From rrosebru@mta.ca Tue Jan 3 09:39:35 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 03 Jan 2006 09:39:35 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1EtmJf-0005Fl-24 for categories-list@mta.ca; Tue, 03 Jan 2006 09:35:07 -0400 X-ME-UUID: 20060103122330543.849715800088@mwinf3114.me.freeserve.com Message-ID: <015c01c61060$4db2b4e0$04844c51@brown1> From: "Ronald Brown" To: "\"Categories\"" References: Subject: categories: Re: Terminology again + Note from moderator Date: Tue, 3 Jan 2006 12:21:59 -0000 MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk X-IMAPbase: 1144781837 43 Status: RO X-Status: X-Keywords: X-UID: 1 Thanks to all who wrote on this - it has helped me to see the background and issues in this important area for Categories for the Working Mathematician! Ronnie > [Note from moderator: This is to let you know that I am invoking the > (not recently used) 48 hour rule for this subject: postings received > by noon on Wednesday will be sent; after that the discussion may > obviously continue, but not on the list. > Best wishes to all for 2006, Bob Rosebrugh] From rrosebru@mta.ca Tue Jan 3 09:39:36 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 03 Jan 2006 09:39:36 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1EtmHs-00059p-9K for categories-list@mta.ca; Tue, 03 Jan 2006 09:33:16 -0400 Mime-Version: 1.0 (Apple Message framework v746.2) Content-Type: text/plain; charset=US-ASCII; delsp=yes; format=flowed Message-Id: Content-Transfer-Encoding: 7bit From: "Hans-E. Porst" Subject: categories: Re: Terminology re fibrations and opfibrations of categories Date: Mon, 2 Jan 2006 17:20:57 +0100 To: categories@mta.ca, Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 2 Note that the suggestion below is standard terminology since about 30 years. See also Adamek, Herrlich, Strecker: Abstract and concrete categories; Wiley 1990 (also available at http://katmat.math.uni-bremen.de) H.-E. Porst Am 26.12.2005 um 22:57 schrieb Eduardo Dubuc: > I am just writing a paper with Luis Espannol where we need to > develop (the > basic part of the theory of cartesian and cocartesian arrows) for > families > > we use the following terminology: > > consider a functor U: C ---> S, then: > > 1) a family in C Z _i ---> X > > over R_i ---> S is FINAL iff: > > given S ---> T = UY such that there exists Z_i --->Y over > R_i ---> S ---> T (that is, R_i ---> S ---> T lifts), then there > exists a > unique X ---> Y over S ---> T (that is, S ---> T lifts). > > For topological spaces this is the usual Bourbaki notion of final > topology. > > When U is not understood, we call this "U-FINAL" -- Hans-E. Porst porst@uni-bremen.de Bremen, Germany Fax: +49-421-75643 From rrosebru@mta.ca Tue Jan 3 20:22:41 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 03 Jan 2006 20:22:41 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1EtwJ3-0005nW-AC for categories-list@mta.ca; Tue, 03 Jan 2006 20:15:09 -0400 X-ME-UUID: 20060103165644780.BE6DD1C0020D@mwinf0109.wanadoo.fr Date: Tue, 3 Jan 2006 18:14:14 +0100 Mime-Version: 1.0 (Apple Message framework v543) Content-Type: text/plain; charset=US-ASCII; format=flowed Subject: categories: Tuesday Afternoon From: jean benabou To: Categories Content-Transfer-Encoding: 7bit Message-Id: <5D5E4C50-7C7C-11DA-9546-000393B90F2C@wanadoo.fr> Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 3 A strange title indeed! I have received many reactions to my mail about "prone " and "supine", most of them supporting my position, and I intended to wait a few days, in case I had more, to answer globally to all of them. Especially since I hoped to get a motivation of the proposed change from Paul Taylor and/or Peter Johnstone who proposed such a change. As I sent my mail on 30 Dec 2005, I knew that the period might not be the best, with vacations and celebrations, and I was prepared to wait, say two weeks, before answering in order to avoid repetitions. I received from David Yetter on Jan1 2006 another comment with the following note, hence my title: [Note from moderator: This is to let you know that I am invoking the (not recently used) 48 hour rule for this subject: postings received by noon on Wednesday will be sent; after that the discussion may obviously continue, but not on the list. Best wishes to all for 2006, Bob Rosebrugh] I am still "on the safe side" of wednesday noon, and "hope" my mail will reach you via the Category list. I had NEVER heard of this "48 hour rule", and have many examples where discussions on this list have lasted for much longer, even on subjects that I considered a bit futile. So I would like to know WHEN this rule was LAST applied, and HOW MANY TIMES IN THE PAST IT HAS BEEN APPLIED AT ALL I'd greatly appreciate answers to these two questions. I cannot, of course, imagine that an unknown, or obsolete, ad hoc rule has been unearthed to stop a discussion which has jut started, where my objections, supported by mathematical arguments, and by many members of this list, might happen to displease some person or persons unknown. I realize now that some exceptional questions in Category Theory can have indeed very exciting aspects! I apologize for my English, I didn't have time to "polish" it because I had a deadline to respect. Best wishes to all, Jean Benabou P.S. When I was ready to send this mail, I found via the Category list a mail by Hans Porst ON THE SAME QUESTION OF TERMINOLOGY, but WITHOUT the note from the moderator. This rises two questions: (i)-Is "the rule" EQUALLY VALID for everybody ? (ii)-If I want to answer Porst's mail after noon to-morrow can I do it through the list? From rrosebru@mta.ca Wed Jan 4 09:40:53 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 04 Jan 2006 09:40:53 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1Eu8op-0001B6-4A for categories-list@mta.ca; Wed, 04 Jan 2006 09:36:47 -0400 Date: Wed, 4 Jan 2006 02:59:41 -0800 From: Toby Bartels To: Categories Subject: categories: Re: Terminology again Message-ID: <20060104105940.GA20373@math-rs-n03.ucr.edu> References: Mime-Version: 1.0 Content-Type: text/plain; charset=3Diso-8859-1 Content-Disposition: inline Content-Transfer-Encoding: 8bit In-Reply-To: User-Agent: Mutt/1.4i Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 4 jean benabou wrote in part: >3.4- I can speak, read, and write a little bit of English, but I am >French and might someday have the preposterous idea to lecture on >fibered categories in French. Of course only in France, and to an >audience uniquely composed of french persons. Perhaps MM Taylor and >Johnstone, could suggest adequate french translations for prone and >supine, which I can't seem to find. And they should be ready to do the >same thing for German, Italian, Spanish, and many other languages. >No such problems with cartesian of course, because cartesian.... is >cartesian is cartesian is cartesian! Jean B=E9nabou has three classes of arguments against "prone" and "supine": ethical, mathematical, and linguistic. The ethical argument is particularly popular on this list, and the mathematical argument (given in the post to which I'm replying) seems sound as well. (But I hope that Paul Taylor or Peter Johnstone, who used these words in print and sometimes read this list, will reply, since they've probably thought about these matters too.) However, I cannot accept the linguistic argument. These words are not idiosyncratic, untranslatable English; they are good Latin words with descendants in many languages. It's true that they are both archaic or obsolete in French (a loss for the world's francophones, I would say, since they are useful words in any language), but they have French forms that can be used. Most of the other Romanic languages seem to have kept these words. The Latin originals are (according to the Oxford English Dictionary) "sup=EEn[us/a/um]" and "pr=F4n[us/a/um]" (where I use a cirumflex, instead of the proper macron (TeX \=3D), to indicate a long vowel). One can adapt these to any language that regularly borrows from Latin (I'm afraid that I don't know how other languages handle the Latin and pseudo-Latin that European mathematicians use). I've also found the phrases "en supination" and "en pronation" on francophone websites discussing sports medicine. These are direct translations (at least for hands and feet) of the English "supine" and "prone". However, I don't think that "morphisme en pronation" works as well as "morphisme prone", even if the latter does resort to a 500-year-old word. In Germanic languages (where compound neologisms are easier), one might translate the meaning; a Google search suggests that German words "bauchliegend" and "r=FCckenliegend" have already been invented a few hundred times. -- Toby From rrosebru@mta.ca Wed Jan 4 09:40:53 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 04 Jan 2006 09:40:53 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1Eu8nr-000179-AL for categories-list@mta.ca; Wed, 04 Jan 2006 09:35:47 -0400 Date: Wed, 4 Jan 2006 08:16:17 -0400 (GMT) From: Hvedri Inassaridze To: categories@mta.ca