From rrosebru@mta.ca Tue May 4 08:19:25 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 04 May 2004 08:19:25 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BKxk4-0002sJ-00 for categories-list@mta.ca; Tue, 04 May 2004 08:05:40 -0300 Date: Mon, 3 May 2004 22:07:26 +0200 From: "Int. Center for Computational Logic" Message-Id: <200405032007.i43K7QjN015970@spock.inf.tu-dresden.de> To: categories@mta.ca Subject: categories: ICCL Summer School 2004 - Final Call Reply-To: cl-adverts@janeway.inf.tu-dresden.de Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 1 ICCL Summer School 2004 Proof Theory and Automated Theorem Proving ------------------------------------------ PCC Workshop 2004 ------------------------------- Technische Universitaet Dresden June 14-25, 2004 Call for Participation ---------------------- This two-week meeting consists of two integrated parts, a summer school and a workshop, aimed at graduate students and researchers. The themes for the summer school are proof theory and automated theorem proving, the workshop is about proof, computation and complexity. As in the summer schools at TU Dresden in 2002 and 2003 and in the previous editions of the PCC workshop, people from distinct but communicating communities will gather in an informal and friendly atmosphere. We ask for a participation fee of 200 EUR. We request registration before May 10, 2004; please send an email to , making sure you include a very brief bio (5-10 lines) stating your experience, interests, home page (if available), etc. It will be possible for some students to present their work: please indicate in your application if you would like to do so and give us some information about your proposed talk. We will select applicants in case of excessive demand. A limited number of grants covering all expenses is available, please indicate in your application if the only possibility for you to participate is via a grant. Applications for grants must include an estimate of travel costs and they should be sent together with the registration. We will provide assistance in finding an accommodation in Dresden. Week 1, June 14-17: courses on Term Rewriting Systems Franz Baader (TU Dresden) Deep Inference and the Calculus of Structures Alessio Guglielmi (TU Dresden) Game Semantics and Its Applications C.-H. L. Ong (Oxford) On June 14 Prof Wolfgang Bibel will give an invited lecture June 17-19: workshop For more details, please consult the workshop web page Week 2, June 21-25: courses on Deduction Modulo Claude Kirchner (Loria & INRIA, Nancy) Logic Considered as a Branch of Geometry Francois Lamarche (Loria & INRIA, Nancy) Proofs as Programs Michel Parigot (CNRS - Universite' Paris 7) Automated Reasoning for Substructural Logics John Slaney (NICTA, Canberra and Australian National University) Automated Theorem Proving for Classical Logics Andrei Voronkov (Manchester) Venue ----- Dresden, on the river Elbe, is one of the most important art cities of Germany. You can find world-class museums and wonderful architecture and surroundings. We will organize trips and social events. Organization ------------ This event is organized by the International Center for Computational Logic (ICCL), Paola Bruscoli, Birgit Elbl, Sylvia Epp, Bertram Fronhoefer, Axel Grossmann, Alessio Guglielmi, Steffen Hoelldobler, Reinhard Kahle and Mariana Stantcheva; it is sponsored by Deutscher Akademischer Austausch Dienst (DAAD), under the program `Deutsche Sommer-Akademie', and CoLogNet. Please distribute this message broadly. From rrosebru@mta.ca Tue May 4 08:19:25 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 04 May 2004 08:19:25 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BKxlK-000306-00 for categories-list@mta.ca; Tue, 04 May 2004 08:06:58 -0300 Date: Mon, 3 May 2004 23:11:21 +0100 From: Paul Taylor Message-Id: <200405032211.i43MBLn14037@primrose.cs.man.ac.uk> To: categories@mta.ca Subject: categories: Arithmetic Universes and Abstract Stone Duality Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 2 Arithmetic Universes and Abstract Stone Duality -- Paul Taylor www.cs.man.ac.uk/~pt/ASD (a) Inside every model of Abstract Stone Duality lies an Arithmetic Universe (b) Every Arithmetic Universe is embedded in a model of Abstract Stone Duality. The first is the title of a new draft paper, available from the web page above, on which your comments are invited. I haven't written up the second, but the essence of the argument follows below. The "embedding" in question is (up to equivalence) as exactly the full subcategory of overt discrete objects. ABSTRACT of (a): The first paper published on Abstract Stone Duality showed that the overt discrete objects (those admitting exists and equality internally) form a pretopos, ie admit finite limits, stable disjoint coproducts and stable effective quotients of equivalence relations. Using an N-indexed least fixed point axiom, here we show that this full subcategory is an arithmetic universe, having a free semilattice (KX, "collection of Kuratowski-finite subsets") and a free monoid (List X, "collection of lists") on any overt discrete object. Each finite subset is represented by its pair ([], <>) of modal operators (although a tight correspondence with these depends on a stronger Scott-continuity axiom). Topologically, such subsets are both compact and open and also involve proper open maps. In applications of ASD this can eliminate lists in favour of a continuation-passing interpretation. The three aspects of the paper to which I would like to draw your attention are: The use of modal operators is related to the three powerdomains (in particular to the Plotkin or convex one) in domain theory. The construction itself is a domain-theoretic one, as the object KX is constructed by means of an idempotent that is the solution of a fixed point equation. A novel induction principle is needed to prove the modal laws from the fixed point equation. The final section shows how KX is a "finite powerset" in that it classifies Kuratowski-finite subsets or compact open subspaces of X. More generally, maps Gamma->KX correspond to open relations U subset Gamma x X for which U->Gamma is proper. As this paper is the first serious use of internal induction and recursion in ASD, it forced me to reconsider the definition of the natural numbers object in this category without arbitrary equalisers (cf my message to "categories" on 4 November). Proof-theoretically, this means that the judgements in the ASD lambda-calculus must allow equations as well as assignments of types to variables as hypotheses. Topologically, this may provide a way of extending ASD from locally compact locales to all locales (but as several previous attempts to do this have failed, I'm making no promises here). THE CONVERSE (b) - embedding a given AU in a model of ASD. There are numerous constructions and characterisations of categories of domains using "bases", "information systems", "approximable relations" etc., most notably that in Dana Scott's 1982 "Domains for Denotational Semantics" that defined what have since become known as Scott domains. In these, each domain is encoded as a set of tokens, possibly with other structure such as a closure condition, and each continuous function is encoded as a relation between tokens. Although these constructions were almost invariably presented in very concrete language with "set" meaning "set", the categorically astute observer will notice that they need far less than full set theory in the metalanguage. In fact they require - cartesian products (products) - sets of solutions of equations (equalisers) - disjoint unions (extensivity - stable disjoint coproducts) - relations considered as a notion of function (regularity - stable image factorisation) - relations considered as a notion of equality (exactness - stable effective quotients of equivalence relations) - definition by description and - recursion over lists (free monoids), where the formal categorical names are given in brackets for the various notions that are to be found in a first year "Discrete Math" course. All but the last define a PRETOPOS, and including the last we have an ARITHMETIC UNIVERSE (AU). One way to construct a model of ASD around an AU would be as the category of "abstract bases" and "abstract matrices" defined in my paper "Computably based locally compact spaces". (My abstract bases are similar to the "strong proximity lattices" used by Achim Jung and others to characterise stably locally compact spaces.) However, such a construction would be rather difficult - and unnecessarily so, as "Subspaces in ASD" already provides a general way of adding the monadic property to a given category that has powers of an object Sigma. All we need, therefore, is a category in which the given AU embeds as a full subcategory, in which there are powers of an object Sigma. In classical terms, a suitable such category would be that of disjoint unions of algebraic lattices, with Scott-continuous maps. For convenience, we call such a disjoint union a "predomain". An "information system" construction would encode a predomain as a family of sets of tokens, each set being equipped with a finitary closure relation. The members of the family correspond to the components of the disjoint union. A "family of sets" can be encoded in an AU as a single morphism, and a relation as a subobject. The morphisms are "approximable relations", which are also encoded as subobjects. This category has finite products and stable disjoint coproducts, and the given AU is embedded as a full subcategory: an object N of the AU becomes the predomain encoded as the N-indexed family of empty sets (the morphism 0->N). Sigma is encoded as the family consisting of a single singleton (the morphism 1->1). The exponential Sigma^X exists for any predomain X, encoded as the family whose one member is the set of finite sets of tokens of X - this is where the free semilattice comes in. One striking but actually very simple property of this category of predomains is that Sigma classifies subobjects in the AU: U ----> 1 v | | |--- | top | | v v N ----> Sigma That is, Sigma has exactly the defining property of a subobject classifier (Omega), as if the AU were an elementary topos - except that the object Sigma belongs to the larger category of predomains, not to the given AU. This property is achieved by the same sleight of hand that often makes category theory so powerful - we may encode objects and morphisms of a category as we please, in this case as subobjects (it would be better to say monomorphisms) of a given category. Besides having powers of Sigma and embedding the AU exactly as its full subcategory of overt discrete objects, the category of predomains obeys the Phoa principle, its morphisms are all Scott continuous and its objects are Sigma-split subspaces of Sigma^N. Its "monadic completion" (using "Subspaces in ASD") is therefore exactly the kind of category that is discussed in "Computably based locally compact spaces". In particular, no new overt discrete objects are added by these constructions: the given AU is embedded (up to equivalence) as exactly the full subcategory of overt discrete objects. It seems to me that the "equivalence" between AUs and ASD that is established by these two results should be very significant. Andre' Joyal originally introduced AUs because they are the minimal natural categorical structure in which one can form the free internal thing of the same kind. Since any AU can be embedded in a model of ASD, we can use domain theoretic methods (of which my new paper is a clumsy simple example) to construct free internal algebras (including free categories) and cofree internal coalgebras. The semantics of WHILE programs given in "first order" terms using coequalisers in Section 6.4 of "Practical Foundations" is really the same thing as the better known "higher order" domain-theoretic fixed point semantics. On the other hand, we may construct the free internal AU as a subcategory of the free internal model of ASD. Paul Taylor www.cs.man.ac.uk/~pt pt@cs.man.ac.uk University of Manchester ("East London Campus") From rrosebru@mta.ca Fri May 7 06:29:48 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 07 May 2004 06:29:48 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BM1bU-0007Rs-00 for categories-list@mta.ca; Fri, 07 May 2004 06:25:12 -0300 Message-ID: <40990B35.409@durham.ac.uk> Date: Wed, 05 May 2004 16:41:41 +0100 From: Susan Bates User-Agent: Mozilla/5.0 (Windows; U; Windows NT 5.0; en-US; rv:1.0.1) Gecko/20020823 Netscape/7.0 (CK-ITS) X-Accept-Language: en-us, en MIME-Version: 1.0 To: categories@mta.ca Subject: categories: jobs: 4 LECTURERS IN COMPUTER SCIENCE Content-Type: text/plain; charset=us-ascii; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 4 UNIVERSITY OF DURHAM DEPARTMENT OF COMPUTER SCIENCE 4 Lecturer Posts Up to 4 appointments will be made at the level of Lecturer. It is expected that applicants will range from young researchers who have just completed their PhDs through to established academics with internationally-leading research profiles. Common to all appointments will be a high quality research portfolio or demonstrable potential of such. All positions are tenable from 1st September 2004 or from a mutually acceptable date thereafter. Further particulars can be obtained from the University's jobs pages at: https://jobs.dur.ac.uk/home.asp The Department of Computer Science has recently appointed 8 new members of academic staff, 7 of whom are due to arrive in Durham in summer 2004 and 1 at a later date (see http://www.durham.ac.uk/computer.science for more details). This second phase of our recruitment will take the number of full-time permanent academic staff up to 20, with the intention being to increase this number to 25 by 2006. The appointments will be split across the 2 research groups, which are Theoretical Computer Science, and Software Engineering and Distributed Systems. 