June 2000 - Categories - categories.org.au

Maps as toposes: terminology?
by S.J.Vickers＠open.ac.uk 30 Jun '00

30 Jun '00

As is well-known, given a topos Y then the maps f: X -> Y targeted at it are equivalent to toposes in the generalized universe of sets corresponding to Y. Hence there is a correspondence between properties of maps and constructive properties of toposes. Unfortunately, they often have different names. For instance, in "Proper maps of toposes", Moerdijk and Vermeulen have - compact (for toposes) vs. proper (for maps) strongly compact vs. tidy Stone vs. entire compact Hausdorff vs. separated (a.k.a. proper) Furthermore, sometimes f is genuinely to be thought of as a map, with X and Y toposes over some base topos B, and the properties can be relativized to B. For instance, Moerdijk and Vermeulen define "proper relative to B", and then "proper" unqualified means "proper relative to the target (Y)". More names can arise from this; for instance, "proper relative to 1" has been called - at least for locales - "semiproper", "perfect" or even "proper". Does anyone have suggestions of systematic terminology - other than systematically calling everything "proper" - that avoids this proliferation of names? Steve Vickers Department of Pure Maths Faculty of Maths and Computing The Open University ----------- Tel: 01908-653144 Fax: 01908-652140 Web: http://mcs.open.ac.uk/sjv22

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preprint: "On the Penon method of weakening of algebraic structures"
by mbatanin＠ics.mq.edu.au 30 Jun '00

30 Jun '00

Dear colleagues, a preprint M.Batanin, "On the Penon method of weakening of algebraic structures" is available on http://www.math.mq.edu.au/~mbatanin/papers.html I consider a generalization of the Penon approach to the definition of weak $n$-category and compare his definition with mine. I also correct one construction from my earlier paper about computads. Regards, Michael.

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CALCULEMUS-2000 CFP
by Manfred Kerber 28 Jun '00

28 Jun '00

CALL FOR PARTICIPATION CALCULEMUS-2000 Symposium on the Integration of Symbolic Computation and Mechanized Reasoning 6-7 August 2000 St Andrews, Scotland (collocated with ISSAC 2000) http://www.calculemus.net/meetings/standrews00/ PROGRAMME http://www.calculemus.net/meetings/standrews00/program.html REGISTRATION http://www-history.mcs.st-and.ac.uk/issac2000/registration.shtml SCOPE Both deduction systems and computer algebra systems are receiving growing attention from industry and academia. On the one hand, mathematical software systems have been commercially very successful. Their use is now wide-spread in industry, education, and scientific contexts. On the other hand, the use of formal methods in hardware and software development has made deduction systems indispensable not least because of the complexity and sheer size of the reasoning tasks involved. As many application domains fall outside the scope of existing deduction systems and computer algebra systems, there is still need for improvement and in particular need for the integration of computer algebra and deduction systems. The symposium is intended for researchers and developers interested in combining the reasoning capabilities of deduction systems and the computational power of computer algebra systems. TOPICS Topics of interest for the symposium include all aspects related to the combination of deduction systems and computer algebra systems. We explicitly encourage submissions of results from applications and case studies where such integration results are particularly important. FORMAT The symposium will feature invited talks, contributed presentations with ample time for discussion, and a panel session. Consistent with the tradition of the symposium as a lively forum for discussing controversial ideas, we expect and encourage contributed talks to present work in progress, rather than polished final results. CONFERENCE LOCATION CALCULEMUS 2000 will be held at St Andrews University, Scotland's oldest university. Visitors to St Andrews will discover a city full of charm and historical interest, and golfers will be delighted by the many famous and challenging golf courses in the area. Travel information can be found as http://www-history.mcs.st-and.ac.uk/issac2000/travel.shtml INVITED SPEAKERS - Henk Barendregt, U. Nijmegen, Mathematics and Computer Science - Arjeh Cohen, Eindhoven University of Technology, Dept. Math. - Gaston Gonnet, ETH Z"urich, Institute for Scientific Computation IMPORTANT DATES Symposium: 6-7 August 2000 ISSAC: 7-9 August 2000 13. OpenMath Workshop: 10 August 2000 ORGANIZATION and PROGRAMME CHAIRS Manfred Kerber, U. Birmingham, <M.Kerber(a)cs.bham.ac.uk> Michael Kohlhase, U. Saarbr"ucken, <kohlhase(a)cs.uni-sb.de> LOCAL ORGANIZER Steve Linton, St. Andrews U. <sal(a)dcs.st-and.ac.uk> PROGRAMME COMMITTEE Alessandro Armando, U. Genova Michael Beeson, San Jose State U. Manuel Bronstein, INRIA Sophia Antipolis Bruno Buchberger, RISC, Linz Jaques Calmet, U. Karlsruhe Olga Caprotti, TU. Eindhoven Edmund Clarke, CMU Fausto Giunchiglia, IRST Therese Hardin, Paris VI John Harrison, Intel Corp. Tudor Jebelean, RISC, Linz Helene Kirchner, Nancy LORIA/INRIA Deepak Kapur, U. New Mexico, Albuquerque Steve Linton, St. Andrews U. Ursula Martin, St. Andrews U. Julian Richardson, U. Edinburgh J"org Siekmann, U. Saarbr"ucken Carolyn Talcott, Stanford U. Andrzej Trybulec, U. Bialystok