Subject: categories: Mac Lane volume 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: 5 Dear Colleagues, The journal "Journal of Homotopy and Related Structures" (http://jhrs.rmi.acnet.ge) intends to publish a volume (maybe with two issues) dedicated to the memory of Saunders Mac Lane who died 14 April 2005 in San Francisco. He was one of the most influential mathematicians of the 20th century and he created a new way of thinking about mathematics. The editors of Mac Lane volume are: Michael Barr (mbarr@math.mcgill.ca), Ronald Brown (r.brown@bangor.ac.uk), Peter Freyd (pjf@math.upenn.edu) and George Janelidze as executive editor (gjanel@rmi.acnet.ge). Have promised to contribute Peter May and William Lawvere. We hereby invite you to make a contribution. We are interested in mathematical papers satisfying high standards appropriate for such a volume and related to Mac Lane's interests, but also in papers related to areas of mathematics covered by the scope of JHRS. The submission deadline is end of August 2006. Papers should be submitted to any editor of Mac Lane volume, where they will have the usual refereeing process according to the submission policy of JHRS. The editors of Mac Lane volume could invite other mathematicians as contributers. It would be a great honour for our Editorial Board to contribute and edit a volume dedicated to the memory of Saunders Mac lane. Sincerely yours Hvedri Inassaridze Editor-in-Chief of JHRS ---------------------------------------------------------------------------- Professor Hvedri Inassaridze, Tel.: 995 32 334728 (work) Head of the Department of Algebra, 995 32 230852 (home) A.Razmadze Mathematical Institute, 995 99 157836 (mobile) Georgian Academy of Sciences, Fax: 995 32 001153 M.Alexidze Str.1, Tbilisi 0193, Georgia email: hvedri@rmi.acnet.ge inassari@yahoo.com http://www.rmi.acnet.ge/~hvedri From rrosebru@mta.ca Wed Jan 4 20:02:49 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 04 Jan 2006 20:02:49 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1EuIV6-0003m1-T2 for categories-list@mta.ca; Wed, 04 Jan 2006 19:57:04 -0400 Subject: categories: Re: terminology From: Eduardo Dubuc To: edubuc@dm.uba.ar (Eduardo Dubuc) Date: Wed, 4 Jan 2006 11:59:15 -0300 (ART) Cc: categories@mta.ca (Categories) In-Reply-To: from "Eduardo Dubuc" at Dec 29, 2005 08:17:36 PM X-Mailer: ELM [version 2.5 PL2] MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: RO X-Status: X-Keywords: X-UID: 6 I have been asked why I reacted to the intended reeplacement of the names "cartesian and cocartesian" by "prone and supine". I have given several reasons, but the one underlying the whole issue is the following: The reason is that since a long time I have been worried about the ghetto (in the sense of being isolated from the rest) characteristic of a certain category theory community (or group of people). And P. May has reacted concerning "prone and supine" probably because of reasons related to this. The mathematical community have been using "cartesian and cocartesian" since always, and the introduction of "prone and supine" inside this group will confirm even more the isolation. Examples abound, see M.Barr introduction of "Molecular topos" to replace Grothendieck's "Locally connected topos". No matter how many linguistic points in favor a given name may have (like prone and supine), to replace a well stablished name intoduced by a great mathematician (or school of mathematics) only puts you in ridiculous. P. May probably was feeling somehow that this will be extended by the mathematical community to all category theory practicioners. I profit by this mail to mention that concerning the concept "final" and "initial", I am happy (and not surprised) to learn that these words have been used since a long time to indicate the same categorical concept that myself, and will certainly refer to the indicated bibliography to further justify my use of these words. From rrosebru@mta.ca Wed Jan 4 20:02:49 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 04 Jan 2006 20:02:49 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1EuIWX-0003sH-Bc for categories-list@mta.ca; Wed, 04 Jan 2006 19:58:33 -0400 From: Thomas Streicher Subject: categories: prone and supine To: categories@mta.ca Date: Wed, 4 Jan 2006 19:10:46 +0100 (CET) MIME-Version: 1.0 Content-Transfer-Encoding: 7bit Content-Type: text/plain; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: RO X-Status: X-Keywords: X-UID: 7 Thanks to Toby Bartels I have got now an idea how to translate "prone arrow" and "supine arrow" to German, namely as "Pfeil in Bauchlage" and "Pfeil in Rueckenlage" (in Engl. "arrow lying on the belly" and "arrow lying on the back"). At least in German such terminology would be "frowned upon" and actually it sounds very strange. I haven't got a feeling how strange it sounds in English (but I guess it does!). The "linguistic" problem I have with this terminology is that I don't know what is the "belly" or "back" of an arrow. The intention of the suggested terminology (besides sounding funny) seems to be to replace vertical/cartesian by vertical/horizontal. But then one is sort of forced to call cocartesian arrows "cohorizontal" which sounds a bit like "vertical", isn't it? But actually, the "co" here refers to the fact that there are 2 ways of being horizontal to all vertical arrows (namely a left and a right one because the orthogonality relation is not symmetric). So one might be inclined to call "cartesian" "right horizontal" and cocartesian "left horizontal". For prefibrations and precofibrations one knows that right horizontal coincides with cartesian and left horizontal with cocartesian, respectively. But, unfortunately, for defining pre(co)fibrations one rather needs the notion of pre(co)cartesian arrow which cannot be characterized in terms of orthogonality conditions. As pointed out by Jean for arbitrary functors (already prefoliating ones) horizontal arrows need not be even precartesian (e.g. when all fibres are discrete). Finally, if one prefers to call pullbacks cartesian squares then one might be inclined to prefer the terminology "cartesian" because the cartesian arrows of the fundamental (also often called codomain) fibration are just the pullbacks, i.e. the cartesian squares. I rather have a different problem with "traditional" terminology, namely that sometimes what Jean in his mail called cartesian and precartesian is called hypercartesian and cartesian Usually, i.e. when studying fibrations, this is not a problem because all notions coincide. But if one considers prefibrations the terminology cartesian/precartesian has the advantage that one speaks about existence of cartesian liftings when defining fibrations and about precartesian liftings when speaking about prefibrations. Thomas Streicher From rrosebru@mta.ca Wed Jan 4 20:04:51 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 04 Jan 2006 20:04:51 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1EuIbw-0004Ak-LV for categories-list@mta.ca; Wed, 04 Jan 2006 20:04:08 -0400 To: categories@mta.ca Subject: categories: prone and supine Content-Length: 6611 Message-Id: From: Paul Taylor Date: Wed, 04 Jan 2006 19:09:12 +0000 Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 8 Several people have asked me to explain why I brought category theory into disrepute by introducing the words "prone" and "supine" 480 pages into my book. It's easy to understand why retired people of any generation would want to carve their works in tablets of stone. It's equally clear that they must never be allowed to do so - "Argument by Authority" is a principle of Theology, not of Science. It isn't even a principle of mathematical history: for example, I recently learned from Renato Betti's biography of Lobacevskij that early 19th century series didn't "converge" but "annihilated". As for Jean Benabou, I would pay more attention to his views on fibred category theory if he HAD carved them on tablets of stone (or preferably paper). Or if he paid more professional respect to those (Peter Johnstone, Thomas Streicher and several others) who, in the absence of the book that he promised 30 years ago, have reported and developed the subject in the meantime. Terminology, notation and proofs (should) evolve. Of notation, Riemann said that when you have the right one, you're half way to solving the problem, whilst Eilenberg taught us how category theory eliminates subscripts. It's sad how often new textbooks copy out old and clumsy proofs parrot-fashion - this is why I'm not enthusiastic about mechanising them. Given that category theory unifies older disciplines, it necessarily selects amongst conflicting terminologies - or completely replaces them, with frivolous words like "pushout". For me there are three guiding principles for choosing names for ideas: (1) certain words and qualifiers (such as regular, normal, semi, weak, quasi-, pre-) are already worn out though over-use, and should not be used again; (2) mathematics needs to make more imaginative use of human language; and (3) an ordinary dictionary should, wherever possible, be able to point the student in vaguely the right direction, especially in complicated abstract subjects like fibred category theory. The word "cartesian" fails every one of these principles. Rule (3) is my mitigation for two other offences that I committed in my book, replacing "indiscrete" with "indiscriminate" and "proof irrelevant" with "proof anonymous". Eduardo Dubuc put my rule (2) very nicely: > "strange," "charm," "beauty" and even "quark" itself are beautiful > and poetic names to refer to objects or concepts which precisely we > do not want to associate any precise meaning in everyday language, > and on the other hand, the objects or concepts are introduced with > those names. However, he didn't consider that "prone/supine" fall under it, because they "reflect in everyday language just one aspect of an existing concept". Presumably he has the geometrical aspect of these words in mind. But it was not me who introduced the vertical/horizontal idea into fibred categories: these words are in Benabou's lengthy posting. (I'm not impressed by Benabou's distinction between "cartesian" and "horizontal". As he notes, it does not apply to the subject in question, namely FIBRATIONS of categories. If he had ever written his textbook on the subject, he would have realised that this is just the kind of footnote that prevents students from grasping the key ideas.) "Vertical" and "horizontal" would be fine, apart from the fact that the fibrations that we find in categorical type theory, modules over rings and other subjects are also op-fibrations. This means that there are two different kinds of horizontality. But we are lucky: in the English language there happen to exist two different words for "horizontal". Even more luckily, they happen to be related by rotation from the vertical in exactly the right way, as Peter Johnstone noted very concisely four weeks ago. Nikita Danilov says that we should choose our vocabulary from Latin, so (applying rule (3)) let's look these words up in Cassell's (1959) Dictionary: > pronus, -a, -um: inclined forward, stooping forward. > ... Transferred meaning: ... well disposed, favourable > supinus, -a, -um (from "sub", cf Greek hyptios): > lying on the back, face upwards. > ... Transferred meaning: ... careless, negligent, lazy. As Toby Bartels has pointed out, les memes mots existent aussi en francais, ed anche in italiano, y sin embargo in espanol tambien, pero mi diccionario es pequeno. QED You may be wondering how all this fuss started. Ronnie Brown asked for my comments on a small fragment of the book he's writing about generalisations of the van Kampen theorem. He was using fibrations to construct colimits in the category of groupoids, which I said was a sledgehammer to crack a nut. However, I also told him that he is the best qualified person I could think of to explain how "canonical" isomorphisms conspire to form non-trivial groups, and so why fibred categories are needed in "semantic" subjects in place of indexed ones. In "syntactic" subjects (categorical type theory) there really are canonical isomorphisms, not just arbitrary choices of them, and indexed categories are appropriate. In my opinion, however, both indexed and fibred categories obfuscate categorical logic. I spent ten years scratching my head, trying to work out why people used them. Eventually, I learned something from Bart Jacobs: indexations arise because predicates depend on variables that range over a set, but not vice versa. Hence the way I treated indexed category theory in Section 9.2 of "Practical Foundations". Chapters VIII and IX develop dependent type theory in the way in which I think it should be done, using "display maps" and not fibrations or hyperdoctrines. In particular, - dependent sums, existential quantifiers and colimits are treated using factorisation systems - or almost, since not every map needs to factorise; and - dependent products, universal quantifiers, exponentials and limits are reduced to partial products. I would invite Jean Benabou to read these two chapters of the book that I HAVE written, and only THEN form a judgement on whether I have "made a major contribution to the field of fibred categories". Paul Taylor www.cs.man.ac.uk/~pt/book PS I drafted this text this morning, and had some friendly private discussions about it with Eduardo Dubuc. We agree on many things, but he maintains that established terminology shouldn't be changed. As I have said, I believe terminology does and should evolve. Also, it seems that I misunderstood the second bit that I quoted from him, for which I apologise, but as Bob says, it's time to bring the subject to a close. From rrosebru@mta.ca Wed Jan 4 20:06:55 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 04 Jan 2006 20:06:55 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1EuIdt-0004Gt-S5 for categories-list@mta.ca; Wed, 04 Jan 2006 20:06:09 -0400 Date: Wed, 4 Jan 2006 19:51:43 -0400 (AST) From: Bob Rosebrugh To: categories Subject: categories: discussion deadlines 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: 9 Jean Benabou has enquired, and this is also to inform other relatively recent subscribers who, like him, may be unfamiliar with an informal procedure used during the 16 years the categories mailing list has been operating. On roughly a half dozen occasions, though none in at least a couple of years, I have judged that a discussion was becoming, as Jean Benabou wrote, `a bit futile', usually after a couple of weeks. In those cases, as in the current one, subscribers were invited to post any further comments within a short period. Making this procedure formal was not necessary in the past, and I do not intend to make it so now. The deadline today was, of course, equally valid for everybody. Best wishes, Bob Rosebrugh From rrosebru@mta.ca Fri Jan 6 15:59:01 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 06 Jan 2006 15:59:01 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1Euxc9-0003BE-MH for categories-list@mta.ca; Fri, 06 Jan 2006 15:51:05 -0400 Message-ID: <1136529330.43be0fb2a6bce@mail.inf.ed.ac.uk> Date: Fri, 6 Jan 2006 06:35:30 +0000 From: ajp@inf.ed.ac.uk To: cmcs06@cs.nott.ac.uk Subject: categories: CMCS 06 Final CFP: deadline 8 January MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit User-Agent: Internet Messaging Program (IMP) 3.2.3 Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 10 *** Final Call for Papers: Deadline 8 January (but do ask if you need another few days) *** CMCS 2006 8th International Workshop on Coalgebraic Methods in Computer Science http://conferences.inf.ed.ac.uk/cmcs06/cmcs06.html Vienna, Austria March 25-27, 2006 The workshop will be held in conjunction with the 9th European Joint Conferences on Theory and Practice of Software ETAPS 2006 March 25 - April 2, 2006 Aims and Scope During the last few years, it has become increasingly clear that a great variety of state-based dynamical systems, like transition systems, automata, process calculi and class-based systems, can be captured uniformly as coalgebras. Coalgebra is developing into a field of its own interest presenting a deep mathematical foundation, a growing field of applications and interactions with various other fields such as reactive and interactive system theory, object oriented and concurrent programming, formal system specification, modal logic, dynamical systems, control systems, category theory, algebra, analysis, etc. The aim of the workshop is to bring together researchers with a common interest in the theory of coalgebras and its applications. The topics of the workshop include, but are not limited to: the theory of coalgebras (including set theoretic and categorical approaches); coalgebras as computational and semantical models (for programming languages, dynamical systems, etc.); coalgebras in (functional, object-oriented, concurrent) programming; coalgebras and data types; (coinductive) definition and proof principles for coalgebras (with bisimulations or invariants); coalgebras and algebras; coalgebraic specification and verification; coalgebras and (modal) logic; coalgebra and control theory (notably of discrete event and hybrid systems). The workshop will provide an opportunity to present recent and ongoing work, to meet colleagues, and to discuss new ideas and future trends. Previous workshops of the same series have been organized in Lisbon, Amsterdam, Berlin, Genova, Grenoble, Warsaw and Barcelona. The proceedings appeared as Electronic Notes in Theoretical Computer Science (ENTCS) Volumes 11,19, 33, 41, 65.1, 82.1 and 106. You can get an idea of the types of papers presented at the meeting by looking at the tables of contents of the ENTCS volumes from those workshops ENTCS Location CMCS 2006 will be held in Vienna on March 25-27, 2006. It will be a satellite workshop of ETAPS 2006, the European Joint Conferences on Theory and Practice of Software. Programme Committee John Power (chair,Edinburgh), Luis Barbosa (Minho), Neil Ghani (Nottingham), H. Peter