2 Lectureships will support the new Professor of Computer Science, Professor Hajo Broersma, and 2 Lectureships will support the Software Engineering and Distributed Systems research group. As regards the 2 Lectureships in Theoretical Computer Science, applications are welcomed from candidates with research interests ranging across the subject, but applications are particularly encouraged from candidates with research interests in: algorithmic graph theory; computational complexity; graph theory and combinatorics; communications networks; and probabilistic and randomised algorithms. As regards the 2 Lectureships in Software Engineering and Distributed Computing, applications are welcomed from candidates whose research interests lie within the broad area covered by these subjects. However, applicants with research interests in visualisation and distributed architectures as they relate to e-Science or in inter-disciplinary applications are particular welcome. Applicants unsure as to whether their research expertise falls under that described above are encouraged to informally contact Professor Iain Stewart who can provide advice and guidance. As mentioned earlier, the first phase of our reorganisation commenced with the advertisement of positions in October 2003. Given that about 7 months have elapsed since then and previous applicants personal details may have changed considerably in that time, previous applicants for the positions advertised in October 2003 are encouraged to re-apply if they feel that their situation merits it. Again, any previous applicants who are undecided should contact Professor Iain Stewart for advice and guidance. Further details on the University of Durham can be found via the web-pages at http://www.durham.ac.uk, and on the Department of Computer Science via the web-pages at http://www.durham.ac.uk/computer.science. Informal enquiries about any of the positions may be made to Professor Iain Stewart: telephone +44 (0)191 3341720; e-mail i.a.stewart@durham.ac.uk. From rrosebru@mta.ca Fri May 7 06:29:48 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 07 May 2004 06:29:48 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BM1e1-0007mK-00 for categories-list@mta.ca; Fri, 07 May 2004 06:27:49 -0300 Message-ID: <20040507052915.76625.qmail@web12207.mail.yahoo.com> Date: Thu, 6 May 2004 22:29:15 -0700 (PDT) From: Galchin Vasili Subject: categories: Naive question: game semantics vs game theory To: cat group MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 5 Hello, What relation if any is there between game semantics and game theory a la von Neumann/Nash? Also what is relationship between game theory in model theory and von Neumann/Nash game theory? Kind regards, Bill Halchin From rrosebru@mta.ca Mon May 10 04:35:42 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 10 May 2004 04:35:42 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BN5EZ-0006wm-00 for categories-list@mta.ca; Mon, 10 May 2004 04:29:55 -0300 Date: Fri, 07 May 2004 12:32:10 +0100 From: Peter McBurney User-Agent: Mozilla/5.0 (X11; U; Linux i686; en-US; rv:1.0.2) Gecko/20030708 X-Accept-Language: en-us, en MIME-Version: 1.0 To: Subject: categories: Re: Naive question: game semantics vs game theory References: <20040507052915.76625.qmail@web12207.mail.yahoo.com> Content-Type: text/plain; charset=us-ascii; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 6 Bill -- One difference is that von Neumann/Nash games typically assume a payoff (a reward or loss) to participants upon termination of the game, whereas the abstract games discussed in game semantics usually do not assume this. Players in the latter either just win or lose, or the game is drawn, at termination; there is no other reward to the players. Accordingly, the games of game semantics are closer in spirit and design to the dialogue games studied and played by philosophers since at least the time of Aristotle, and which now form the basis for design of computer interaction protocols. Presumably the reseach funding agencies who sponsored Aristotle's research will be pleased that it is, at long last, being exploited commercially! Best, -- Peter McBurney University of Liverpool From rrosebru@mta.ca Tue May 11 04:14:08 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 11 May 2004 04:14:08 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BNRQR-0005Fw-00 for categories-list@mta.ca; Tue, 11 May 2004 04:11:39 -0300 Message-Id: <5.2.0.9.0.20040510085027.01b18198@pop.cwru.edu> X-Sender: cxm7@pop.cwru.edu (Unverified) X-Mailer: QUALCOMM Windows Eudora Version 5.2.0.9 Date: Mon, 10 May 2004 09:00:52 -0400 To: categories@mta.ca From: Colin McLarty Subject: categories: Re: Naive question: game semantics vs game theory In-Reply-To: References: <20040507052915.76625.qmail@web12207.mail.yahoo.com> Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii"; format=flowed Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 7 At 12:32 07/05/2004 +0100, Peter McBurney wrote: >One difference is that von Neumann/Nash games typically assume a payoff >(a reward or loss) to participants upon termination of the game, whereas >the abstract games discussed in game semantics usually do not assume >this. That is a nice point. In consequence, so far as I know, no one is interested in `mixed strategies' for games in set theory or semantics. There is no sense to the `average/expected payoff' for a randomized strategy as there is no payoff. Mixed strategies are the focus of most economic and such uses of game theory. The usual question is how to find optimal mixed strategies when there is no winning one. The usual question for games in set theory or semantics is just whether one player has a winning strategy. That is the only question in the uses I know of. From rrosebru@mta.ca Tue May 11 04:14:08 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 11 May 2004 04:14:08 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BNRP2-0005D1-00 for categories-list@mta.ca; Tue, 11 May 2004 04:10:12 -0300 Date: Mon, 10 May 2004 09:16:28 -0300 From: "Robert J. MacG. Dawson" Subject: categories: Re: Naive question: game semantics vs game theory To: categories@mta.ca Message-id: <409F729C.2875CBB0@stmarys.ca> MIME-version: 1.0 X-Mailer: Mozilla 4.7 [en] (WinNT; U) Content-type: text/plain; charset=us-ascii Content-transfer-encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 8 Peter McBurney wrote: > > Bill -- > > One difference is that von Neumann/Nash games typically assume a payoff > (a reward or loss) to participants upon termination of the game, whereas > the abstract games discussed in game semantics usually do not assume > this. Although it seems that three-player generalizations of the latter type of games may need something more nuanced than just "win" or "lose" to ensure that there is not a situation in which a player who cannot himself win may make an arbitrary choice of which other player does so. One obvious solution is to declare a "winner" and "loser" [who has to pay the winner, wash the winner's car, or whatever], and (for instance,in a Nim-type game) to declare that the player due to play immediately after the winner is the loser. It is then not a matter of indifference to any player how the game turns out. However, there are wheels within wheels: for in a game that is not completely trivial [a trivial game would be like Nim with N piles of size 1, in which there are no bad moves] there is the possibility that the player who is due to come in second if everybody plays to maximize their immediate position may choose to "throw" the game, moving to third place and putting the erstwhile loser into the lead. This would be an irrational play on its own, but in combination with a pact for the new leader to throw the game in turn, both conspirators would end up ahead of their original positions. The question now is - is there honor among hustlers? Will the original loser renege? Can the pact be enforced? This lands us fair and square in the middle of the von Neumann/Nash kind of game theory. What if anything this says about generalizations of game sematics I do not know. John H. Conway told me when I was a graduate student that this area was under active investigation by somebody or other, but I haven't heard of anything that came of it. -Robert Dawson From rrosebru@mta.ca Tue May 11 16:04:03 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 11 May 2004 16:04:03 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BNcNW-0000pZ-00 for categories-list@mta.ca; Tue, 11 May 2004 15:53:22 -0300 Date: Tue, 11 May 2004 18:45:08 +0200 From: bourn User-Agent: Mozilla/5.0 (Windows; U; Windows NT 5.0; fr-FR; rv:1.0.2) Gecko/20021120 Netscape/7.01 X-Accept-Language: fr-fr, fr MIME-Version: 1.0 To: categories@mta.ca Subject: categories: book: Mal'cev, Protomodular, Homological and Semi-Abelian Categories Content-Type: text/plain; charset=us-ascii; format=flowed Content-Transfer-Encoding: 7bit X-ULCO-MailScanner-Information: Please contact the ISP for more information X-ULCO-MailScanner: Found to be clean Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 9 This is to announce the publication of the following book Truly yours Francis Borceux and Dominique Bourn Mal'cev, Protomodular, Homological and Semi-Abelian Categories -------------------------------------------------------------- by Francis Borceux and Dominique Bourn Mathematics and its Applications, volume 566, 2004 Kluwer Academic Publishers, Dordrecht, Boston, London ISBN 1-4020-1961-0 The purpose of the book is to take stock of the situation concerning Algebra via Category Theory in the last fifteen years, where the new and synthetic notions of Mal'cev, protomodular, homological and semi-abelian categories emerged. These notions force attention on the fibration of points and allow a unified treatment of the main algebraic: homological lemmas, Noether isomorphisms, commutator theory. The book gives full importance to examples and makes strong connections with Universal Algebra. One of its aims is to allow appreciating how productive the essential categorical constraint is: knowing an object, not from inside via its elements, but from outside via its relations with its environment. The book is intended to be a powerful tool in the hands of researchers in category theory, homology theory and universal algebra, as well as a textbook for graduate courses on these topics. The table of contents is the following: Preface Metatheorems ------------ 0.1 The Yoneda embedding 0.2 Pointed categories 1. Intrinsic centrality ----------------------- 1.1 Spans and relations 1.2 Unital categories 1.3 Cooperating and central morphisms 1.4 Commutative objects 1.5 Symmetrizable morphisms 1.6 Regular unital categories 1.7 Associated abelian object 1.8 Strongly unital categories 1.9 Gregarious objects 1.10 Linear and additive categories 1.11 Antilinear and antiadditive categories 1.12 Complemented subobjects 2. Mal'cev categories --------------------- 2.1 