April 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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Post-doc position at Birmingham: toposes and quantum theory
by Steve Vickers 21 May '09

21 May '09

Research project: "Applications of geometric logic to topos approaches to quantum physics". [I have already announced a PhD studentship on this project, but a 3 yr post-doc position has now come available.] I have received EPSRC funding for a 3-year project with a post-doctoral research position and PhD studentship attached, to be conducted in the School of Computer Science in the University of Birmingham, UK, and to start between now and October. I would be very pleased to receive applications. The essential area of expertise for the post-doc is constructive reasoning (with toposes and point-free topology), but the researcher will also need to have or acquire some familiarity with quantum theory. The funding allows for appointment at a high salary grade for a suitably qualified and experienced researcher. The "topos approaches" referred to are those of Isham and Doering (at Imperial) and Heunen, Landsman and Spitters (at Nijmegen). By working internally in suitable toposes, they are able to find (commutative) Gelfand-Naimark spectra for systems that, externally, are non- commutative. The hope is that this might lead to a style of reasoning about quantum systems that, while logically non-classical, is physically classical. My project will look at trying to keep the intuitionistic, topos- valid, internal reasoning within its geometric part. Insofar as this is possible (and there is mounting evidence that substantial amounts of practical mathematics can be done this way), it enables a language of points, stalks, fibres and bundles for the point-free topology involved. It is hoped that this will allow the topos approach to be conducted in terms that are more conceptually transparent (in particular to physicists), but also make it technically palatable to move from the present presheaf toposes to sheaf toposes. Initial work will focus on the geometric content of the Banaschewski/Mulvey account of Gelfand-Naimark duality. Further information can be found on my web site, at http://www.cs.bham.ac.uk/~sjv/geophysics.php#phd I can also supply a more detailed project description on request. Steve Vickers.

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EPTCS, a new open access proceedings series
by Rob van Glabbeek 30 Apr '09

30 Apr '09

With this email, we are launching Electronic Proceedings in Theoretic Computer Science (EPTCS) a new international refereed open access venue for the rapid electronic publication of the proceedings of workshops and conferences, and of festschrifts, etc, in the general area of theoretical computer science, broadly construed. We do not charge authors or event organisers for electronic publication in EPTCS in any way. If hard-copies of proceedings are desired, event organisers have the choice of organising the printing themselves or taking advantage of a standard contract we will make with a printing house. Copyright on all papers is retained by the author, and full-text electronic access to all papers is freely available, without any need for registration or subscription. Permanent archival of EPTCS publications is ensured by organising EPTCS as an overlay of the Computing Research Repository (CoRR): see arXiv.org. The content of EPTCS will be indexed by DBLP. Only original papers will be considered for publication in EPTCS: manuscripts are accepted for review by an EPTCS conference or workshop with the understanding that the same work has not been published, nor is presently submitted, elsewhere. However, full versions of extended abstracts published in EPTCS, or substantial revisions, may later be published elsewhere. The submission and refereeing process is handled entirely by the organisation of the conference, workshop or festschrift to which the paper is submitted. Our editorial board carefully selects which workshops and conferences can be trusted to select scientific papers of quality only, and only those events will be granted a contract to fill a volume of EPTCS. Our editorial board consists of: Luca Aceto Rob van Glabbeek Gordon Plotkin Rajeev Alur Lane A. Hemaspaandra Vladimiro Sassone Krzysztof R. Apt Matthew Hennessy Robert H. Sloan Lars Arge Bartek Klin Wolfgang Thomas Ran Canetti Evangelos Kranakis Irek Ulidowski Luca Cardelli Shay Kutten Dorothea Wagner Rocco De Nicola Nancy Lynch Martin Wirsing Jose' Luiz Fiadeiro Aart Middeldorp Moti Yung Wan Fokkink Benjamin Pierce Further information can be found on our website: http://eptcs.org/. In the hope this initiative will benefit the theoretical computer science community, Rob van Glabbeek (Editor in Chief)

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list interruption / gmane archive
by Bob Rosebrugh 30 Apr '09