Gumm (Marburg), Marina Lenisa (Udine), Stefan Milius (Braunschweig), Larry Moss (Bloomington), Jan Rutten (Amsterdam), Hendrik Tews (Dresden), Tarmo Uustalu (Tallinn), Hiroshi Watanabe (Osaka). Keynote Speaker: Peter O'Hearn (Queen Mary, University of London) Invited Speakers: Corina Cirstea (University of Southampton) Alexander Kurz (University of Leicester) Submissions Two sorts of submissions will be possible this year: Papers to be evaluated by the programme committee for inclusion in the ENTCS proceedings: These papers must be written using ENTCS style files and be of length no greater than 20 pages. They must contain original contributions, be clearly written, and include appropriate reference to and comparison with related work. If a submission describes software, software tools, or their use, it should include all source code that is needed to reproduce the results but is not publicly available. If the additional material exceeds 5 MB, URL's of publicly available sites should be provided in the paper. Short contributions: These will not be published but will be compiled into a technical report of the University of Nottingham. They should be no more than two pages and may describe work in progress, summarise work submitted to a conference or workshop elsewhere, or in some other way appeal to the CMCS audience. Both sorts of submission should be submitted in postscript or pdf form as attachments to an email to cmcs06@cs.nott.ac.uk. The email should include the title, corresponding author, and, for the first kind of submission, a text-only one-page abstract. After the workshop, we expect to produce a journal proceedings of extended versions of selected papers to appear in Theoretical Computer Science. Important Dates Deadline for submission of regular papers: January 8, 2006. Notification of acceptance of regular papers: February 6, 2006. Final version for the preliminary proceedings: February 13, 2006. Deadline for submission of short contributions: February 28, 2006. Notification of acceptance of short contributions: March 6, 2006. For more information, please write to cmcs06@cs.nott.ac.uk. From rrosebru@mta.ca Sat Jan 7 16:03:39 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 07 Jan 2006 16:03:39 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1EvK6a-0001pf-U8 for categories-list@mta.ca; Sat, 07 Jan 2006 15:52:01 -0400 To: categories@mta.ca Subject: categories: MPC 2006 2nd Call for Papers Mime-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable Date: Sat, 07 Jan 2006 13:39:26 +0200 From: Tarmo Uustalu Message-Id: <20060107113919.8DF44BF08F@sool.cc.ioc.ee> Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 11 NEWS: - Invited speakers: = Robin Cockett, University of Calgary Olivier Danvy, Aarhus Universitet Oege de Moor, University of Oxford = - The paper submission system is open. - Two satellite workshops: Constructive Methods for Parallel Programming, CMPP Mathematically Structured Functional Programming, MSFP SECOND CALL FOR PAPERS 8th International Conference on = Mathematics of Program Construction MPC '06 Kuressaare, Estonia, 3-5 July 2006 http://cs.ioc.ee/mpc-amast06/mpc/ colocated with AMAST '06 Background The biennial MPC conferences aim to promote the development of mathematical principles and techniques that are demonstrably useful and usable in the process of constructing computer programs. Topics of interest range from algorithmics to support for program construction in programming languages and systems. The previous conferences were held in Twente, The Netherlands (1989), Oxford, UK (1992), Kloster Irsee, Germany (1995), Marstrand, Sweden (1998), Ponte de Lima, Portugal (2000), Dagstuhl, Germany (2002) and Stirling, UK (2004, colocated with AMAST '04). The 2006 conference will be held at Kuressaare, Estonia, colocated with AMAST '06. Invited speakers Robin Cockett, University of Calgary Olivier Danvy, Aarhus Universitet Oege de Moor, University of Oxford Important dates * Submission of abstracts: 27 January 2006 * Submission of full papers: 3 February 2006 * Notification of authors: 17 March 2006 * Camera-ready version: 14 April 2006 Topics Papers are solicited on mathematical methods and tools put to use in program construction. Topics of interest range from algorithmics to support for program construction in programming languages and systems. Some typical areas are type systems, program analysis and transformation, programming language semantics, program logics. Theoretical contributions are welcome provided their relevance for program construction is clear. Reports on applications are welcome provided their mathematical basis is evident. Submission and publication Submission is in two stages. Abstracts (plain text) must be submitted by 27 January 2006. Full papers (pdf) adhering to the llncs style must be submitted by 3 February 2006. There is no official page limit, but authors should strive for brevity. The web-based submission system is open. Papers must report previously unpublished work and not be submitted concurrently to another conference with refereed proceedings. PC members may submit. Accepted papers must be presented at the conference by one of the authors. The proceedings of MPC '06 will be published in the Lecture Notes in Computer Science series of Springer-Verlag. After the conference, the authors of the best papers will be invited to submit revised versions to a special issue of the Science of Computer Programming journal of Elsevier. = Programme committee Tarmo Uustalu, Institute of Cybernetics, Tallinn (chair) Roland Backhouse, University of Nottingham Eerke Boiten, University of Kent Venanzio Capretta, University of Ottawa Sharon Curtis, Oxford Brookes University Jules Desharnais, Universit=E9 de Laval Jeremy Gibbons, University of Oxford Lindsay Groves, Victoria University of Wellington Ian Hayes, University of Queensland William Harrison, University of Missouri Johan Jeuring, Universiteit Utrecht Dexter Kozen, Cornell University Christian Lengauer, Universit=E4t Passau Lambert Meertens, Kestrel Institute Bernhard M=F6ller, Universit=E4t Augsburg Shin-Cheng Mu, University of Tokyo Jos=E9 Oliveira, Universidade do Minho Alberto Pardo, Universidad de la Rep=FAblica Ross Paterson, City University London Ingrid Rewitzky, University of of Stellenbosch Varmo Vene, University of Tartu Satellite workshops Two workshops will be held in conjunction with MPC 2006 as satellites on 2 July 2006: 5th International Workshop on Constructive Methods for = Parallel Programming, CMPP 2006 Workshop on Mathematically Structured Functional Programming, = MSFP 2006 Venue Kuressaare (pop. 16000) is the main town on Saaremaa, the second-largest island of the Baltic Sea. Kuressaare is a charming seaside resort on the shores of the Gulf of Riga highly popular with Estonians as well as visitors to Estonia. The scientific sessions of MPC/AMAST 2006 will take place at Saaremaa Spa Hotel Meri, one among the several new spa hotels in the town. The social events will involve a number of sites, including the 14th-century episcopal castle. Accommodation will be at Saaremaa Spa Hotels Meri and R=FC=FCtli. To get to Kuressaare and away, one must pass through Tallinn (pop. 402000), Estonia's capital city. Tallinn is famous for its picturesque medieval Old Town, inscribed on UNESCO's World Heritage List. Local organizers MPC/AMAST 2006 is organized by Institute of Cybernetics, a research institute of Tallinn University of Technology. The local organizers are Tarmo Uustalu (chair), Monika Perkmann, Juhan Ernits, Ando Saabas, Olha Shkaravska, Kristi Uustalu. Contact email address: mpc06(at)cs.ioc.ee. From rrosebru@mta.ca Mon Jan 9 09:44:58 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 09 Jan 2006 09:44:58 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1EvxAP-0001zU-Bx for categories-list@mta.ca; Mon, 09 Jan 2006 09:34:33 -0400 X-ME-UUID: 20060109084236378.5C49724000EA@mwinf0909.wanadoo.fr Date: Mon, 9 Jan 2006 10:00:19 +0100 Mime-Version: 1.0 (Apple Message framework v543) Content-Type: text/plain; charset=US-ASCII; format=flowed Subject: categories: Back to mathematics From: jean benabou To: Categories Content-Transfer-Encoding: 7bit Message-Id: <5BCD1DA2-80EE-11DA-82B7-000393B90F2C@wanadoo.fr> Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 12 1 - Let P: C ---> B be a functor. I recall that V(P) denotes the subcategory of C having as maps all vertical maps. I have been working for many years now on the following kind of questions. Given an arbitrary subcategory V of a category C, (i) - When is it of the form V(P) for some P ? (ii) - If it is, what relation is there between all the P's such that V=V(P) ? 