a.m. Break 11:00-12:00 Vaughan Pratt - Euclid's postulates at all dimensions. The following paragraphs repeat the information from the 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. The meeting begins with a reception at 6pm in the Ruth Blair room in Walter Gage Towers on the UBC campus on Thursday May 28, 2009. 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 register early if you would like to be considered for a talk. Graduate student participation is particularly encouraged at FMCS. Registration details will appear in the next announcement. 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 Organizer: John MacDonald (UBC) [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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Applying Category Theory to Improve ...
by mjhealy＠ece.unm.edu 27 May '09

27 May '09

Our full account of an application of colimits and limits to improving upon a standard neural architecture is soon to appear in the journal Neurocomputing. In case this interests you, a preprint is obtainable from my website, http://www.ece.unm.edu/~mjhealy , or else contact me for a copy. The blurb: Applying Category Theory to Improve the Performance of a Neural Architecture Michael J. Healy, Richard D. Olinger, Robert J. Young, Shawn E. Taylor, Thomas P. Caudell, and Kurt W. Larson Abstract: A recently-developed mathematical semantic theory explains the relationship between knowledge and its representation in connectionist systems. The semantic theory is based upon category theory, the mathematical theory of structure. A product of its explanatory capability is a set of principles to guide the design of future neural architectures and enhancements to existing designs. We claim that this mathematical semantic approach to network design is an effective basis for advancing the state of the art. We offer two experiments to support this claim. One of these involves multispectral imaging using data from a satellite camera. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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sketch theory
by Andre.Rodin＠ens.fr 26 May '09

26 May '09

Dear Charles and others: this http://www.cwru.edu/artsci/math/wells/pub/pdf/sketch.pdf is your very useful overview of Sketch theory dated back to 1993. I wonder how much it omits today: are there significant research programmes in this field emerged during last 15 years? What should I look at first of all? Many thanks in advance. Andrei

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