Slices, coslices and points 2.2 Mal'cev categories 2.3 Abelian objects in Mal'cev categories 2.4 Naturally Mal'cev categories 2.5 Regular Mal'cev categories 2.6 Connectors in Mal'cev categories 2.7 Connector and cooperator 2.8 Associated abelian object and commutator 2.9 Protoarithmetical categories 2.10 Antilinear Mal'cev categories 2.11 Abelian groupoids 3. Protomodular categories -------------------------- 3.1 Definition and examples 3.2 Normal subobjects 3.3 Couniversal property of the product 3.4 Groupoids, protomodularity and normality 4. Homological categories ------------------------- 4.1 The short five lemma 4.2 The nine lemma 4.3 The Noether isomorphism theorems 4.4 The snake lemma 4.5 The long exact homology sequence 4.6 Examples of homological categories 5. Semi-abelian categories -------------------------- 5.1 Definition and examples 5.2 Semi-direct products 5.3 Semi-associative Mal'cev varieties 6. Strongly protomodular categories ----------------------------------- 6.1 Centrality and normality 6.2 Normal subobjects in the fibres 6.3 Normal functors 6.4 Strongly protomodular categories 6.5 A counterexample 6.6 Connector and cooperator 7. Essentially affine categories -------------------------------- 7.1 The fibration of points 7.2 Essentially affine categories 7.3 Abelian extensions Appendix -------- A.1 Algebraic theories A.2 Internal relations A.3 Internal groupoids A.4 Variations on epimorphisms A.5 Regular and exact categories A.6 Monads A.7 Fibrations Classification table of the fibration of points From rrosebru@mta.ca Tue May 11 16:05:08 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 11 May 2004 16:05:08 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BNcQv-00018e-00 for categories-list@mta.ca; Tue, 11 May 2004 15:56:53 -0300 From: "Marta Bunge" To: categories@mta.ca Subject: categories: note, review, preprint Date: Tue, 11 May 2004 14:09:48 -0400 Mime-Version: 1.0 Content-Type: text/plain; format=flowed Message-ID: Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 10 This is to call attention to three recent items in my homepage. 1) A note: "On a class of pullbacks preserved by the presheaf functor" (with J.Funk, in connection with ongoing work with M.Jibladze and T. Streicher). http://www.math.mcgill.ca/~bunge/pbthm.dvi (pbthm.ps) 2) A review of F.W.Lawvere and S.Schanuel, "Matematicas Conceptuales", Siglo XXI, Mexico, 2002. In Spanish. (Translation only on request and eventually.) http://www.math.mcgill.ca/~bunge/LS.dvi (LS.ps, LS.pdf) 3) A preprint "Definable completeness" (with J.Funk, M.Jibladze, and T. Streicher), to appear in Cahiers de Top. et Geo. Diff. Categoriques. http://www.math.mcgill.ca/~bunge/defcomp.dvi (defcomp.ps) Please let me know if you have any problems downloading. Greetings, Marta Bunge **************************************************************************** Marta Bunge Professor Emerita Dept of Mathematics and Statistics McGill University 805 Sherbrooke St. West Montreal, QC, Canada H3A 2K6 T: (514) 398-3810 F: (514) 933-8741 marta.bunge@mcgill.ca http://www.math.mcgill.ca/~bunge ************************************************ From rrosebru@mta.ca Thu May 13 04:17:50 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 13 May 2004 04:17:50 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BOANI-00001E-00 for categories-list@mta.ca; Thu, 13 May 2004 04:11:24 -0300 Date: Wed, 12 May 2004 18:12:20 -0600 (MDT) From: robin@cpsc.ucalgary.ca Subject: categories: FMCS 2004 To: categories@mta.ca MIME-Version: 1.0 Content-Type: TEXT/plain; charset=us-ascii Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: RO X-Status: X-Keywords: X-UID: 11 Final announcement for FMCS 2004: ------------------------------------------------------------------------- FFFFFFF M M CCC SSS F MM MM C S FFFFF M MM M C SSS F M M C S F M M CCC SSS 2004 (CALGARY) ------------------------------------------------------------------------- http://pages.cpsc.ucalgary.ca/~robin/FMCS/FMCS_04/index.html ------------------------------------------------------------------------- This year's meeting on Foundational Methods in Computer Science (FMCS 2004) will be hosted by the Programming Languages Group at the University of Calgary, June 4th -- June 6th and will be held at the Kananaskis Field Station. Next years meeting will be in Vancouver at UBC. ------------------------------------------------------------------------- FOUNDATIONAL METHODS IN COMPUTER SCIENCE The workshop is an informal meeting to bring together researchers in mathematics and computer science with a focus on the applications of category theory in computer science. It is a three day meeting, June 4th-6th which includes tutorials by: -- Andrea Schalk: Double Gluing -- Pieter Hofstra: Realizability -- Phil Scott: Geometry of Interaction -- Ernie Manes: Guarded Semigroups and has two days of contributed research talks. If you wish to participate please let us know before 21st May 2004. If, in addition, you wish to give a presentation you must provide an abstract and title to Robin Cockett or Craig Pastro (see e-mail address below) before Friday 21st May (although we appreciate notification on this as early as possible). Student participation at FMCS is particularly encouraged. __________________________________________________________ Organizer: Robin Cockett (robin at cpsc.ucalgary.ca) Local organizer: Craig Pastro (pastroc at cpsc.ucalgary.ca) From rrosebru@mta.ca Sat May 15 15:39:28 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 15 May 2004 15:39:28 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BP3zi-0002kO-00 for categories-list@mta.ca; Sat, 15 May 2004 15:34:46 -0300 From: Topos8@aol.com Message-ID: <110.32145623.2dd7aeae@aol.com> Date: Sat, 15 May 2004 13:34:38 EDT Subject: categories: Error in "Omega Categories I" To: categories@mta.ca MIME-Version: 1.0 Content-Type: text/plain; charset="US-ASCII" Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 12 Peter May and another colleague have kindly pointed out to me that section 6 of my paper "Omega Categories I" is complete rubbish. In that section I claimed to offer a simple proof of the Baez-Dolan stabilization conjecture but clearly I have completely misunderstood the substance of that conjecture. I expect to have more to say on this subject another day but meantime will be content with the observation that the rest of the paper is independent of the seriously flawed section 6. I offer my apology to those who were mislead or confused by that section of the paper and would like to thank Peter et. al. for their interest and help. Carl Futia From rrosebru@mta.ca Sat May 15 15:39:28 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 15 May 2004 15:39:28 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BP3zC-0002j6-00 for categories-list@mta.ca; Sat, 15 May 2004 15:34:14 -0300 Message-ID: <40A49BF5.4030508@csc.liv.ac.uk> Date: Fri, 14 May 2004 11:14:13 +0100 From: Peter McBurney User-Agent: Mozilla/5.0 (X11; U; Linux i686; en-US; rv:1.0.2) Gecko/20030708 X-Accept-Language: en-us, en MIME-Version: 1.0 To: CATEGORIES LIST Subject: categories: CFP: Logic, Games and Philosophy: Foundational Perspectives Content-Type: text/plain; charset=windows-1252; format=flowed Content-Transfer-Encoding: quoted-printable X-MIME-Autoconverted: from 8bit to quoted-printable by tethys.server.csc.liv.ac.uk id i4EAEDf12886 Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 13 * With apologies for multiple posting ** =09 CALL FOR PAPERS Logic, Games and Philosophy: Foundational Perspectives Prague International Colloquium www.flu.cas.cz/Logica/Aconf/col2004.html Organised by Department of Logic, Institute of Philosophy, Academy of Sciences of the Czech Republic, and Department of Philosophy, University of Helsinki 28 September =E2=80=93 1 October 2004, Prague, Czech Republic SYNOPSIS Games, like logics, are tools for investigating the world, language, and their relationship. Semantic, dialogic, evolutionary, interrogative, argumentative, and pragmatic methods have been included into the toolkit. Following the recent increase in investment on games and game-theoretic methods in logic, language, computation and communication, we still need = a better understanding of the possibilities of forming converging methodologies underlying these diverse contemporary currents. The purpose= of the Prague Conference on Logic, Games and Philosophy: Foundational Perspectives is to explore the interfaces between logic and games with th= e eye on philosophical, methodological and foundational issues. Preference is given to papers that make a definite contribution to philosophical, methodological and foundational issues underlying game-theoretic approaches to logical, computational or linguistic researc= h, including relevant historical and philosophical issues on the Theory of Games itself. Relevant topics include, but are not limited to: * Wittgenstein, C. S. Peirce * Language Games * Game-Theoretic Semantics * Dialogue Games * Interrogative Games/Philosophy of Science * Evolutionary Games * Diachronicity/Semantic-Pragmatic Change * Game-Theoretic Methods in Logic, Language, Computation, Communication Among the invited speakers of the colloquium are Mathieu Marion (Qu=C3=A9= bec =C3 Montr=C3=A9al), Shahid Rahman (Lille 3), Gabriel Sandu (Helsinki), Wim Ve= ldman (Nijmegen). Potential contributors are asked to submit a two page (including referenc= es) abstract; the deadline is 15 June 2004. Abstracts are to be submitted by e-mail (preferably as PDF, PS or MS Word files) prepared for anonymous reviewing. (To prevent problems caused by e-mail failures, the receipt of every abstract will be confirmed within one week.) Notification of acceptance will be distributed by 15 July 2004. Contributed papers are scheduled for approx. 40 minutes (including discussion). Please direct your abstracts to: lanna@site.cas.cz The proceedings of the Prague International Colloquium will be offered to Kluwer Academic Publishers for inclusion in their series Logic, Epistemol= ogy and the Unity of Science (the papers will be reviewed). If you need more information, please contact us at: lanna@site.cas.cz The conference website is http://www.flu.cas.cz/Logica/Aconf/col2004.html Program Committee: Gabriel Sandu (Chair, Helsinki) Johan van Benthem (Amsterdam, Stanford) Mathieu Marion (Qu=C3=A9bec =C3 Montr=C3=A9al) =09 Jaroslav Peregrin (Prague)=09 Ahti-Veikko Pietarinen (Helsinki) Shahid Rahman (Lille 3) Tero Tulenheimo (Helsinki) Wim Veldman (Nijmegen) Organising Committee: Ondrej Majer (Prague) Ahti-Veikko Pietarinen (Helsinki) Tero Tulenheimo (Helsinki) -------------------------------------------------------------------------= - From rrosebru@mta.ca Mon May 17 15:13:03 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 17 May 2004 15:13:03 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BPmX0-0004zd-00 for categories-list@mta.ca; Mon, 17 May 2004 15:08:06 -0300 From: Markus Michelbrink Subject: categories: jobs: Professorships, Readerships, Lectureships, Tutorships Date: Mon, 17 May 2004 14:34:03 +0100 User-Agent: KMail/1.5.4 To: categories@mta.ca MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit Content-Disposition: inline Message-Id: <200405171434.03906.m.michelbrink@swan.ac.uk> Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 14 ** With apologies for multiple posting ** Professorships, Readerships, Lectureships, Tutorships. ====================================================== The department of computer science at Swansea (Wales, UK) is currently advertising academic positions at all levels. We hope expecially to expand our groups in visual computing and in logic/theoretical computer science. Our department was rated 5 in the last research assessment exericse. It has a strong group in logic and theoretical computer science which is amongst the biggest in UK. The members of that group are Ulrich Berger (proof theory, computability theory, type theory), Phil Grant (artificial intelligence), Andy Gimblett (algebraic specification), Neal Harman (hardware verification, models of computation, algebraic specification), Oliver Kullmann (satisfiability problems), Markus Michelbrink (category theory, proof theory, type theory), Faron Moller (automata theory, modal and temporal logic), Markus Roggenbach (algebraic specification), Monika Seisenberger (proof theory, type theory, computability theory), Anton Setzer (proof theory, type theory) and John Tucker (algebraic specification, algebraic