2 - Before I go further into these questions, especially (ii) let me examine a very important special case where complete answers to (i) and (ii) are well known, namely when C is a group, the answers of course are: (i) - When V is a normal subgroup of G (ii) - If V is normal, let P: C ---> C/V be the canonical surjection on the quotient , and P': C ---> B' be a functor such that V=V(P') , (I'm not assuming that B' is a group), then there is a unique functor Q: C/V ---> B' such that P'=Q.P , and moreover this Q is faithful . I apologize for such trivialities but they will permit me to comment on 1-(i)and (ii) and to sharpen them 3 - The "functor" P of 2 (i) is surjective, but FOR GROUPS this is equivalent to ; P is a fibration, which immediately suggests the following questions for C an arbitrary category and V a subcategory (i) - If V=V(P) for SOME P, is there a FIBRATION P' such that V=V(P'). If it is not always the case, which V's are of the form V(P) for a FIBRATION P ? And of course 1 (ii) can be modified by asking; what relation is there between all the FIBRATIONS P which have the same category V of vertical maps ? This is now purely a question on fibered categories. (ii) There are many variations on (i) e.g. replacing fibration by prefibration, but even for those who don't like prefibrations, here is another kind of variation: A group is a category with pull-backs, and group homomorphisms preserve pull-backs, so in general one might ask : If C is a category with pull-backs, which V's are of the form V(P) for a functor P WHICH PRESERVES PULL-BACKS ? 4 - Let us return to groups. If C is a group and V a subgroup, not necessarily normal, one can denote by C/V the coset space (say right cosets) it is of course not a group but inherits a rich structure from the action of C on it. Now if C is a category, what does one need to assume on a subcategory V of C to be able to construct an analogous C/V and what structure does it inherit ? I have studied many of he previous questions, and in detail the question 4 for which I defined prefoliated and foliated categories which are, roughly speaking, to categorical prefibrations and fibrations, what topological foliafions are are to fibered spaces. The quotient C/V is then a graph, not a category, with extra structure induced by the action of C, which for obvious reasons I call the "transverse graph" . Maybe some persons might consider this as "futile" mathematics. I shall not try to convince them of the contrary. I'm personally very happy to do this kind of mathematics, and my motto in this matter, and many others, is "live and let live" Greetings to all From rrosebru@mta.ca Wed Jan 11 21:08:31 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 11 Jan 2006 21:08:31 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1EwqpI-0003Ar-TO for categories-list@mta.ca; Wed, 11 Jan 2006 21:00:28 -0400 Date: Wed, 11 Jan 2006 19:00:53 +0100 From: Andree Ehresmann To: Categories Subject: categories: Partial answer to Jean Benabou MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 User-Agent: Internet Messaging Program (IMP) 3.2.6 Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 13 In answer to the question raised by Jean: >if C is a category, what does one need to assume on a subcategory V of C to be able to construct an analogous C/V and what structure does it inherit ? Charles Ehresmann had studied the problem of the existence of a quotient = (or at least 'quasi-quotient') category of a category by a sub-category, which h= ad led to the introduction of the notion of a "proper subcategory" (generalizing distinguished sub-groups). His results, summarized in a Note (CRAS Paris= 260, 2116) are developed in the paper on non-abelian cohomology "Cohomologie a valeurs dans une categorie dominee" (Collloque Topologie Bruxelles, CBRM = 1866) . Both papers are reprinted in "Charles Ehresmann: Oeuvres completes et commentees" Part III-2 (and partially taken back in his book "Categories = et structures", Dunod 1965). With all my best wishes Andree Ehresmann. From rrosebru@mta.ca Wed Jan 11 22:19:10 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 11 Jan 2006 22:19:10 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1Ews0o-0007OR-Ja for categories-list@mta.ca; Wed, 11 Jan 2006 22:16:26 -0400 Date: Wed, 11 Jan 2006 17:08:52 -0400 (AST) Subject: categories: CT 2006 - Consider Booking Accommodation Now From: "Dorette Pronk" To: categories@mta.ca User-Agent: SquirrelMail/1.4.3a MIME-Version: 1.0 Content-Type: text/plain;charset=iso-8859-1 Importance: Normal Content-Transfer-Encoding: quoted-printable Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 14 International Category Theory Conference CT 2006 June 25 - July 1, 2006 White Point, Nova Scotia http://www.mathstat.dal.ca/~selinger/ct2006/ The organizers of CT2006 would like to remind prospective participants that early booking of rooms at White Point Beach Resort is important to ensure a good choice of room. Note that not all rooms are isomorphic; there are single bedroom cabins (with ocean view or river view), shared cabins, and hotel style rooms. http://www.whitepoint.com/ Even more importantly, if early registration to the management of White Point Beach Resort that this is going to be a small conference they will adjust the size of the block booking downward accordingly. At the moment we have potential access to most of the rooms at the resort, but this wil= l be reviewed at the end of the month. Please book your accommodation by contacting White Point directly. Tel: 1-800-565-5068 (U.S. and Canada) Tel: +1-902-354-2711 (international) Fax: +1-902-354-7278 Email reservations: greatday@whitepoint.com If you have not yet booked accommodation because you are uncertain of whether you will be able to attend, please note that their cancellation policy is extremely reasonable (a $5 administration fee for a timely cancellation). White Point Beach Resort have informed us that family members may share your room for no extra charge, paying only for meals. The following optio= ns are available: Adults - $37 for breakfast and dinner, $49 for three meals per day Youths 11-18 yrs - $23 for breakfast and dinner, $32 for three meals per day Children 10 & under - $11 for breakfast and dinner, $17 for three meals per day Or people can choose to pay as they go. If for reasons of economy or sociability you wish to share a multiple bedroom cottage but do not have a housemate lined up, White Point have indicated that they are willing to arrange shared accomodation (with people from our conference). Further information about the conference can be found on our (updated) website www.mathstat.dal.ca/~selinger/ct2006/ We hope to see you there! The Organizing Committee, Robert Dawson (Saint Mary's University, Halifax) Dorette Pronk (Dalhousie University, Halifax) Peter Selinger (Dalhousie University, Halifax) From rrosebru@mta.ca Thu Jan 12 09:37:52 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 12 Jan 2006 09:37:52 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1Ex2aS-0006ab-2w for categories-list@mta.ca; Thu, 12 Jan 2006 09:33:56 -0400 Date: Wed, 11 Jan 2006 19:35:57 -0800 From: Toby Bartels To: categories@mta.ca Subject: categories: Re: CT 2006 - Consider Booking Accommodation Now Message-ID: <20060112033557.GA5773@math-rs-n03.ucr.edu> References: Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Disposition: inline In-Reply-To: User-Agent: Mutt/1.4i Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 15 Dorette Pronk wrote in part: >The organizers of CT2006 would like to remind prospective participants >that early booking of rooms at White Point Beach Resort ... > http://www.whitepoint.com/ If you have trouble getting past this front page, then go to the real home page of the restort at . Despite what the broken front page claims, you do not need Flash installed to use the site (although you do seem to need it to view the rooms, and you need Javascript and cookies to book them). -- Toby From rrosebru@mta.ca Thu Jan 12 09:37:52 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 12 Jan 2006 09:37:52 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1Ex2b1-0006dh-EM for categories-list@mta.ca; Thu, 12 Jan 2006 09:34:31 -0400 Date: Thu, 12 Jan 2006 07:23:56 -0600 From: Peter May Message-Id: <200601121323.k0CDNuhZ028616@math.uchicago.edu> To: categories@mta.ca Subject: categories: MacLane Memorial Conference Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 16 There will be a conference on category theory and its applications in memory of Saunders Mac Lane, April 7 through April 11, 2006, at the University of Chicago. The opening event will be a memorial service, or more accurately a celebration of Mac Lane's life, on the morning of April 7. A number of Mac Lane's students, colleagues, collaborators, and friends will speak during the conference, including Steve Awodey (his last student), Peter Freyd, Andre Joyal, Peter Johnstone, William Lawvere, and Peter May. The mathematical focus will be on recent applications of category theory. The conference will be held in conjunction with the 2006 Unni Namboodiri Lectures, which will be given by John Baez on the afternoons of April 7, 10, and 11, under the general title: ``Higher category theory, higher gauge theory''. As MacLane's book ``Categories for the working mathematician'' emphasized, he was interested both in the internal development of category theory and in