30 Apr '09

[From the moderator:] Your moderator will have only intermittent email contact May 3-15, so there will be delays in posting during that period. As noted below, archives of the categories list are now available in a user friendly format. An archive in mail file format will continue to be maintained and available from the list web page: http://www.mta.ca/~cat-dist/categories.html and the link below will be included there soon. ---------- Forwarded message ---------- Date: Wed, 29 Apr 2009 18:26:16 +0200 From: "Emilio [utf-8] Jesús Gallego Arias" <egallego(a)babel.ls.fi.upm.es> To: Bob Rosebrugh <rrosebru(a)mta.ca> Subject: Re: Categories mailing list request for gmane archival. Dear Prof. Rosebrugh, Bob Rosebrugh <rrosebru(a)mta.ca> writes: > Thanks for your interest in the list. Eventually I'll announce the > availability of this more user-friendly archive. It took a while but categories(a)mta.ca archives starting from 1997 have been successfully imported into gmane. It will take a while until all the messages are correctly sorted by date. The archives are accessible at http://dir.gmane.org/gmane.science.mathematics.categories Merit for the import should go to gmane's administrator, Lars Magne Ingebrigtsen <larsi(a)gnus.org> Thanks a lot for your help. Yours sincerely, Emilio Jesús Gallego Arias >> Gmane is a mail to news gateway, so it basically serves two purposes: >> >> - Allows everyone to read and post to mailing lists with a more >> convenient news reader. >> >> - Archives mail in a web-friendly way. >> >> Additionally, Gmane can import list archives so the full posting history >> of the list is available through it. >> >> The archives at http://www.mta.ca/~cat-dist/archive/ would be an >> excellent source for replaying categories(a)mta.ca history. However the >> Gmane administrators request that the list moderator approves the >> inclusion, see: >> >> http://gmane.org/import.php >> >> Would you approve it?

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Classifying Space...
by Hugo.BACARD＠unice.fr 28 Apr '09

28 Apr '09

Dear category theorists, Sorry for my following stupid questions , but i would like: -Given a monoidal category M , for first assumed to be strict, What kind of thing do we obtain when we take it's classifying space ?: we take the nerve of M and then realising the simplicial sets obtained Explicitely there are theses questions : 1) Does the nerve of M "preserve" (or "reflect") the monoidal structure of M ? -Is it a monoid in the category of simplicial sets ? -If yes , can we have conditions on a monoid of sSet to be the nerve of a monoidal category ? I mean, does some kind of "segal condition" ? 2) And What kind of topological spaces of the realization of the nerve -Is it a topological monoid , with some extra structure ? 3) And what hapen if M is not strict, or is symmetric, or braided , etc... Thank you and sorry if these are completely stupid questions

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Workshop at McGill, 18 June 09
by Robert Seely 25 Apr '09

25 Apr '09

Workshop announcement: 18 June 2009 at Burnside Hall, McGill, Montreal. We wish to announce a one-day workshop seminar, a "prequel" to the Makkaifest which is being held at CRM 19-20 June (with a reception on the evening of 18 June). http://www.crm.umontreal.ca/Makkaifest09/ http://www.crm.umontreal.ca/Makkaifest09/index_e.php This workshop is intended for the participants of the Makkaifest, and will end in time to allow attendance at the reception at 6pm. If you are interested in attending the workshop, please let us (Phil Scott or Robert Seely) know so we can book a room of suitable size. Any participants who would like to give a talk in the workshop should contact one of the workshop organisers (Phil Scott or Robert Seely) *as soon as possible*, as places are very limited. The themes of the workshop are those of the Makkaifest itself, and should reflect the interests shown by Michael Makkai over his career. We will announce a schedule of talks later, probably late May or early June. We expect the talks to start around 9am and to finish by 5pm, so there'll be time to get to the reception at CRM at 6pm. The workshop will be an informal affair - there will be no registration, and no "refreshments" (people can buy their own coffee, and lunch will be "dutch treat"). Phil Scott (phil(a)site.uottawa.ca) Robert Seely (rags(a)math.mcgill.ca) -- <rags(a)math.mcgill.ca> <www.math.mcgill.ca/rags>