methods, computability theory). We have as well strong links to the mathematics department, with Roger Hindley (lambda-calculus) and Jiang-Lun Wu (nonstandard analysis). The deadline for application is 25 June 2004 (I have been signalled that late applications might still be acceptable). The official advertisements can be found at http://www.jobs.ac.uk/jobfiles/IS433.html and http://www.jobs.ac.uk/jobfiles/IS434.html -- ----------------------------------------------------------------------------- Anton Setzer Telephone: Department of Computer Science (national) (01792) 513368 University of Wales Swansea (international) +44 1792 513368 Singleton Park Fax: Swansea SA2 8PP (national) (01792) 295708 UK (international) +44 1792 295708 Visiting address: Email: a.g.setzer@swan.ac.uk Faraday Building, WWW: Computer Science Dept. http://www.cs.swan.ac.uk/~csetzer/ 2nd floor, room 211. ---------------------------------------------------------------------------- -- ------------------------------------------------------- -- Dr. Markus Michelbrink Dept. of Computer Science University of Wales Swansea Singleton Park Swansea SA2 8PP United Kingdom From rrosebru@mta.ca Mon May 17 15:13:03 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 17 May 2004 15:13:03 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BPmWL-0004x8-00 for categories-list@mta.ca; Mon, 17 May 2004 15:07:25 -0300 Date: Mon, 17 May 2004 11:37:33 +0200 From: Ralf Treinen To: categories@mta.ca Subject: categories: UNIF 2004 workshop @ IJCAR : extended deadline Message-ID: <20040517093733.GD10945@figue.lsv.ens-cachan.fr> Mime-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Content-Disposition: inline User-Agent: Mutt/1.4.1i Organization: LSV, CNRS UMR 8643, ENS de Cachan Content-Transfer-Encoding: quoted-printable Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 15 Call for Papers/Abstracts/System descriptions ***** Deadline extentended until Friday, Mai 21 ******* UNIF 2004 18th International Workshop on Unification July 4-5, 2004, Cork, Ireland Affiliated with IJCAR'04 http://www.faculty.iu-bremen.de/mkohlhase/event/unif04/ UNIF is the main international meeting on unification. Unification is concerned with the problem of identifying given terms, either syntactically or modulo a given logical theory. Syntactic unification is the basic operation of most automated reasoning systems, and unification modulo theories can be used, for instance, to build in special equational theories into theorem provers. The aim of UNIF 2004, as that of the previous meetings, is to to bring together people interested in unification, present recent (even unfinished) work, and discuss new ideas and trends in unification and related fields. In particular, it is intended to offer a good opportunity for young researches and researchers working in related areas to get an overview of the current state of the art in unification theory and get in contact with the experts in the field. ---------------------------------------------------------------------- TOPICS OF INTEREST ---------------------------------------------------------------------- A non-exclusive list of topics of interest is: * Unification * E-unification * Unification Algorithms=20 * Higher-Order Unification=20 * String Unification=20 * Context Unification=20 * Combination problems=20 * Disunification=20 * Typed Unification * Related Topics * Constraint Solving=20 * Tree Descriptions=20 * Matching=20 * Narrowing * Applications * Type Checking and Type Inference=20 * Automated Deduction=20 * Rewriting=20 * Functional and Logic Programming=20 * Grammars=20 * Computational Linguistics * Implementations ---------------------------------------------------------------------- INVITED SPEAKERS ---------------------------------------------------------------------- There will be two invited speakers. =20 ---------------------------------------------------------------------- IMPORTANT DATES ---------------------------------------------------------------------- NEW: Deadline for electronic submission: Friday, May 21, 2004 Email: unif04@iu-bremen.de Notification of acceptance: Monday, May 24, 2004 Deadline for camera-ready papers: Monday, June 7, 2004 Workshop: July 4 - 5, 2004 ---------------------------------------------------------------------- SUBMISSION DETAILS ---------------------------------------------------------------------- Authors are invited to submit via email an abstract (1-5 pages), a paper (no longer than 15 pages), or a system description (no more than 5 pages) in Postscript or PDF format to: unif04@iu-bremen.de before May 14, 2004. Authors are encouraged to use LaTeX2e and the Springer llncs class. ---------------------------------------------------------------------- PUBLICATION ---------------------------------------------------------------------- Accepted papers, abstracts and system descriptions will be included in th= e proceedings which will be available at the workshop. ---------------------------------------------------------------------- ORGANIZING COMMITTEE ---------------------------------------------------------------------- Michael Kohlhase (International University Bremen, Germany) Hitoschi Ohsaki (National Institute of Advanced Industrial Sc= ience=20 and Technology, Amagasaki, Japan) Steve Prestwich (Universtity College, Cork, Ireland) Ralf Treinen (Ecole Normale Superieure, Cachan, France) Manfred Schmidt-Schauss (Johann Wolfgang Goethe-Universit"at Frankfur= t am Main, Germany) --=20 Ralf Treinen Laboratoire Sp=E9cification et V=E9rification CNRS & =C9cole Normale Sup=E9rieure de Cachan http://www.lsv.ens-cachan.fr/~treinen From rrosebru@mta.ca Mon May 17 15:13:03 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 17 May 2004 15:13:03 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BPmVi-0004ux-00 for categories-list@mta.ca; Mon, 17 May 2004 15:06:46 -0300 From: Wan.Fokkink@cwi.nl Date: Mon, 17 May 2004 11:36:07 +0200 (MEST) Message-Id: To: categories@mta.ca Subject: categories: SOS Workshop - final CfP Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 16 Call for Papers Structural Operational Semantics http://www.cs.auc.dk/~luca/SOS-WORKSHOP/ A Satellite Workshop of CONCUR 2004 30 August, 2004, London, United Kingdom Structural operational semantics (SOS) provides a framework for giving operational semantics to programming and specification languages. A growing number of programming languages from commercial and academic spheres have been given usable semantic descriptions by means of structural operational semantics. Because of its intuitive appeal and flexibility, structural operational semantics has found considerable application in the study of the semantics of concurrent processes. Moreover, it is becoming a viable alternative to denotational semantics in the static analysis of programs, and in proving compiler correctness. Recently, structural operational semantics has been successfully applied as a formal tool to establish results that hold for classes of process description languages. This has allowed for the generalization of well-known results in the field of process algebra, and for the development of a meta-theory for process calculi based on the realization that many of the results in this field only depend upon general semantic properties of language constructs. The proposed SOS workshop aims to be a forum for researchers, students and practitioners interested in new developments and directions for future investigation in the field of structural operational semantics. One of the specific goals of the workshop is to establish synergies between the concurrency and programming language communities working on the theory and practice of SOS. The workshop will also mark the publication of a special issue of the Journal of Logic and Algebraic Programming, devoted to SOS. Together with original research papers on SOS, this special issue will feature a definitive version of Gordon Plotkin's 1981 DAIMI memo on SOS, together with a piece by Plotkin on the origins of SOS. Specific topics of interest include (but are not limited to): * programming languages * process algebras * higher-order formalisms * rule formats for operational specifications * meaning of operational specifications * comparisons between denotational, axiomatic and SOS * compositionality of modal logics with respect to operational specifications * congruence with respect to behavioural equivalences * conservative extensions * derivation of proof rules from operational specifications * software tools that automate, or are based on, SOS Papers reporting on applications of SOS to software engineering and other areas of computer science are welcome. Paper submission: We solicit unpublished papers reporting on original research on the general theme of SOS. Prospective authors are invited to submit a pdf or postscript file with their extended abstract, whose length should not exceed 15 pages, by email to all of the co-chairs at their respective email addresses. The email message with the submission should also include, in plain text, contact information for the author(s), together with the title and abstract of the submission. Submissions are to be received by Sunday, 6 June, 2004. Authors will be notified of acceptance by Wednesday, 30 June, 2004. Submissions from the PC members are allowed. Proceedings: Preliminary proceedings containing the abstracts of the talks will be published as a volume in the BRICS Notes Series, and will be available at the meeting. The final proceedings of the workshop will appear as a volume in the ENTCS series. If the quality and quantity of the submissions warrant it, the co-chairs plan to arrange a special issue of an archival journal devoted to full versions of selected papers from the workshop. Important Dates: * Submission: Sunday 6 June 2004 * Notification: Wednesday 30 June 2004 * Final version: Friday July 16 2004 * Workshop: Monday 30 August 2004 Invited Speakers: Andrew Pitts (Cambridge, United Kingdom) Gordon Plotkin (Edinburgh, United Kingdom) (To be confirmed) Program Committee: Luca Aceto (BRICS, Aalborg, Denmark, co-chair) Wan Fokkink (CWI, The Netherlands, co-chair) Rob van Glabbeek (NICTA, Sydney, Australia) Ralf Laemmel (CWI, The Netherlands) Peter Mosses (BRICS, Aarhus, Denmark) David Sands (Chalmers, Sweden) Alex Simpson (Edinburgh, United Kingdom) Simone Tini (Insubria, Italy) Irek Ulidowski (Leicester, United Kingdom, co-chair) Erik de Vink (Eindhoven, The Netherlands) Organizing Committee: Luca Aceto, email: luca AT cs.auc.dk, Wan Fokkink, email: wan AT cwi.nl, Irek Ulidowski, email iu3 AT mcs.le.ac.uk From rrosebru@mta.ca Tue May 18 17:11:31 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 18 May 2004 17:11:31 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BQArP-0003tc-00 for categories-list@mta.ca; Tue, 18 May 2004 17:06:47 -0300 X-Sender: grandis@pop4.dima.unige.it Message-Id: Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Date: Tue, 18 May 2004 16:20:24 +0200 To: categories@mta.ca From: Marco Grandis Subject: categories: the graph of an adjunction Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 17 An adjunction has a functorial mono-epi factorization, so natural to be likely well known. I would like to have a *reference* for this. Let F -| G, where F: X --> A and G: A --> X. Then our adjunction has an obvious factorisation through the isomorphic comma categories: W = (F | A) = (X | G) using the full coreflective embedding of X in W, and the full reflective embedding of A in W. W might be called the 'graph' of the adjunction; or has it been called differently? R. Pare and myself, we have used a similar result for double categories, for a colax double functor left adjoint to a lax one: Thm. 3.7 in 'Adjoints for double categories', to appear in 'Cahiers'. But I need now the result for ordinary categories, for applications to directed homotopy. Best regards Marco Grandis From rrosebru@mta.ca Thu May 20 18:58:08 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 20 May 2004 18:58:08 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BQvUz-00041l-00 for categories-list@mta.ca; Thu, 20 May 2004 18:54:45 -0300 X-Sender: grandis@pop4.dima.unige.it Message-Id: Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Date: Thu, 20 May 2004 15:03:12 +0200 To: categories@mta.ca From: Marco Grandis Subject: categories: Preprint: The shape of a category up to directed homotopy Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 