its development with a view towards applications in other areas of mathematics. The conference will highlight recent work that introduces new category theory aimed directly at applications in differential geometry (and hence to mathematical physics) and in algebraic topology. As Saunders would have liked, most of the speakers will be young mathematicians actively engaged in just such research. A web page at the address http://www.math.uchicago.edu/~may/MacLane with fuller details will be posted shortly. From rrosebru@mta.ca Thu Jan 12 14:40:43 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 12 Jan 2006 14:40:43 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1Ex7Ir-0001xv-Dz for categories-list@mta.ca; Thu, 12 Jan 2006 14:36:05 -0400 Date: Thu, 12 Jan 2006 08:56:56 -0600 (CST) From: Peter May Message-Id: <200601121456.k0CEuuPw010088@tachyon.uchicago.edu> To: categories@mta.ca Subject: categories: Correction Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 17 Secretarial error: Ieke Moerdijk will also be speaking at the MacLane Memorial Conference: From rrosebru@mta.ca Sun Jan 15 10:53:36 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 15 Jan 2006 10:53:36 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1Ey97B-0001Lh-AE for categories-list@mta.ca; Sun, 15 Jan 2006 10:44:17 -0400 Date: Sat, 14 Jan 2006 21:03:20 -0500 (EST) From: James Stasheff To: Categories Subject: categories: Re: Partial answer to Jean Benabou 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: RO X-Status: X-Keywords: X-UID: 18 see also Drinfeld's paper onthe arXiv @2002 on DG categories Jim Stasheff jds@math.upenn.edu Home page: www.math.unc.edu/Faculty/jds As of July 1, 2002, I am Professor Emeritus at UNC and I will be visiting U Penn but for hard copy the relevant address is: 146 Woodland Dr Lansdale PA 19446 (215)822-6707 On Wed, 11 Jan 2006, Andree Ehresmann wrote: > > In answer to the question raised by Jean: > > >if C is a category, what does one need to assume on a subcategory > V of C to be able to construct an analogous C/V and what structure does > it inherit ? > > Charles Ehresmann had studied the problem of the existence of a quotient = > (or at > least 'quasi-quotient') category of a category by a sub-category, which h= > ad led > to the introduction of the notion of a "proper subcategory" (generalizing > distinguished sub-groups). His results, summarized in a Note (CRAS Paris= > 260, > 2116) are developed in the paper on non-abelian cohomology "Cohomologie a > valeurs dans une categorie dominee" (Collloque Topologie Bruxelles, CBRM = > 1866) > . Both papers are reprinted in "Charles Ehresmann: Oeuvres completes et > commentees" Part III-2 (and partially taken back in his book "Categories = > et > structures", Dunod 1965). > With all my best wishes > Andree Ehresmann. > > > > From rrosebru@mta.ca Tue Jan 17 08:46:54 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 17 Jan 2006 08:46:54 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1Eyq99-0002OD-Ru for categories-list@mta.ca; Tue, 17 Jan 2006 08:41:11 -0400 Date: Tue, 17 Jan 2006 09:51:24 +0100 From: gumm@Mathematik.Uni-Marburg.de Organization: Philipps-Uni Marburg, FB Mathematik & Informatik User-Agent: Mozilla/5.0 (Windows; U; Windows NT 5.1; en-US; rv:1.7.2) Gecko/20040804 Netscape/7.2 (ax) X-Accept-Language: en-us, en MIME-Version: 1.0 To: categories Subject: categories: PhD-Position (Mitarbeiterstelle) in Coalgebra, Algebra, Formal Methods References: <42C3F961.4030401@tzi.de> In-Reply-To: <42C3F961.4030401@tzi.de> Content-Type: text/plain; charset=ISO-8859-2; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 19 The Department of Mathematics and Computer Science at the University of Marburg, Germany, offers a full time PhD-Position - Wissenschaftl. Mitarbeiter/in (BAT IIa) - in the area Universal Coalgebra / Universal Algebra, Verification, Formal Methods. Prerequisites: Excellent degree (Diplom or Master) in Computer Science or Mathematics. Strong background in one or more of the above areas. German language fluency. Tasks: Service (organization, preparation, counselling) in teaching and research at the undergraduate and graduate level. PhD-Research The contract is initially for 1 year, with the possibility for extensions to a total of at most 5 years If you are interested, please get in touch with Prof. Dr. H.Peter Gumm gumm@mathematik.uni-marburg.de The official advertisement can be found at http://www.mathematik.uni-marburg.de/~gumm/Stelle/Stelle.pdf From rrosebru@mta.ca Tue Jan 17 16:14:57 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 17 Jan 2006 16:14:57 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1EyxAY-0001VV-5I for categories-list@mta.ca; Tue, 17 Jan 2006 16:11:06 -0400 Message-ID: <43CD0053.606@uwo.ca> Date: Tue, 17 Jan 2006 09:33:55 -0500 From: Rick Jardine User-Agent: Mozilla Thunderbird 1.0.7-1.1.fc4 (X11/20050929) X-Accept-Language: en-us, en MIME-Version: 1.0 To: categories@mta.ca Subject: categories: Fields program on homotopy theory, 2007 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: 20 Announcement: Thematic Program on Geometric Applications of Homotopy Theory Fields Institute, Toronto, Canada January-June, 2007 Online forms for program registration and application for financial support and office space are now available at the program web site: http://www.fields.toronto.edu/programs/scientific/06-07/homotopy/index.html These forms should be filled out all those (including graduate students) who would like to participate in the program and have not already been invited. Early applications are very strongly encouraged. The conference web page now has a link to a preliminary list of confirmed participants, and all other currently available information about the program can be found there. If you have any questions or concerns about the program, please do not hesitate to contact one of the program organizers: Rick Jardine, jardine@uwo.ca Gunnar Carlsson, gunnar@math.stanford.edu Dan Christensen, jdc@uwo.ca We look forward to hearing from you. From rrosebru@mta.ca Tue Jan 17 16:14:57 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 17 Jan 2006 16:14:57 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1EyxBi-0001ce-LW for categories-list@mta.ca; Tue, 17 Jan 2006 16:12:18 -0400 Subject: categories: Chair in geom/top at Glasgow From: Tom Leinster To: categories@mta.ca Content-Type: text/plain Date: Tue, 17 Jan 2006 16:25:20 +0000 Message-Id: <1137515120.25980.6.camel@tl-linux.maths.gla.ac.uk> Mime-Version: 1.0 X-Mailer: Evolution 2.2.1 Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 21 Another job vacancy at Glasgow: we have a new Chair (professorship), the Thomas Muir Chair. This is reserved for someone who can describe themselves as a topologist or geometer. See http://www.jobs.ac.uk/jobfiles/TI146.html for how to apply, and http://www.maths.gla.ac.uk for more about the department. Best wishes, Tom -- Tom Leinster From rrosebru@mta.ca Tue Jan 17 16:14:57 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 17 Jan 2006 16:14:57 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1EyxCU-0001iL-QB for categories-list@mta.ca; Tue, 17 Jan 2006 16:13:06 -0400 Mime-Version: 1.0 (Apple Message framework v733) Content-Transfer-Encoding: 7bit Message-Id: <2E4D67C3-627B-45FA-B9BF-D72905B344F4@dima.unige.it> Content-Type: text/plain; charset=US-ASCII; delsp=yes; format=flowed To: categories@mta.ca From: Marco Grandis Subject: categories: Normal quotients of categories Date: Tue, 17 Jan 2006 19:12:30 +0100 X-Mailer: Apple Mail (2.733) Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 22 Following Andree Ehresmann's posting, and again in partial reply to Jean Benabou, I would like to add some considerations on the quotient of a category modulo a subcategory. With best regards Marco Grandis ------ 1. Generalised quotients of categories. A very general notion of generalised congruence in a category - also involving objects - can be found in a paper by Bednarczyk, Borzyszkowski and Pawlowski [BBP]. Here we will only consider a particular case, determined by the maps which we want to become identities. More precisely, given a category X and a set A of its arrows, X/A will denote the quotient of X modulo the generalised congruence generated by declaring every arrow in A to be equivalent to the identity of its domain. (It exists, because the generalised congruences of a category form a complete lattice, see [BBP].) The quotient p: X -> X/A is determined by the obvious universal property: - for every functor f: X -> Y which takes all the maps of A to identities, there is a unique functor f': X/A -> Y such that f = f'p. It is interesting to note that p automatically satisfies a 2- dimensional universal property, as one can easily deduce from the fact that natural transformations can be viewed as functors X -> Y^2, with values in the category of morphisms of Y. 2. Kernels and normal quotients of categories. This particular case can be made clearer when viewed at the light of general considerations on kernels