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Tony-San
by Peter Freyd 26 Jun '00

26 Jun '00

On 4 January I posted: The Queen's New Years Honours list announced a knighthood for C.A.R. Hoare (the first person to find an application for 2-categories). Today: The Chronicle of Higher Education Monday, June 26, 2000 Computer Scientist, Biologist, Philosopher Win Kyoto Prizes Japan's Inamori Foundation on Friday named a computer scientist, a biologist, and a philosopher as this year's winners of the Kyoto Prizes, which are awarded annually to honor individuals who contribute to the scientific, cultural, or spiritual betterment of society. The winners will receive a special certificate and 50-million yen (approximately $477,000) at a ceremony in Kyoto on November 10. The winners and their achievements cited by the foundation, are: * Sir Charles Antony Richard Hoare, a professor emeritus of computer science at the University of Oxford, in Britain, for "pioneering and fundamental contributions to software science." * Walter Jacob Gehring, a professor of developmental biology at the University of Basel, in Switzerland, for his "discovery of conserved developmental mechanisms." * Paul Ricoeur, a professor emeritus of philosophy at the University of Paris, in France, and at the University of Chicago, for "an imposing construct of hermeneutic phenomenology that embraces a new concept of ethics."

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Categorical Studies in Italy
by Renato Betti 24 Jun '00

24 Jun '00

Readers of the catnet may be interested in looking at Categorical Studies in Italy the "Supplemento ai Rendiconti del Circolo Matematico di Palermo", serie II, n. 64, 2000, which has recently appeared. This is a collection of 15 papers by various authors connected with Italian category theorists. Most of the papers were presented at a meeting held in Perugia, May 1-3, 1997. The occasion was the 25th anniversary of the course on Category Theory and Topos Theory given in Perugia by Bill Lawvere.(The Rendiconti are available in most libraries.) Renato Betti

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Adjoints in bicategories
by Frank Atanassow 23 Jun '00

23 Jun '00

I'm looking for definitions of (the weak 2-dimensional analogues of 1-) products and coproducts for bicategories, and also adjoints. In his 1967 article "Introduction to Bicategories, Part I" Benabou promises to treat biadjoints in a sequel, but I gather this was never published. Gray treats a notion of "quasi-adjointness" in "Formal Category Theory"; is this accepted as the "right" generalization? Pointers to definitions of these concepts in one of the approaches to weak n-categories would be welcome as well. -- Frank Atanassow, Dept. of Computer Science, Utrecht University Padualaan 14, PO Box 80.089, 3508 TB Utrecht, Netherlands Tel +31 (030) 253-1012, Fax +31 (030) 251-3791

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A question on: <newsgroup sci.math>
by Ross Street 21 Jun '00

21 Jun '00

I thought the CatNet would be interested in the following question which appeared on <newsgroup sci.math>. The letter was pointed out to me by a colleague at Macquarie. --Ross ************************************************* From: mathwft(a)math.canterbury.ac.nz (Bill Taylor) Newsgroups: sci.math Subject: Query about Category Theory. Date: 18 Jun 2000 05:36:30 GMT Organization: Department of Mathematics and Statistics, University of Canterbury, Christchurch, NewZealand Does anyone know of any cases where Category Theory (morphisms, functors & all that) has helped solve an unsolved problem? That is, a problem in some other branch of math, posed without reference to categorical ideas, and previously unsolved, that was first solved via Category T. I realize that CT provides a unifying framework for many seemingly disparate ideas in math, and that is a fine thing of course; but I was just wondering if it had this problem-solving capability. TIA for any helpful responses. ---------------------------------------------------------------------------- --- Bill Taylor W.Taylor(a)math.canterbury.ac.nz