18 The following preprint is available: M. Grandis, The shape of a category up to directed homotopy, Dip. Mat. Univ. Genova, Preprint 509 (May 2004), 44 p. Abstract. This work is a contribution to a recent field, Directed Algebraic Topology. Categories which appear as fundamental categories of 'directed structures', e.g. ordered topological spaces, have to be studied up to appropriate notions of directed homotopy equivalence, wider than ordinary equivalence of categories. Here we introduce 'past' and 'future equivalences' of categories - sort of symmetric versions of an adjunction - and use them and their combinations to get 'directed models' of a category; in the simplest case, these are the join of the least full reflective and the least full coreflective subcategory. MSC: 55Pxx, 18A40, 68Q85. Keywords: homotopy theory, adjunctions, reflective subcategories, directed algebraic topology, fundamental category, concurrent processes . Available as pdf or ps: http://www.dima.unige.it/~grandis/Shp.pdf http://www.dima.unige.it/~grandis/Shp.ps With best regards Marco Grandis Dipartimento di Matematica Universita` di Genova via Dodecaneso 35 16146 GENOVA, Italy e-mail: grandis@dima.unige.it tel: +39.010.353 6805 fax: +39.010.353 6752 http://www.dima.unige.it/~grandis/ From rrosebru@mta.ca Thu May 20 18:59:27 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 20 May 2004 18:59:27 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BQvY1-00049k-00 for categories-list@mta.ca; Thu, 20 May 2004 18:57:53 -0300 Date: Thu, 20 May 2004 19:13:09 +0100 (BST) From: Paul B Levy To: categories@mta.ca Subject: categories: existence of initial algebras Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 19 Hi, I was teaching some students recently that there are 2 kinds of inductive definition of a set: (a) By giving an "ambient" set A, and a family of relations A^{n}-->A. This defines the least subset of A closed under all these relations, i.e. the least prefixed point of the monotone endofunction on powerset(A) mapping each subset B to the set of all elements related to B. (b) By giving a signature. This defines the initial algebra for (the endofunctor on Set determined by) the signature. I also wanted to treat the countably infinitary case, so (a) could allow relations A^{omega}-->A, and (b) could allow operations of arity omega. And I wanted to further generalize both (a) and (b) to the many-sorted setting. (Though in (a), the many-sorted situation can be reduced to the single-sorted one by taking the sum of the ambient sets.) ----------------------- I then proceeded to ask them: how do we know that (a) the least prefixed point and (b) the initial algebra exist? For (a) I gave 3 proofs: (i) take the intersection of all such subsets of A (ii) start from the empty set, and iteratively apply the monotone endofunction on the powerset of A that maps C to the set of all elements related to elements of C, taking unions at countable limit ordinals and terminating at the first uncountable limit (iii) take the set of elements of A for which there exists at least one wellfounded prooftree. For (b) I gave 2 proofs: (i) start from the empty set, and iteratively apply the signature, taking colimits at countable limit ordinals and terminating at the first uncountable limit (ii) take the set of all wellfounded operation-trees. And all these 5 proofs adapt to the coinductive setting, except that (a)(ii) and (b)(i) terminate already at omega. However, coinduction was not covered in the course. --------------------------------------- I thought that (a)(iii) and (b)(ii) were actually the most important constructions to teach the students, since they describe our basic intuition. But they require an appropriate definition of "tree". In (b)(ii), an operation-tree can be thought of a strategy for the following game: - Player picks an operation c_0 from the signature, - Opponent picks an index i_0 in the arity of c_0 - Player picks an operation c_1 from the signature etc. And, as we know, there are several equivalent ways of defining strategy. I just picked one of them: a prefix-closed set sigma of Opponent-awaiting plays c_0 i_0 c_1 i_1 ... c_n subject (in this setting) to the constraint that any Player-awaiting play c_0 i_0 c_1 i_ 1 ... c_{n-1} i_{n-1} which is consistent with sigma (i.e. every Opponent-awaiting prefix is in sigma) has a unique one-place extension in sigma. With this definition of operation-tree, it was easy to complete proof (b)(ii). And (a)(iii) is similar, except that Player moves by supplying an operation together with a tuple of A-elements. My question is: where do these tree proofs appear in the literature? Surely something so basic must appear somewhere? The best I could find, for (b), was to build a set of "terms" as a subset of an ambient set of strings (they could be strings of operations, parentheses and commas, or just strings of operations). But it is quite unnecessary to use any ambient set for (b), and, besides, that method would not work for the infinitary or coinductive cases. Paul From rrosebru@mta.ca Fri May 21 17:01:45 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 21 May 2004 17:01:45 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BRGAg-0006YE-00 for categories-list@mta.ca; Fri, 21 May 2004 16:59:10 -0300 Date: Fri, 21 May 2004 04:23:48 -0400 (EDT) From: Andreas Blass X-X-Sender: ablass@liberty.math.lsa.umich.edu To: categories@mta.ca Subject: categories: Re: existence of initial algebras In-Reply-To: Message-ID: References: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 20 Some of what Paul Levy asked about --- building initial lagebras as sets of well-founded trees --- is in an old paper of mine, Words, free algebras, and coequalizers (Fund. Math. 117 (1983) 117--160), but even then the idea certainly wasn't new. That paper was concerned (partly) with what happens in varieties of algebras with infinitary operations --- so there are identities to be imposed on the terms. As a result, even the existence of free algebras with countable-ary operations depends on the axiom of choice. Andreas Blass From rrosebru@mta.ca Fri May 21 17:01:45 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 21 May 2004 17:01:45 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BRG9c-0006OW-00 for categories-list@mta.ca; Fri, 21 May 2004 16:58:05 -0300 Message-Id: <5.1.0.14.2.20040520232118.0235f070@mailbox.syr.edu> X-Sender: lglewis@mailbox.syr.edu X-Mailer: QUALCOMM Windows Eudora Version 5.1 Date: Thu, 20 May 2004 23:28:18 -0400 To: categories@mta.ca From: Gaunce Lewis Subject: categories: comparing cotriples via an adjoint pair Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii"; format=flowed Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 21 I have encountered a situation in which I have two categories C, D which are related by a pair of adjoint functors L from C to D and R from D to C. Also, there is a cotriple S on C and a cotriple T on D. Finally, there is a natural isomorphism f from RT to SR. It seems that if a couple of diagrams relating f to the structure maps of the cotriples commute, then there is an induced adjoint pair relating the two coalgebra categories. Is this, or something similar to it, in the literature in some easily referenced place? Thanks, Gaunce From rrosebru@mta.ca Fri May 21 17:02:41 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 21 May 2004 17:02:41 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BRGCp-0006qB-00 for categories-list@mta.ca; Fri, 21 May 2004 17:01:23 -0300 Message-ID: <40ADBC8B.201@mcs.le.ac.uk> Date: Fri, 21 May 2004 09:23:39 +0100 From: "V. Schmitt" X-Accept-Language: en MIME-Version: 1.0 To: categories@mta.ca, Bob Rosebrugh Subject: categories: parameterised accessiblity Content-Type: text/plain; charset=us-ascii; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 22 Dear all, I am pleased to advert a paper that has been for (too)long in limbo. I eventually put the paper on the math archive in march http://arXiv.org/abs/math.CT/0403164 I acknowledge F. Borceux that suggested me a major improvement. This work was first presented in Amiens in Nov. 03. and at the last PSSL in Cambridge (Thank you all for your feedback). Here is a short abstract. The notion of P-flatness and Q-acessibility are introduced where the prameters P and Q stand for family of indexes in the sense of Borceux-Kelly. The following points are proved. Fixing a family P of indexes and Q denoting the family of P-flat indexes: - for a small category A, a presheaf on A is P-flat if and only if it is a Q-colimit of representables. - The full subcategory of the category of presheaves on a small A generated by P-flat presheaves is the free Q-cocompletion of A. Conversely Q-accessible categories occur as categories of P-flat presheaves on small A's. This correspondence yields meaningful internal description for free-Q-cocomplete objects for suitable Q's. For instance Lawvere's Cauchy-complete categories are exactly the full subcategories of P0-flat presheaves on small A's for P0 the family of ALL indexes. Remarkably this theory of accessibility extends to the enriched context (the only constraint on the base V is that it should be sym. & closed). Actually it is very likely that the whole theory might be developed in a 2-category with a Yoneda structure. Other completions by means of P-flat preshaves may be considered. For instance one obtains this way completions of metric spaces in terms of asymmetric Cauchy-filters. One also retrieves the algebraic completions of partial orders. Best regards to you all, Vincent. From rrosebru@mta.ca Sun May 23 18:00:11 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 23 May 2004 18:00:11 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BRzzv-0005HF-00 for categories-list@mta.ca; Sun, 23 May 2004 17:55:07 -0300 Date: Fri, 21 May 2004 16:30:36 -0400 (EDT) From: Michael Barr To: Categories list Subject: categories: Re: comparing cotriples via an adjoint pair In-Reply-To: <5.1.0.14.2.20040520232118.0235f070@mailbox.syr.edu> Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 23 Although I cannot be sure, this looks an awful lot like an adjoint triple. I think Charles and I had a section of TTT on this. It was certainly not new with us and may have even been in Harry Appelgate's thesis back around 40 years ago. Michael On Thu, 20 May 2004, Gaunce Lewis wrote: > I have encountered a situation in which I have two categories C, D which > are related by a pair of adjoint functors L from C to D and R from D to > C. Also, there is a cotriple S on C and a cotriple T on D. Finally, there > is a natural isomorphism f from RT to SR. It seems that if a couple of > diagrams relating f to the structure maps of the cotriples commute, then > there is an induced adjoint pair relating the two coalgebra categories. Is > this, or something similar to it, in the literature in some easily > referenced place? > > Thanks, > Gaunce > > > > From rrosebru@mta.ca Sun May 23 18:00:11 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 23 May 2004 18:00:11 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BS025-0005Mj-00 for categories-list@mta.ca; Sun, 23 May 2004 17:57:21 -0300 Date: Sat, 22 May 2004 11:17:59 -0400 (EDT) From: Oswald Wyler To: categories@mta.ca Subject: categories: Re: comparing cotriples via an adjoint pair In-Reply-To: <5.1.0.14.2.20040520232118.0235f070@mailbox.syr.edu> Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 24 On Thu, 20 May 2004, Gaunce Lewis wrote: > I have encountered a situation in which I have two categories C, D which > are related by a pair of adjoint functors L from C to D and R from D to > C. Also, there is a cotriple S on C and a cotriple T on D. Finally, there > is a natural isomorphism f from RT to SR. It seems that if a couple of > diagrams relating f to the structure maps of the cotriples commute, then > there is an induced adjoint pair relating the two coalgebra categories. Is > this, or something similar to it, in the literature in some easily > referenced place? > > Thanks, > Gaunce This situation has been encountered since at least 1970 by various categorists, including myself. A relevant paper is: D. Pumpl\"un, Eine Bemerkung \"uber Monaden und adjungierte Funktoren, Math. Annalen 185, 329-337 (1970). If Gaunce's two commuting diagrams are the usual ones, then his conjecture is correct. Observe that in this situation, we have not just a pair but a quadruple of dual