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2 PhD positions at Onera Toulouse, France
by David CHEMOUIL 24 Apr '09

24 Apr '09

Dear colleagues, would you please forward this e-mail to the students of yours that may be interested by these 3-year PhD positions, proposed at Onera (the French Aerospace Research Center) in Toulouse. Fluency in French *or* in English is mandatory. This subjects are part of a research agenda aiming at helping define and verify large and complex (non-software) systems by using categorical methods as already used in computer science. Best regards, dc -- David CHEMOUIL ONERA/DTIM - 2 avenue Édouard Belin - F-31055 Toulouse Tel: +33 (0) 5 6225 2936 - Fax: +33 (0) 5 6225 2593 http://www.onera.fr/staff/david-chemouil FOUNDATIONS FOR SPACE SYSTEMS MODELING —PhD Position at ONERA, Toulouse, France— Reference: TIS-DTIM2009-02 Application deadline: 2009-05-31 PhD direction: David Chemouil and Virginie Wiels (ONERA), Jean-Paul Bodeveix (IRIT) Contact: David Chemouil ONERA/DTIM 2 avenue Édouard Belin F-31055 Toulouse, France david.chemouil+phd[AT]onera.fr http://www.onera.fr/staff/david-chemouil Subject: The development of space systems (including on-board and ground systems) requires complex engineering and relies upon various disciplines. Until now, the success of such projects has relied upon the quality and experience of engineers as well as on partly-automated development processes. However, although some technical artifacts (e.g: mathematical model of a battery, satellite simulator) are used in such developments, there is still —and mainly— a huge amount of paper documentation expressed in natural language. This complexity and diversity of technical means mitigate the validation of a whole space system. Systems model-based development, inspired by similar approaches in the software field, is gaining more and more importance both in the industrial and academic communities. However, the mainstream solutions currently proposed are still unsatisfactory, notably on two major points: – on one hand, the requirement capture phase and its further refinement towards a formal specification are not well taken into account; – on the other hand, there is still a lack of formal semantics for architectural models. Both these points have obviously a strong impact on the verification and validation of such systems. The objective of this PhD is to propose relevant concepts for a modeling language addressing these questions. The solution to the first problem may rely on goal-oriented requirement engineering, in the style of KAOS or Tropos methods... The second question will be addressed by devising formal architectural concepts with further (semi-)automated verification in mind. Categorical and/or algebraic approaches, process calculi, model-oriented techniques (such as the B method) will be favoured. Results from software engineering, such as component-based development will be taken into account. The results of the PhD will be backed up by a case study and may be implemented in a software prototype. Candidate profile: MSc in computer science, having followed some “theory” courses (e.g logic, λ-calculus, process algebra, algebraic specification, B or Z method, etc.). Fluency in English. Gross salary: ranging 1680-2140 EUR /month depending on the profile. 3-year position. Localisation: Onera is the French Aerospace Research Center, affiliated to the French Ministry of Defence. The PhD will be carried out at Toulouse premises. Located in southwest France, Toulouse is a lively city, the 4th most important town in France, and the 2nd one as far as the student population is concerned (see <http://en.wikipedia.org/wiki/Toulouse>). A FORMAL SETTING FOR VIEWPOINT COMPOSITION —PhD Position at ONERA, Toulouse, France— Reference: TIS-DTIM2009-01 Application deadline: 2009-05-31 PhD direction: David Chemouil and Virginie Wiels (ONERA), Sergei Soloviev(IRIT) Contact: David Chemouil ONERA/DTIM 2 avenue Édouard Belin F-31055 Toulouse, France david.chemouil+phd[AT]onera.fr http://www.onera.fr/staff/david-chemouil Subject: A current approach to the engineering of systems (software systems, sociotechnical systems, systems of systems, etc.) consists in modeling them, during specification and design phases, according to various viewpoints. This approach aims at helping engineers handle extremely complex systems by providing them with a view corresponding to their sole business (e.g air or space regulation, dependability, realtime performance, etc.), abstracting from other concerns. Of course, the viewpoints that are useful may strongly vary on the context, henceforth entailing the recurring definition of new multi-view modeling languages. This definition is usually ad-hoc, which forces language designers either to ignore semantic matters and remain on a purely syntactic definition, or to propose a new formal semantics and demonstrate a certain number of otherwise standard results. The aim of this PhD is to propose a theoretical setting to assist in the creation of multi-view languages out of “small” predefined modeling languages (each one being concerned with only one topic). The major question is then to determine under which conditions it is possible to deduce the formal semantics of the multi-view language from the semantics of its constituent languages. Another way to state this problem is to say that we aim at provding a formal semantics to aspect-oriented metamodeling. The foreseen theoretical solutions essentially rely on categorical approaches: algebraic speci- fication, theory of institutions, graph grammars, etc. The results of the PhD will be backed up by a case study and may be implemented in a software prototype. Candidate profile: MSc in computer science or in logic, having followed some “theory” courses (e.g logic, λ-calculus, process algebra, algebraic specification, etc.). Fluency in English. Gross salary: ranging 1680-2140 EUR /month depending on the profile. 3-year position. Localisation: Onera is the French Aerospace Research Center, affiliated to the French Ministry of Defence. The PhD will be carried out at Toulouse premises. Located in southwest France, Toulouse is a lively city, the 4th most important town in France, and the 2nd one as far as the student population is concerned (see <http://en.wikipedia.org/wiki/Toulouse>).