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Three questions about fibrations
by Michael Abbott 16 Jun '00

16 Jun '00

I am wondering if anyone can give references for three remarks Wesley Phoa makes in the chapter on fibrations of his paper "An introduction to fibrations, topos theory, the effective topos and modest sets". 1. Essentially Algebraic Theories In the footnote on page 7 Phoa comments: "[fibrations] are the models for a first-order, 'essentially algebraic' theory". I'm not quite sure what he means here, and this sounds like it must be a standard and well known connection. I'd be glad of a reference. 2. Splitting Fibrations At the bottom of page 14 Phoa observes: "Every fibration .. is equivalent to a split fibration (there is an elegant proof due to John Power). However, it's not clear how to extend this result to more complicated structures. This is the coherence problem ..." Now I know that any fibration is equivalent to a split fibration via the "fibred Yoneda lemma" (Borceux, "Handbook of Categorical Algebra 2", 8.2.7 and Jacobs, "Categorical Logic and Type Theory"), but I don't think that's the only splitting available, and I'm not sure that this correspondence helps very with coherence questions. I am aware of another, different, equivalent splitting, and I wonder if there are any references. In particular, can anyone guess what reference by John Power Phoa was referring to? In particular, I'd be very interested in any other observations on the "coherence problem". 3. Generalising the Definition In the footnote on page 12, in reference to the definition of a fibration, Phoa says: "If one really wants to take .. 2-categorical issues seriously, one needs .. a more sophisticated definition of 'fibration'." I can make some promising looking guesses. Any references? Many thanks. Michael Abbott

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Festival Workshop in Foundations and Computations
by Fairouz Kamareddine 14 Jun '00

14 Jun '00

Festival Workshop in Foundations and Computations Heriot-Watt University, Edinburgh Sunday 16 July-Tuesday 18 July 2000 http://www.cee.hw.ac.uk/~fairouz/festival/workshop1/ This workshop is a part of a research festival at Heriot-Watt University, Edinburgh, during parts of the summer of 2000. During the festival, international and national researchers spend short/long time at Heriot-Watt during which a lively research environment will take place. There will be many seminars during the festival details of which are advertised separately. When the visits coincide with a particular theme, a workshop will be held on that theme. If you like to take part in the festival and/or give a talk, contact fairouz(a)cee.hw.ac.uk. Grants are available for parts or all of the registration fees and accommodation. Contact fairouz(a)cee.hw.ac.uk for details. The first workshop in the festival is a workshop on foundations and computations. If you have a relevant talk, submit a three page abstract to fairouz(a)cee.hw.ac.uk by 25 June 2000. You will be informed of acceptance by 5 July 2000. Speakers and Topics Gilles Dowek (INRIA-Rocquencourt, FR): About Folding-Unfolding Cuts Jan van Eijck(University of Amsterdam, NL): Dynamic First Order Logic Jacques Fleuriot (University of Edinburgh, UK): Automating Newton's calculus in Isabelle Therese Hardin (Paris 6 and INRIA-Rocquencourt, FR): The calculus of contexts of lambda-sigma Roger Hindley (University of Swansea, UK): The birth of lambda-calculus and combinatory logic Alan Mycroft (Cambridge University and AT&T Labs, UK): Type Based Decompilation Gopalan Nadathur (University of Chicago, USA): proof theory and procedures for fragments of intuitionistic logic Gopalan Nadathur (University of Chicago, USA): implementation of higher-order logic programming languages Iain Stewart (University of Leicester, UK): A programming approach to descriptive complexity theory Grants Grants cover part or all of the registration fee and accommodation. We strongly welcome applications from women researchers, researchers who work in industry, and researchers whose place of work is in a less-favoured region. If you are not sure about eligibility, send an email to fairouz(a)cee.hw.ac.uk. The form for application for funding can be found on the above URL. Deadline for receipt of grant applications is 30 June 2000. You will receive notification of acceptance/rejection by 5 July 2000. In order to guarantee accommodation, it is advisable that your application is sent as soon as possible. The summer is a very busy time in Edinburgh.