categories, replacing C and D by their duals, or inverting the direction of arrows, or both. This may just be a "folk theorem", but it should have been published by someone, somewhere, and I would also like to have an easily accessible reference, or references. Oswald Wyler From rrosebru@mta.ca Sun May 23 18:00:11 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 23 May 2004 18:00:11 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BS015-0005Jh-00 for categories-list@mta.ca; Sun, 23 May 2004 17:56:19 -0300 Date: Fri, 21 May 2004 21:54:06 +0100 (BST) From: "Prof. Peter Johnstone" To: categories@mta.ca Subject: categories: Re: comparing cotriples via an adjoint pair In-Reply-To: <5.1.0.14.2.20040520232118.0235f070@mailbox.syr.edu> Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-DPMMS-Scan-Signature: 52b2ec4a892cc9295ce0dcc23e061bcd Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 25 On Thu, 20 May 2004, Gaunce Lewis wrote: > I have encountered a situation in which I have two categories C, D which > are related by a pair of adjoint functors L from C to D and R from D to > C. Also, there is a cotriple S on C and a cotriple T on D. Finally, there > is a natural isomorphism f from RT to SR. It seems that if a couple of > diagrams relating f to the structure maps of the cotriples commute, then > there is an induced adjoint pair relating the two coalgebra categories. Is > this, or something similar to it, in the literature in some easily > referenced place? > > Thanks, > Gaunce > See (for the dual situation) an old paper of mine: Adjoint lifting theorems for categories of algebras, Bull London Math. Soc. 7 (1975), 294--297. I should say (before others say it for me) that this was not the first place the result appeared: it (and much more) was in the famous unpublished (and largely unwritten) thesis of Bill Butler. But Gaunce asked for a published reference. Peter Johnstone From rrosebru@mta.ca Tue May 25 15:47:23 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 25 May 2004 15:47:23 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BSguO-0007VW-00 for categories-list@mta.ca; Tue, 25 May 2004 15:44:16 -0300 Date: Mon, 24 May 2004 09:09:26 +0200 From: "Int. Center for Computational Logic" Message-Id: <200405240709.i4O79QXO011589@spock.inf.tu-dresden.de> To: cl-adverts@spock.inf.tu-dresden.de Subject: categories: International Masters Program in COMPUTATIONAL LOGIC Reply-To: cl-adverts@janeway.inf.tu-dresden.de Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 26 International Masters Program in COMPUTATIONAL LOGIC The International Center for Computational Logic at the Technische Universitaet Dresden is offering a two-year study program, in English, leading to a master of science (M.Sc.) in computer science. This is a joint program with the Universidade Nova de Lisboa and the Technische Universitaet Wien. Courses focus on logic and constraint programming, artificial intelligence, knowledge representation and reasoning, type theory, model theory, proof theory, equational reasoning, databases, natural language processing, planning and formal methods, among others. The tuition fees are waived. At the end of the programme a research master thesis has to be prepared. Prerequisites are a good knowledge of the basics of logic, and familiarity with mathematical reasoning. Knowledge of foundations of artificial intelligence and logic programming is desirable. It is indispensable being fluent in English; German is not necessary at all, but there are facilities for studying it if desired. A bachelor in Computer Science, or equivalent degree, is required by the beginning of courses, in October 2004. Dresden, on the river Elbe, is one of the most important art cities of Germany. The economy is growing rapidly and Dresden is a top high-tech centre. AMD built the most modern chip factory in Europe, Infineon Technologies, Siemens and many other companies invest here. The possibilities of getting a job after the master are excellent. The University is very well equipped and the teachers/students ratio is close to 1. International contacts make it easy for interested students to continue pursuing a career in research. Deadline for applications is June 15, 2004, but applications are processed as they come. To apply, please send all the relevant documents by post to the address below. Further information is on the web at . Paper information material is available on request. Please give this message broad distribution. Sylvia Epp, secretary International Center for Computational Logic Technische Universitaet Dresden, D-01062 Dresden, Germany Tel: [49] (351) 463-38341 Fax: [49] (351) 463-38342 email: cl-secretary@Inf.TU-Dresden.DE From rrosebru@mta.ca Tue May 25 15:47:23 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 25 May 2004 15:47:23 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BSgwi-0007jh-00 for categories-list@mta.ca; Tue, 25 May 2004 15:46:40 -0300 Date: Mon, 24 May 2004 13:21:52 GMT Message-Id: <200405241321.i4ODLqtm013086@mercury.comlab.ox.ac.uk> X-Authentication-Warning: mercury.comlab: jg set sender to jg@mercury.comlab using -f From: Jeremy Gibbons To: categories@mta.ca Subject: categories: MPC2004: Call for participation Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 27 MPC 2004 7th International Conference on MATHEMATICS OF PROGRAM CONSTRUCTION 12--14 July, 2004, Stirling, Scotland, UK http://www.cs.cornell.edu/Projects/MPC2004 Organised in conjunction with AMAST '04 CALL FOR PARTICIPATION We are happy to announce that registration for MPC2004 is now open. Please follow the link from the conference web page (URL above). Note that the early registration deadline is Monday 14th June. After that date, we cannot guarantee that accommodation will be available. (Our apologies if you receive multiple copies of this announcement.) Jeremy Gibbons on behalf of the MPC programme committee -- Jeremy.Gibbons@comlab.ox.ac.uk Oxford University Computing Laboratory, TEL: +44 1865 283508 Wolfson Building, Parks Road, FAX: +44 1865 273839 Oxford OX1 3QD, UK. URL: http://www.comlab.ox.ac.uk/oucl/people/jeremy.gibbons.html From rrosebru@mta.ca Tue May 25 15:47:23 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 25 May 2004 15:47:23 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BSgvC-0007ZY-00 for categories-list@mta.ca; Tue, 25 May 2004 15:45:06 -0300 Message-ID: <40B1BAA6.1010204@cs.bham.ac.uk> Date: Mon, 24 May 2004 10:04:38 +0100 From: Steve Vickers User-Agent: Mozilla/5.0 (Windows; U; Windows NT 5.0; en-US; rv:1.3) Gecko/20030312 X-Accept-Language: en-us, en MIME-Version: 1.0 To: categories@mta.ca Subject: categories: Re: comparing cotriples via an adjoint pair References: <5.1.0.14.2.20040520232118.0235f070@mailbox.syr.edu> In-Reply-To: <5.1.0.14.2.20040520232118.0235f070@mailbox.syr.edu> Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 28 This paper may also be relevant (again in the dual situation, with monads): Jean-Pierre Meyer "Induced functors on categories of algebras", Mathematische Zeitschrift 142 (1975) 1-14. This relaxes the condition that it should be a natural isomorphism between RT and SR. Instead it has a monad functor from (D,T) to (C,S) and a left adjoint monad opfunctor. It constructs an adjoint pair of functors between the algebra categories. However, it does assume that one of the algebra categories has coequalizers. For monad functors and opfunctors see Ross Street "The formal theory of monads", Journal of Pure and Applied Algebra 2 (1972) 149-168. Steve Vickers. Gaunce Lewis wrote: > I have encountered a situation in which I have two categories C, D which > are related by a pair of adjoint functors L from C to D and R from D to > C. Also, there is a cotriple S on C and a cotriple T on D. Finally, > there > is a natural isomorphism f from RT to SR. It seems that if a couple of > diagrams relating f to the structure maps of the cotriples commute, then > there is an induced adjoint pair relating the two coalgebra > categories. Is > this, or something similar to it, in the literature in some easily > referenced place? > > Thanks, > Gaunce From rrosebru@mta.ca Tue May 25 15:48:23 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 25 May 2004 15:48:23 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BSgxz-00002O-00 for categories-list@mta.ca; Tue, 25 May 2004 15:47:59 -0300 Mime-Version: 1.0 (Apple Message framework v613) Content-Type: text/plain; charset=ISO-8859-1; delsp=yes; format=flowed Message-Id: <3AD7522A-AE66-11D8-9D0D-000A95D05E0E@itu.dk> Content-Transfer-Encoding: quoted-printable From: Thomas Hildebrandt Subject: categories: CF Participation: CTCS Conference and Summer School Date: Tue, 25 May 2004 18:11:50 +0200 To: Categories list X-Mailer: Apple Mail (2.613) X-Virus-Scanned: by amavisd-new at itu.dk Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 29 -CALL FOR PARTICIPATION-CALL FOR PARTICIPATION-CALL FOR PARTICIPATION- --- APPSEM II --- 10th CONFERENCE ON CATEGORY THEORY AND COMPUTER SCIENCE (CTCS'04) AUGUST 12-14, 2004 AND GRADUATE STUDENT SUMMER SCHOOL AUGUST 9-11, 2004 AND 3rd WORKSHOP ON CATEGORICAL METHODS FOR CONCURRENCY, INTERACTION AND MOBILITY (CMCIM 2004) AUGUST 11, 2004 IT University of Copenhagen (ITU) Copenhagen, Denmark www.itu.dk/research/theory/ctcs2004/ ------------------------------------------------------------------------=20= --- Important Dates: April 16th, 2004: CTCS Submission deadline (closed) June 1st, 2004: CTCS Notification of authors of accepted papers June 21st, 2001: Submission of abstracts for CMCIM Workshop July 1st, 2004: CTCS Registration (and special hotel rates) = deadline ------------------------------------------------------------------------=20= ---- CTCS'04 is the 10th Conference on Category Theory and Computer Science, with the purpose to advance the foundations of computing using the =20 tools of category theory. Invited Speakers for the CTCS 2004 Conference: * Francois Bergeron (Queb=E9c) * Martin Hyland (Cambridge) * Robin Milner (Cambridge) * Andrew Pitts (Cambridge) * Thomas Streicher (Darmstadt) Typical topics at CTCS include category-theoretic aspects of the =20 following: coalgebras and computing concurrent and distributed systems constructive mathematics declarative programming and term rewriting domain theory and topology foundations of computer security linear logic modal and temporal logics models of computation program logics, data refinement, and specification programming language semantics type theory Previous conferences have been held in Guildford (Surrey), Edinburgh =20 (twice), Manchester, Paris, Amsterdam, Cambridge, S. Margherita Ligure (Genova), =20= and Ottawa. More information and registration form at: http://www.itu.dk/research/theory/ctcs2004/ ---------------------------------------------------------------------- CTCS 2004 PhD SUMMER SCHOOL The summer school is aimed at both graduate and undergraduate students, =20= with basic knowledge of category theory. The school will offer mini-courses (5 =20 lectures each) in: * Stone Duality, Coalgebras, and Modal Logic (Alexander Kurz) * Game Semantics (Guy McCusker) * Operational Semantics (Pawel Sobocinski) * Categorical Models for Concurrency (Thomas Hildebrandt) More information and registration at: http://www.itu.dk/research/theory/ctcs2004/summerschool.html -------------------------------------------------------------------- CMCIM 2004 WORKSHOP In between the summer school and the CTCS conference, August 11th, there will be an informal half-day workshop on Categorical Methods in Concurrency, Interaction and Mobility. The workshop has previously been held in connection with CONCUR 2002 and CONCUR 2003. We invite submissions of extended abstracts (less than 5 pages), presenting status reports, recent results, challenges or work in progress. There will be no formal proceedings of the workshop, informal proceedings will be distributed at the workshop. Thus, accepted material may be published elsewhere at a later date. Workshop participation is FREE, but requires registration before 1st of July. Submissions should be sent before 21th of June. More information and registration at: http://www.itu.dk/research/theory/ctcs2004/summerschool.html ----------------------------------------------------------------- Organisation: CTCS 2004 PROGRAMME COMMITTEE: Lars Birkedal, Chair (IT University of Copenhagen) Marcelo Fiore (University of Cambridge) Masahito Hasegawa (Kyoto University) Bart Jacobs (University of