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2nd CFP: Special Issue on Hybrid Logics of the LJ-IGPL
by Carlos Areces 23 Apr '09

23 Apr '09

*************************************************************** Please excuse for multiple posts and distribute as widely as possible *************************************************************** CALL FOR PAPERS Logic Journal of the IGPL Special issue on Hybrid Logic DEADLINE FOR SUBMISSIONS: 31st May 2009 *************************************************************** Hybrid logic is a branch of modal logic allowing direct reference to worlds/times/states. It is easy to justify interest in hybrid logic on the grounds of applications, as the additional expressive power is very useful. In addition, hybrid-logical machinery improves the behaviour of the underlying modal formalism. For example, it becomes considerably simpler to formulate modal proof systems, and one can prove completeness and interpolation results of a generality that is not available in orthodox modal logic. But more generally, the topic of this special issue is not only standard hybrid-logical machinery (like nominals, satisfaction operators, binders, etc.) but also extensions of modal logic that increase its expressive power in one way or other. For more general background on hybrid logic, and many of the key papers, see the Hybrid Logics homepage (http://hylo.loria.fr/) The special issue will welcome papers in a wide range of topics, including description logic, feature logic, applied modal logics, temporal logic, and labelled deduction. We welcome both theoretical work and work describing systems and applications on hybrid logics, broadly conceived. All submissions will be peer reviewed with respect to the usual journal criteria. Authors are invited to submit original, previously unpublished, research papers written in English. SUBMISSION DETAILS: Papers should not exceed 25 pages including references. Authors are required to prepare their submissions in latex, using the style available at http://hylo.loria.fr/content/SI/2009 Submissions should be sent as .pdf files to areces (at) loria.fr DEADLINE FOR SUBMISSIONS: 31st May 2009 GUEST EDITORS: Carlos Areces (INRIA Nancy Grand Est, areces at loria.fr) Patrick Blackburn (INRIA Nancy Grand Est, blackbur at loria.fr)

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Category of categories with pullbacks is cartesian closed
by John Bourke 23 Apr '09

23 Apr '09

Dear category theorists, I noticed recently that the category whose objects are categories with pullbacks and whose morphisms are pullback preserving functors is cartesian closed. Given a pair of categories with pullbacks A and B, the internal hom [A,B] has objects: pullback preserving functors from A to B, and morphisms: cartesian natural transformations. I have posted a short paper on the arxiv proving this fact: http://arxiv.org/abs/0904.2486 It seems like a fairly natural fact but is not to my knowledge in the literature. I am wondering whether anyone was previously aware of this result, and if so whether it might be mentioned somewhere in the literature? Thanks, John Bourke, University of Sydney.

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