and cokernels with respect to an *assigned ideal* of "null" arrows, studied in [Gr] - independently of the existence of a zero object. (For kernels with respect to an ideal, see also Ehresmann [Eh] and Lavendhomme [La].) Take, in Cat, the ideal of *discrete* functors, i.e. those functors which send every map to an identity; or, equivalently, consider as *null* objects in Cat the discrete categories and say that a functor is *null* if it factors through such a category (we have thus a *closed* ideal, according to an obvious Galois connection between set of maps and set of objects, see [Gr]). This ideal produces - by the usual universal properties formulated *with respect to null functors* - a notion of kernels and cokernels in Cat. Precisely, given a functor f: X -> Y, its kernel is the wide subcategory of all morphisms of X which f sends to identities of Y (V(f), in Benabou's notation), while its cokernel is the quotient Y -> Y/B, produced by the set-theoretical "arrow-image" B of f. A normal subcategory X' of X, by definition, is a kernel of some functor starting at X, or, equivalently, the kernel of the cokernel of its embedding. It is necessarily a wide subcategory; but, of course, there are wide subcategories which are not normal. Dually, a normal quotient p: X -> X' is the cokernel of some functor with values in X (or, equivalently, the cokernel of its kernel). A normal quotient is always surjective on objects (as it follows easily using its factorisation through its full image), but - of course - need not be surjective on maps. Now, the normal quotients of X are precisely those we have considered in point 1. Indeed, given a set A of arrows of X, the quotient X -> X/A is necessarily the cokernel of some functor f with values in X (eg, take the free category A' on the graph A and the resulting functor f: A' -> X). The normal quotients of a category X form a *lattice*, anti- isomorphic to the lattice of normal subcategories of X, via kernels and cokernels. (More generally, this holds replacing Cat with any category equipped with a closed ideal, and having kernels and cokernels wrt it; see [Gr].) 3. References [BBP] M.A. Bednarczyk - A.M. Borzyszkowski - W. Pawlowski, Generalized congruences-epimorphisms in Cat, Theory Appl. Categ. 5 (1999), No. 11, 266-280. [Eh] C. Ehresmann, Cohomologie a valeurs dans une categorie dominee, Extraits du Colloque de Topologie, Bruxelles 1964, in: C. Ehresmann, Oeuvres completes et commentees, Partie III-2, 531-590, Amiens 1980. (See also the Comments in the same volume, p. 845-847.) [Gr] M. Grandis, On the categorical foundations of homological and homotopical algebra, Cah. Topol. Geom. Diff. Categ. 33 (1992), 135-175. [La] R. Lavendhomme, Un plongement pleinement fidele de la categorie des groupes, Bull. Soc. Math. Belgique, 17 (1965), 153-185. From rrosebru@mta.ca Thu Jan 19 13:25:31 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 19 Jan 2006 13:25:31 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1EzdRn-0004jQ-Fw for categories-list@mta.ca; Thu, 19 Jan 2006 13:19:43 -0400 Date: Wed, 18 Jan 2006 14:52:14 +0100 From: Jiri Rosicky To: categories@mta.ca Subject: categories: research positions Message-ID: <20060118135213.GA25007@queen.math.muni.cz> Mime-Version: 1.0 Content-Type: text/plain; charset=iso-8859-2 Content-Disposition: inline User-Agent: Mutt/1.5.9i Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 23 Eduard Cech center had been established in 2005 as the national research center focusing its attention to interactions between algebra, geometry, and logic (and their applications in cryptology, computer science, etc.). It is jointly operated by mathematicians from Masaryk University in Brno, Charles University in Prague and Academy of Sciences of the Czech Republic, with offices both in Brno and Prague. The Center invites applications for several research positions commencing during the year 2006 at the date depending on mutual agreement. The positions are initially for one year with a possibility of extension for another year. The candidates must be recent PhD's that obtained their degree not earlier than 2 years before the beginning of their contract with the Eduard Cech Center. Candidates should submit a letter of application accompanied by a CV, list of publications and an outline of their research project to Professor Jan Slovak (slovak@muni.cz) not later than March 15, 2006. They should also arrange for at least 2 letters of recommendation (one can be from a Czech mathematician) to be mailed directly to slovak@muni.cz before March 15, 2006. The successful applicants will be notified as soon as possible but not later than April 15, 2006. Further information about the Eduard Cech Center can be found at http://ecc.sci.muni.cz From rrosebru@mta.ca Thu Jan 19 13:25:31 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 19 Jan 2006 13:25:31 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1EzdPr-0004ZU-8l for categories-list@mta.ca; Thu, 19 Jan 2006 13:17:43 -0400 Date: Wed, 18 Jan 2006 15:07:18 +0000 To: categories@mta.ca Subject: categories: Funding for attending CiE 2006 Message-ID: <43CE59A6.mail2SZ1NM29E@cs-svr1.swan.ac.uk> User-Agent: nail 11.4 8/29/04 MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit From: A.Beckmann@swansea.ac.uk (Arnold Beckmann) Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 24 Please forward this to interested researchers and students. ***************************************************************** FUNDING OPPORTUNITIES TO ATTEND COMPUTABILITY IN EUROPE 2006 This is just to clarify the various opportunities offered throught the organisers of CiE 2006 for PhD students and researchers from the Former Soviet Union to obtain funding to attend the conference. The deadline for all the funding schemes has been fixed for MARCH 31, 2006 Full details of how to apply are available via the webpage: http://www.cs.swan.ac.uk/cie06/give-page.php?14 ASL FUNDING: CiE 2006 is an ASL sponsored meeting, so PhD students who have taken advantage of the ASL very favourable membership terms (or intend to do so soon), will be able to apply direct to them for a grant to attend. See: http://www.aslonline.org/studenttravelawards.html EPSRC FUNDING FOR UK-BASED PhD STUDENTS: CiE 2006 has obtained generous support from the UK Engineering and Physical Sciences Research Council for UK-based PhD students. For these grants, application is direct to the conference organisers at cie06@swansea.ac.uk - see the website for details. LMS FUNDING FOR UK-BASED PhD STUDENTS, AND fSU RESEARCHERS: The London Mathematical Society funding for students is similar to that from EPSRC. In addition, there is funding for researchers from the Former Soviet Union, including some support for travel, as well as for accommodation, registration, etc. Again - application is direct to the organisers. PRESENTERS OF PAPERS AT CiE 2006: It is important to note that in allocating funding, the organisers will prioritise presenters of papers at CiE 2006. The deadline for submission for the LNCS Proceedings volume is: THURSDAY FEBRUARY 9th, 2006 For details of the submission procedure, see: http://www.cs.swan.ac.uk/cie06/give-page.php?12 Similarly, giving a talk at CiE 2006 will improve the chances of getting funding through the ASL scheme. ***************************************************************** From rrosebru@mta.ca Thu Jan 19 13:25:31 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 19 Jan 2006 13:25:31 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1EzdP2-0004VD-Gc for categories-list@mta.ca; Thu, 19 Jan 2006 13:16:52 -0400 From: "Reinhard Boerger" Organization: FernUniversitaet To: categories@mta.ca Date: Wed, 18 Jan 2006 09:36:09 +0200 MIME-Version: 1.0 Content-type: text/plain; charset=US-ASCII Content-transfer-encoding: 7BIT Subject: categories: re: Normal quotients of categories Message-ID: <43CE0C08.32295.302D02@localhost> Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 25 Hello, let me add some remarks to Marco Grandis' posting. > 1. Generalised quotients of categories. > > A very general notion of generalised congruence in a category - > also involving objects - can be found in a paper by Bednarczyk, > Borzyszkowski and Pawlowski [BBP]. I have not yet looked at that paper, but I think the "natural" thing is to consider equivalence relations R on a category C, which are subcategories of CxC (i.e. closed under composition, not necessary full; identities are in R by relexivity of R). In my diplomarbeit "Kongruenzrelationen auf Kategorien" from 1977, I considered that, but I was not the first one. Some years earlier there was a paper by Jacques Mersch from Liege (Belgium), which unfortunately appeared only in an internal publication of the university of Liege. Moreover, I think I remember that John Isbell did something on this subject. > The quotient p: X -> X/A is determined by the obvious > universal property: The universal property is also obvious in the general situation. For small categories, a functor with this property always exists, let's call it