Nijmegen) Ugo Montanari (University of Pisa) Valeria de Paiva (Palo Alto Research Center) Dusko Pavlovic (Kestrel Institute) John Power (University of Edinburgh) Edmund Robinson (Queen Mary, University of London) Peter Selinger (University of Ottawa) CTCS ORGANIZING COMMITTEE E. Moggi, Chair, (Genova) S. Abramsky (Oxford) P. Dybjer (Chalmers) B. Jay (Sydney) A. Pitts (Cambridge) CTCS 2004 LOCAL ORGANIZING COMMITTEE C. Butz T. Hildebrandt A.L. Moerk CMCIM 2004 Workshop Organizers: Thomas Hildebrandt Alexander Kurz --------------------------------------- SPONSORSHIP The conference and summer school are APPSEM-II events, sponsored by the FIRST graduate school (www.first.dk) and the Department of Theoretical Computer Science at the IT University of =20 Copenhagen (http://www.itu.dk/Internet/sw648.asp). From rrosebru@mta.ca Tue May 25 15:49:00 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 25 May 2004 15:49:00 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BSgyp-00009A-00 for categories-list@mta.ca; Tue, 25 May 2004 15:48:51 -0300 Mime-Version: 1.0 (Apple Message framework v613) Content-Type: text/plain; charset=WINDOWS-1252; delsp=yes; format=flowed Message-Id: <31696467-AE69-11D8-9D0D-000A95D05E0E@itu.dk> Content-Transfer-Encoding: quoted-printable From: Thomas Hildebrandt Subject: categories: CFP: CMCIM 2004, WORKSHOP ON CATEGORICAL METHODS FOR CONCURRENCY, INTERACTION AND MOBILITY Date: Tue, 25 May 2004 18:33:03 +0200 To: Categories list X-Mailer: Apple Mail (2.613) X-Virus-Scanned: by amavisd-new at itu.dk Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 30 CALL FOR PAPERS AND PARTICIPATION: 3rd WORKSHOP ON: CATEGORICAL METHODS FOR CONCURRENCY, INTERACTION AND MOBILITY (CMCIM 2004), AUGUST 11, 2004 affiliated with the 10th conference in Category Theory and Computer =20 Science (CTCS 2004) ,August 12th-14th, and Graduate Student Summer School in Category Theory and Computer =20 Science, August 9th-11th. IT University of Copenhagen (ITU) Copenhagen, Denmark www.itu.dk/research/theory/ctcs2004/cmcim.html ------------------------------------------------------------------------=20= --- Important Dates: * June 21st, 2001: Submission of abstracts for CMCIM Workshop * July 1st, 2004: CTCS Registration (and special hotel rates) deadline ------------------------------------------------------------------------=20= ---- Just before the CTCS 2004 conference, August 11th, there will be an =20 informal half-day workshop on Categorical Methods in Concurrency, Interaction =20 and Mobility. The workshop has previously been held in connection with CONCUR 2002 =20 and CONCUR 2003. We invite submissions of extended abstracts (less than 5 pages), =20 presenting status reports, recent results, challenges or work in progress. There will be no formal proceedings of the workshop, informal =20 proceedings will be distributed at the workshop. Thus, accepted material may be published elsewhere at a later date. Topics of interest include: =95 categorical algebras of processes =95 categorical methods in game semantics and geometry of = interaction =95 categorical models of term/graph rewriting or rewriting = logic =95 Chu spaces =95 coalgebras, bialgebras, coinduction =95 comparing models of concurrency =95 enriched categories of processes =95 interaction categories =95 bigraphs =95 presheaf semantics Workshop participation is free, but requires registration before 1st of =20= July, by sending an email to hilde@itu.dk, containing =20 `CMCIM2004-registration' in the subject, and your full name and =20 affiliation in the body. Submissions should be sent before 21th of June, as PostScript files to: =20= hilde@itu.dk, containing `CMCIM-submission' in the subject, and in the =20= body the full names of the author(s), title, and a text-only abstract. CMCIM 2004 Workshop Organizers: Thomas Hildebrandt Alexander Kurz More information and registration at: http://www.itu.dk/research/theory/ctcs2004/cmcim.html --------------------------------------- SPONSORSHIP The conference and summer school are APPSEM-II events, and are as the =20= workshop sponsored by the FIRST graduate school (www.first.dk) and the Department of Theoretical Computer Science at the IT University of =20 Copenhagen (http://www.itu.dk/Internet/sw648.asp). From rrosebru@mta.ca Thu May 27 17:02:01 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 27 May 2004 17:02:01 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BTR0S-000164-00 for categories-list@mta.ca; Thu, 27 May 2004 16:57:36 -0300 Date: Wed, 26 May 2004 22:25:07 -0700 (PDT) From: John MacDonald To: categories@mta.ca Subject: categories: CT04 Abstracts and Early Registration Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 31 FIFTH ANNOUNCEMENT INTERNATIONAL CATEGORY THEORY CONFERENCE (CT04) July 18-24, 2004 University of British Columbia Vancouver, Canada This conference will be held on the University of British Columbia campus. It will begin with a reception at 6pm on Sunday July 18, 2004, and will end at 1pm on Saturday July 24, 2004. All those interested in category theory and its applications are welcome. Information about deadlines for abstracts, registration and accommodation may be found at the end of this letter as well as on the conference website http://www.pims.math.ca/science/2004/CT04 If you think that you will attend or may attend, and have not previously made any indication of this to the organizer, then please send a note to johnm@math.ubc.ca with the words "will attend" or "may attend", as appropriate. The issue involved here is whether the PIMS new lecture room can be used for the talks or whether something bigger will have to be booked. Some important deadlines are as follows: Abstracts - May 31, 2004. If you would like to give a talk at the conference, then please send in a short abstract of length about half a page but not longer than one page. Please submit this on the form from the conference website http://www.pims.math.ca/science/2004/CT04/abstracts.html Due to the potentially large number of submissions it may not be possible to reserve a place on the program for all those who submit an abstract. Registration Deposit or Early Registration payment - May 31, 2004 Please see the website http://www.pims.math.ca/science/2004/CT04/registration.html It is possible to make payment by bank transfer in addition to the option of payment by cheque. Details of the address and account number can be supplied on request. Accommodation - June 18, 2004. After this date the block of rooms reserved for CT04 will be released to the general public, although reservations can still be made if space is available. Early booking is recommended, especially for those with accompanying persons. Extra spaces for the excursion or banquet for accompanying persons - June 30, 2004. The opening reception, excursion and banquet for delegates is included in the conference fee as well as morning and afternoon coffee breaks, lecture room rentals and other miscellaneous conference expenses. Accommodation and meals are not included in the fee. CT04 Advisory Committee: Jiri Adamek, University of Braunschweig, Germany Michael Barr, McGill University, Canada Eduardo Dubuc, University of Buenos Aires, Argentina Marco Grandis, University of Genoa, Italy George Janelidze, Capetown, South Africa Michael Johnson, Macquarie University, Australia P. T. Johnstone, Cambridge University, UK F. W. Lawvere, University at Buffalo, USA J. MacDonald, University of British Columbia, Canada S. Niefield, Union College, USA T. Porter, University of Wales, UK Jiri Rosicky, Masaryk University, Czech Republic Phil Scott, University of Ottawa, Canada Robert Seely, McGill University, Canada Art Stone, Vancouver, Canada Ross Street, Macquarie University, Australia Enrico Vitale, Louvain-la-Neuve, Belgium Walter Tholen, York University, Canada R. J. Wood, Dalhousie University, Canada This conference is being organized with help from the Pacific Institute of Mathematics(PIMS) and the UBC Conference Centre. John MacDonald, Vancouver From rrosebru@mta.ca Sun May 30 19:38:37 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 30 May 2004 19:38:37 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BUYt5-0007lU-00 for categories-list@mta.ca; Sun, 30 May 2004 19:34:39 -0300 From: Peter Selinger Message-Id: <200405291621.i4TGLvi15870@quasar.mathstat.uottawa.ca> Subject: categories: Call for Participation: Workshop on Quantum Programming Languages To: categories@mta.ca (Categories List) Date: Sat, 29 May 2004 12:21:57 -0400 (EDT) X-Mailer: ELM [version 2.5 PL3] MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 32 CALL FOR PARTICIPATION 2nd International Workshop on Quantum Programming Languages (QPL2004) July 12-13, 2004, Turku, Finland Affiliated with LICS 2004 http://quasar.mathstat.uottawa.ca/~selinger/qpl2004/ * * * Registration for this workshop is now available, please see below for registration information and a list of talks. OVERVIEW: The goal of this workshop is to bring together researchers working on mathematical formalisms and programming languages for quantum computing. In the last few years, there has been a growing interest in logical tools, languages, and semantical methods for analyzing quantum computation. These foundational approaches complement the more mainstream research in quantum computation which emphasizes algorithms and complexity theory. Possible topics include the syntax and semantics of quantum programming languages, new paradigms for quantum programming, specification of quantum algorithms, higher-order quantum computation, quantum data types, reversible computation, axiomatic approaches to quantum computation, concurrent and distributed quantum computation, compilation of quantum programs, semantical methods in quantum information theory, and categorical models for quantum computation. The first workshop in this series was held June 15-16, 2003, in Ottawa, Canada. REGISTRATION: Registration and local arrangements will be handled through the LICS 2004 main conference (http://www.dcs.ed.ac.uk/home/als/lics/lics04/). There will be a small fee for attending the workshop, which will cover lunch, coffee, and the informal proceedings. INVITED SPEAKER: * Richard Jozsa (Bristol): "On the structure of quantum algorithms and the role of classical mathematics" CONTRIBUTED TALKS: * Samson Abramsky, Ross Duncan: "A categorical quantum logic" * Pablo Arrighi, Gilles Dowek: "Operational semantics for formal tensorial calculus" * Alexandru Baltag, Sonja Smets: "A dynamic logic for quantum programming" * Bob Coecke: "Quantum, concretely, abstractly" * Ellie D'Hondt, Prakash Panangaden: "Quantum weakest preconditions" * Simon Gay, Rajagopal Nagarajan: "Communicating quantum processes" * Philippe Jorrand, Marie Lalire: "A process algebraic approach to concurrent and distributed quantum computation: operational semantics" * Peter Selinger: "Towards a semantics for higher-order quantum computation" * K. M. Svore, A. W. Cross, A. V. Aho, I. L. Chuang, S. A. Edwards, I. L. Markov: "Toward a software architecture for quantum computing design tools" * Benoit Valiron: "Quantum typing" * Paolo Zuliani: "Non-deterministic quantum programming" PROGRAM COMMITTEE: Samson Abramsky (Oxford) Prakash Panangaden (McGill) Peter Selinger (Ottawa) CONTACT INFORMATION: Organizer: Peter Selinger Department of Mathematics and Statistics University of Ottawa, Canada Email: selinger@mathstat.uottawa.ca CONFERENCE WEBSITE: http://quasar.mathstat.uottawa.ca/~selinger/qpl2004/ (revised May 29, 2004) From rrosebru@mta.ca Sun May 30 19:38:37 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 30 May 2004 19:38:37 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BUYtn-0007mt-00 for categories-list@mta.ca; Sun, 30 May 2004 19:35:23 -0300 Date: Sat, 29 May 2004 19:08:24 -0400 (EDT) From: Oswald Wyler To: categories@mta.ca Subject: categories: \phi for the golden ratio? Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 33 In seventh or eighth grade -- a long time ago -- , I learned the name "goldener Schnitt" (golden ratio, ratio aurea) for the positive solution of the equation x^2 = x + 1. Recently, I read an article, I forgot where, discussing this number and using \phi as the "accepted symbol" for it. The old name was never mentioned. So far, I have only met three real or complex numbers with universally accepted one-letter symbols: \pi, e, i. Have I missed something? Oswald Wyler From rrosebru@mta.ca Tue Jun 1 08:40:09 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 01 Jun 2004 08:40:09 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BV7b4-0000jr-00 for categories-list@mta.ca; Tue, 01 Jun 2004 08:38:22 -0300 Message-ID: <40BB6D64.1060706@Wesleyan.edu> Date: Mon, 31 May 2004 13:37:40 -0400 From: "Fred E.J. Linton" Reply-To: FLinton@Wesleyan.edu Organization: Wesleyan U. Math/CS User-Agent: Mozilla/5.0 (Windows; U; Windows NT 5.1; en-US; rv:1.0.1) Gecko/20020823 Netscape/7.0 (nscd2) X-Accept-Language: en-us, en, fr, de, it, pl MIME-Version: 1.0 To: categories@mta.ca Subject: categories: Announcing two abstracts Content-Type: text/plain; charset=ISO-8859-2; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 34 An abstract of my proposed talk for next month's CT04 at UBC Vancouver has just been put up at http://fej.math.wes.home.att.net/CT04-Abstract.htm . My talks at Union College, Bangalore, and Calcutta last November, December, and January, respectively, are abstracted in the item http://b.mikolajewska.home.att.net/text/SIPRfejAbstrct.htm , which also provides links to two browser-optimized versions (one for Netscape, one for MSIE; I hope that other browsers will find that at least one of these renders acceptably) of a uniform write-up of what I had to say at those events. Comments, suggestions, errata, broken HTML? Please call these all to my attention. Thanks. -- F.E.J. Linton (Math/CS, Wesleyan U., Middletown, CT 06459 USA) From rrosebru@mta.ca Tue Jun 1 08:40:09 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 01 Jun 2004 08:40:09 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BV7Y9-0000ZL-00 for categories-list@mta.ca; Tue, 01 Jun 2004 08:35:21 -0300 Message-ID: <40BB388C.9020905@cs.queensu.ca> Date: Mon, 31 May 2004 09:52:12 -0400 From: Claudio Hermida User-Agent: Mozilla/5.0 (Macintosh; U; PPC Mac OS X Mach-O; en-US; rv:1.4) Gecko/20030624 Netscape/7.1 X-Accept-Language: en-us, en, fr-ca, es-ar, it MIME-Version: 1.0 To: categories@mta.ca Subject: categories: Re: comparing cotriples via an adjoint pair Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 35 Gaunce Lewis wrote: > I have encountered a situation in which I have two categories C, D which > are related by a pair of adjoint functors L from C to D and R from D to > C. Also, there is a cotriple S on C and a cotriple T on D. Finally, > there > is a natural isomorphism f from RT to SR. It seems that if a couple of > diagrams relating f to the structure maps of the cotriples commute, then > there is an induced adjoint pair relating the two coalgebra > categories. Is > this, or something similar to it, in the literature in some easily > referenced place? > > Thanks, > Gaunce Here's a related reference: the appendix of C.Hermida and B.Jacobs, Structural Induction and Coinduction in a fibrational setting, Information and Computation 145(2) 107-152,1998. stablishes the suitable 2-functoriality of categories of (co)algebras for endofunctors as inserters (which does not follow straightforwardly from their weighted limit formulation) and the more or less immediate corollaries of induced adjoints, without any coequalisers or additional structure. It is remarkably simple but fairly useful. The result (and the argument) extends literally to the case of Eilenberg-Moore algebras for monads: using the (old) notion of morphism of monads from (a), given a pseudo-morphism of monads (f,\theta):M -> N (where \theta is iso), if f has a right adjoint g, adjoint transposition of \theta yields (g,\theta'):N -> M right adjoint to (f,\theta) in Mnd (b), and 2-functoriality of algebras yields the desired adjunction between the categories of algebras (commuting with the forgetful functors, of course). Once again, no structure is required on the categories involved. (a) R. Street, The formal theory of monads, JPAA 2 (1972) 149-168 (b) R. Street, Two constructions on lax functors, Cahiers top. et geom. diff. 13 (1972) 217-264. Claudio PS: There is a more liberal notion of 2-cell for Mnd, essentially arising from internal category theory, but I don't know its impact in the above adjoint results. From rrosebru@mta.ca Wed Jun 2 18:19:14 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 02 Jun 2004 18:19:14 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BVd3j-0003IG-00 for categories-list@mta.ca; Wed, 02 Jun 2004 18:14:03 -0300 Date: Sun, 30 May 2004 19:23:30 -0400 (EDT) From: Robert Seely To: categories@mta.ca Subject: Re: categories: \phi for the golden ratio? In-Reply-To: Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 36 [note from moderator: several replies were received on this item - which is admittedly off-topic; they are digested below.] There are a number of books on the subject - or on the related Fibonacci numbers - which call it "the golden ratio", "the golden number", "the divine proportion", as well as phi. (Check out Amazon for example.) I think the name isn't as "fixed" as pi, e, or i, but it's pretty standard, within a small orbit. (Maple doesn't know it - unlike Pi!) Actually, in a sense, i isn't as standard as pi or e - at least in engineering circles, some prefer J (or j). (I've never seen a *mathematical* writer use J though - anyone?) Of course there are lots of non-real, non-complex, numbers with universally accepted one-letter symbols. (omega ... do you allow subscripts?) But real or complex? (And presumably not constants from physics ...) No others spring to mind, though I'm willing to bet that 5 minutes after I hit "send" one will do so! Close? There are a few, like the Euler constant gamma (lim_{n->\infty} (sum_{k=1}^n 1/k - ln n), but I suspect most mathematicians would have to look such cases up, so they hardly qualify. (I only know about gamma because it came up in conversation this past semester at work!) -= rags =- On Sat, 29 May 2004, Oswald Wyler wrote: > In seventh or eighth grade -- a long time ago -- , I learned the name > "goldener Schnitt" (golden ratio, ratio aurea) for the positive solution > of the equation x^2 = x + 1. Recently, I read an article, I forgot > where, discussing this number and using \phi as the "accepted symbol" > for it. The old name was never mentioned. > > So far, I have only met three real or complex numbers with universally > accepted one-letter symbols: \pi, e, i. Have I missed something? > > Oswald Wyler > -- ------------------------------------------------------------------------------ From: Robert Knighten Date: Sun, 30 May 2004 16:46:52 -0700 I have no idea if you've missed something, but at least in the English speaking world \phi as the name for the golden ratio has indeed become the "accepted symbol". Asking Google about 'phi number "golden ratio"' produced 8120 pages containing all of those. This includes, for example, A biography of the number phi: The Golden Ratio: The Story of Phi: The World's Most Astonishing Number Mario Livio Broadway Books, 320 pp, $24.95 I don't know if the use of \phi for the golden ratio is common in other languages, but I suspect the pervasive effect of the English usage has had its effect. -- Bob -- Robert L. Knighten Robert@Knighten.org ----------------------------------------------------------------------- Date: Sun, 30 May 2004 19:05:29 -0400 From: Steve Stevenson This month's "Discover" magazine had an article on the golden ratio. steve ---------------------------------------------------------------------- Date: Mon, 31 May 2004 10:21:41 -0300 From: "Robert J. MacG. Dawson" As a generalization: "Golden ratio" is used by geometers being informal, autodidacts, historians, popular math writers, and crackpots. $\phi$ is used by popular math writers, autodidacts, and the better class of crackpots. $\tau$ is used by most mathematicians. A not-entirely-correct analogy: golden ratio:$\phi$:\tau$ :: blue vitriol : copper sulphate: copper(II) sulphate pentahydrate -Robert Dawson ------------------------------------------------------------------------------------ Date: Mon, 31 May 2004 10:29:36 -0400 (EDT) From: Peter Freyd Subject: "phi and gamma" Oswald Wyler writes: I have only met three real or complex numbers with universally accepted one-letter symbols: \pi, e, i. Have I missed something? Going by today's final arbiter of the universal, Google switches into calculator mode when queried for "e", "phi" and "pi" (delivering for each its numerical value to 8 decimal places -- it also names "phi" as "the golden ratio"). Google does not switch into calculator mode for "gamma" or "i" but it does for "1*gamma" (naming it as "1 * Euler's constant") and "1*i" (with no name). If you're willing to count dimensioned numbers then it also recognizes (and names) "c", "h", "k", and "u" if, in each case, you preface it with "1*". If you go beyond single letters then who knows? A few I've found are "1*au", "1*googol" and "1*mark twain". (Alas, Google has not yet learned to recognize "1*millihelen".) ------------------------------------------------------------------------ Date: Mon, 31 May 2004 10:12:38 -0700 (PDT) From: "John Baez" I don't know what this has to do with categories, but it gives me the chance to recycle some trivia I recently learned. This number 1.618... is widely called phi, but also Phi - and also tau. It was named Phi after the Greek sculptor Phidias, who helped design the Parthenon. But it was named this only in 1914, in a book called The Curves of Life, by the artist Theodore Cook. And it was Cook who first started calling 1.618... the golden ratio! Before him, 0.618... was called the golden ratio. Cook dubbed this number "phi", the lower-case baby brother of Phi. In fact, the whole "golden" terminology can only be traced back to 1826, when it showed up in a footnote to a book by one Martin Ohm, brother of Georg Ohm, the guy with the law about resistors. Before then, a lot of people called 1/G the "Divine Proportion". And the guy who started that was Luca Pacioli, a pal of Leonardo da Vinci who translated Euclid's Elements. In 1509, Pacioli published a 3-volume text entitled Divina Proportione, advertising the virtues of this number. > So far, I have only met three real or complex numbers with universally > accepted one-letter symbols: \pi, e, i. Have I missed something? Sure - the Euler-Mascheroni constant, gamma = 0.5772156649015... = lim_{n->infinity} (integral_1^n dx/x) - (1/1 + 1/2 + ... + 1/n) See: http://mathworld.wolfram.com/Euler-MascheroniConstant.html By the way, engineers often call i "j". Best, jb From rrosebru@mta.ca Wed Jun 2 18:19:14 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 02 Jun 2004 18:19:14 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BVd5Z-0003N7-00 for categories-list@mta.ca; Wed, 02 Jun 2004 18:15:57 -0300 Date: Tue, 1 Jun 2004 09:21:10 +0200 To: categories@mta.ca From: Nils Andersen Subject: categories: Re: \phi for the golden ratio? Content-Type: text/plain; charset="us-ascii" ; format="flowed" X-Spam-Checker-Version: SpamAssassin 2.63 (2004-01-11) on nhugin.diku.dk Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: RO X-Status: X-Keywords: X-UID: 37 [and one more...] In reply to the question from Oswald Wyler let me quote from Donald E. Knuth, The Art of Computer Programming (1968, 1973), Section 1.2.8: The number $\phi$ itself has a very interesting history. Euclid called it the "extreme and mean ratio"; the ratio of A to B is the ratio of (A+B) to A, if the ratio of A to B is $\phi$. Renaissance writers called it the "divine proportion"; and in the last century it has commonly been called the "golden ratio". In the art world, the ratio of $\phi$ to 1 is said to be the most pleasing proportion aesthetically, and this opinion is confirmed from the standpoint of computer programming aesthetics as well. For the story of $\phi$, see the excellent article "The Golden Section, Phyllotaxis, and Whythoff's Game", by H.S.M. Coxeter, Scripta Math. 19 (1953), 135-143, and see also Chapter 8 of The 2nd Scientific American Book of Mathematical Puzzles and Diversions, by Martin Gardner (New York: Simon and Schuster, 1961). -- Nils Andersen >In seventh or eighth grade -- a long time ago -- , I learned the name >"goldener Schnitt" (golden ratio, ratio aurea) for the positive solution >of the equation x^2 = x + 1. Recently, I read an article, I forgot >where, discussing this number and using \phi as the "accepted symbol" >for it. The old name was never mentioned. > >So far, I have only met three real or complex numbers with universally >accepted one-letter symbols: \pi, e, i. Have I missed something? > >Oswald Wyler