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ANNOUNCEMENT Tbilisi Summer School
by besick dundua 13 Jun '00

13 Jun '00

ANNOUNCEMENT Tbilisi Summer School in Language, Logic, and Computation 29th August - 8 September 2000 Tbilisi, Georgia The Georgian Centre for Language, Logic, and Speech, based at the Tbilisi State University, will host Tbilisi Summer School, main purpose of which is to make the students and young scholars acquainted with the modern state of affairs in the mentioned fields of science, and - at the same time - to further contacts and scientific collaboration between Western and Eastern Scholars LECTURERS Jurij Apresjan, Moscow Matthias Baaz, Vienna Pascal Boldini, Paris Marina Glavinskaja, Moscow Michel Parigot, Paris Carl Vogel,Dublin Andrej Voronkov, Manchester COURSES - Foundations of linguistic semantics (Ju.Apresjan) - On the generalisation of proofs and calculations (M.Baaz) - Type theories for semantics and cognition (P.Boldini) - Semantics of aspect (M.Glavinskaja) - Proofs as programs (M.Parigot) - Cognitive constraints on linguistic theory. (C.Vogel) - Logical Foundations of deductive databases. (A.Voronkov). STUDENTS Besides local audience we shall be glad to see at the School foreign students also. Participants fee for such persons will amount to $120 (excursion, banquet, reprints, etc.). They could be comfortably accommodated at Georgian families (with two meals) - $40 per day. LOCATION AND SIGHTSEEING TOURS Georgia is the ancient country situated between Black and Caspian seas, Caucasus Mountains and Turkey. This is the country of Golden Fleece, myth of Argonauts, Jason and Medea, Promethee, chained to the Caucasus mountains. Tbilisi - capital of Georgia - has more than 1 million in habitant. It is situated some 100-150 km to the south of main Caucasus ridge, in the beautiful valley of the river Mtkvari, surrounded by the green slopes of the Caucasus spurs. The city has a long (1500 year) history and abounds in historical and cultural memorials. Georgia is famous for its high quality wines, exquisite cuisine and cordial hospitality. The main site of the Symposium, Tbilisi state University, is the chief centre of education in the country, and has several outstanding scholars in science, art and politics among its graduates. As a route of excursion is chosen the Georgian Military Road going via ancient capital of Georgia - Mtskheta, with its abundant architectural and historical monuments, crossing the main ridge of Caucasus by the Cross Pass and reaching the final point of supposed trip - mountain resort Kazbegi with its Trinity Church situated on the top of high peak facing the second (after Elbrus) mountain - peak of Caucasus - Mkinvarcveri (Glacier - mountain). TRAVEL INFORMATION The only real way of arrival in Tbilisi is by air. If direct flight from the point of your departure does not exist, the preferable ways are via Istambul, Frankfurt or Moscow. ORGANISING COMMITTEE: T.Khurodze (Chair, Pro-rector of Tbilisi State University) R.Asatiani (Institute of Oriental Studies) N.Chanishvili (Tbilisi State University) G.Chikoidze (Institute of Control Systems) K.Pkhakadze (Institute of Applied Mathematics) Kh.Rukhaja (Institute of Aplied Mathematics). For additional information, please, use the following addresses: www.geocities.com/summer_school_2000 www.risc.uni-linz.ac.at/people/tkutsia/summerschool/ or contact the organisation comitie: George Chikoidze Dept. of Language Modelling Inst. of Control Systems Georgian Academy of Sciences 34, K. Gamsakhurdia 380060 Tbilisi Georgia Phone: +995 32 382136 E-mail: chiko(a)contsys.acnet.ge Khimuri Rukhaia Institute of Applied Mathematics Phone:+995 32 316825 E-mail: rukhaia(a)viam.hepi.edu.ge Kote Pkhakadze Institute of Applied Mathematics Phone: +995 32 325929 E-mail: pkhakadz(a)viam.hepi.edu.ge Beso Dundua Institute of Applied Mathematics Phone: +995 32 325441 E-mail: b_dundua(a)yahoo.com __________________________________________________ Do You Yahoo!? Yahoo! Photos -- now, 100 FREE prints! http://photos.yahoo.com

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