a quotient functor. For large categories it my happen that the hom-sets of the quotient become large, even if the hom-sets of the original category are small. In general, a congruence as above is not a kernel of a functor; the quotient functor may identify more morphisms. In my diplomarbeit, I rediscovered an example, which had already been found by Mersch. The quotient functors are exactly the regular epis in CAT. But unfortunately, they are not closed under compositon, so a quotient of a quotient of C need not be a quotient of C. > It is interesting to note that p automatically satisfies a 2- > dimensional universal property, as one can easily deduce from the fact > that natural transformations can be viewed as functors X -> Y^2, > with values in the category of morphisms of Y. Of course, this argument also works in the general situation. Greetings Reinhard Boerger From rrosebru@mta.ca Thu Jan 19 13:25:31 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 19 Jan 2006 13:25:31 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1EzdQy-0004eQ-Nz for categories-list@mta.ca; Thu, 19 Jan 2006 13:18:52 -0400 Mime-Version: 1.0 (Apple Message framework v733) Content-Type: text/plain; charset=US-ASCII; delsp=yes; format=flowed Message-Id: Content-Transfer-Encoding: 7bit From: Marco Grandis Subject: categories: Re: Normal quotients of categories Date: Wed, 18 Jan 2006 11:26:00 +0100 To: X-Mailer: Apple Mail (2.733) Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 26 On 18 Jan 2006, at 09:36, V. Schmitt wrote: > Marco I am not very awake this morning but i think that this > construction of formally inverted some arrow is well known > for long (cf for instance Borceux's handbooks on localizations). > Am i wrong? > Cheers, > Vincent > > Categories of fractions are indeed very well-known, but satisfy a different universal property: to make *invertible* the assigned arrows (instead of making them *identities*). But you can view categories of fractions at the light of what I was saying. Take in Cat the (closed) ideal of functors which send every map to an isomorphism, or equivalently of those functors which factor through a groupoid. With respect to this ideal, the kernel of a functor f: X -> Y is the (wide and replete) subcategory of maps which f turns into isomorphisms, while the cokernel is the category of fractions of Y which inverts all arrows reached by f. Best regards Marco G. PS. And - thinking of Jean Pradine's message - yes, of course, quotient of groupoids are important, but have special features of their own; as he is pointing out. From rrosebru@mta.ca Thu Jan 19 13:25:31 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 19 Jan 2006 13:25:31 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1EzdNq-0004Pf-PD for categories-list@mta.ca; Thu, 19 Jan 2006 13:15:38 -0400 Message-ID: <43CD700C.6040205@math.upenn.edu> Date: Tue, 17 Jan 2006 17:30:36 -0500 From: jim stasheff User-Agent: Thunderbird 1.5 (Windows/20051201) MIME-Version: 1.0 To: categories@mta.ca Subject: categories: Re: Normal quotients of categories References: <2E4D67C3-627B-45FA-B9BF-D72905B344F4@dima.unige.it> In-Reply-To: <2E4D67C3-627B-45FA-B9BF-D72905B344F4@dima.unige.it> 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: 27 [Note from moderator: reference was mentioned before, but is more complete below] Don't know if this got through already as myu mail has been acting up: There is also Drinfeld's *math.KT/0210114* [abs , ps , pdf , other ] : Title: *DG quotients of DG categories* Authors: * Vladimir Drinfeld * Comments: 50 pages, Latex; some typographical errors corrected, some references added Subj-class: K-Theory and Homology; Algebraic Geometry; Algebraic Topology; Category Theory jim Marco Grandis wrote: > Following Andree Ehresmann's posting, and again in partial reply to > Jean Benabou, I would like to add some considerations on the quotient > of a category modulo a subcategory. > > With best regards > > Marco Grandis > From rrosebru@mta.ca Fri Jan 20 16:19:05 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 20 Jan 2006 16:19:05 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1F02Zr-0000En-5v for categories-list@mta.ca; Fri, 20 Jan 2006 16:09:43 -0400 Date: Thu, 19 Jan 2006 14:56:36 -0500 From: jim stasheff User-Agent: Thunderbird 1.5 (Windows/20051201) MIME-Version: 1.0 To: Categories List Subject: categories: historical query Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 28 Does anyone have any information on how Grothendieck's yoga for deformation theory was transmitted to Schlessinger and Deligne? or have a reference as to a published or cahier secret of Grothendieck where it is outlined in his own words? jim From rrosebru@mta.ca Fri Jan 20 16:19:05 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 20 Jan 2006 16:19:05 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1F02ZL-0000B4-U1 for categories-list@mta.ca; Fri, 20 Jan 2006 16:09:11 -0400 Mime-Version: 1.0 (Apple Message framework v746.2) Content-Transfer-Encoding: 7bit Message-Id: <28C53251-038A-48DC-810C-9661D2D36BF5@cs.clemson.edu> Content-Type: text/plain; charset=US-ASCII; delsp=yes; format=flowed To: Categories List From: Steve Stevenson Subject: categories: Fuzzy categories Date: Thu, 19 Jan 2006 13:00:24 -0500 X-Mailer: Apple Mail (2.746.2) Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 29 This seems like a natural idea. But the American Math Soc web site has no listings. What is a fundamental reference? -- steve steve@cs.clemson.edu From rrosebru@mta.ca Fri Jan 20 16:19:05 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 20 Jan 2006 16:19:05 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1F02Ys-00008V-Dt for categories-list@mta.ca; Fri, 20 Jan 2006 16:08:42 -0400 From: Gaucher Philippe Organization: PPS To: categories@mta.ca Subject: categories: About accessibility of the weak equivalences of a combinatorial model category Date: Thu, 19 Jan 2006 18:34:02 +0100 User-Agent: KMail/1.8.2 MIME-Version: 1.0 Content-Disposition: inline Content-Type: text/plain; charset="us-ascii" Content-Transfer-Encoding: 7bit Message-Id: <200601191834.02937.gaucher@pps.jussieu.fr> Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 30 Dear All, How can we prove that the class of weak equivalences of a combinatorial model category is accessible ? I know how to prove that the class of weak equivalences of a combinatorial model category is accessibly embedded in the whole class of morphisms. And then it is accessible using Vopenka's principle by [Adamek-Rosicky's book Theorem 6.17] . Can we remove Vopenka's principle from the argument ? Or is this fact in the definition of a "combinatorial model category" (for me, it's a cofibrantly generated model category such that the underlying category is locally presentable) ? Thanks in advance. pg. From rrosebru@mta.ca Tue Jan 24 11:38:22 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 24 Jan 2006 11:38:22 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1F1Q83-0005C4-KK for categories-list@mta.ca; Tue, 24 Jan 2006 11:30:43 -0400 Mime-Version: 1.0 (Apple Message framework v746.2) Content-Type: text/plain; charset=US-ASCII; delsp=yes; format=flowed Message-Id: Content-Transfer-Encoding: 7bit From: Michael Mislove Subject: categories: MFPS 22 Second Call for Papers Date: Sun, 22 Jan 2006 17:03:28 -0600 To: categories@mta.ca Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 31 Dear Colleagues, We are now accepting submissions for MFPS 22, which will take place in Genova, Italy on May 24 - 27, 2006. The invited speakers for MFPS 22 include Marcelo Fiore (Cambridge), Eugenio Moggi (Genova), Prakash Panangaden (McGill), Davide Sangiorge (Bologna), Peter Selinger (Dalhousie) and Steve Zdancewic (Penn). In addition, there will be special sessions on security, on timed systems, and on quantum computing. There also will be a Tutorial Day on May 23 on Separation Logic; the lecturers will be Stephen Brookes (CMU), Peter O'Hearn (QMW) and John Reynolds (CMU). Researchers are encouraged to submit papers in programming semantics, its mathematical and logical foundations and related areas, as well as in the areas listed above. Submissions should be made in the form of a PostScript or pdf file thact can be printed on any standard printer. The deadline for submissions is Midnight, Pacific Standard Time, Wednesday, February 22, 2006. More information about the meeting together with precise instructions about submissions can be found at the MFPS 22 web page http://www.math.tulane.edu/~mfps/mfps22.htm Best regards, Mike Mislove =============================================== Professor Michael Mislove Phone: +1 504 862-3441 Department of Mathematics FAX: +1 504 865-5063 Tulane University URL: http://www.math.tulane.edu/~mwm New Orleans, LA 70118 USA =============================================== From rrosebru@mta.ca Tue Jan 24 11:38:22 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 24 Jan 2006 11:38:22 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1F1QBe-0005WR-6K for categories-list@mta.ca; Tue, 24 Jan 2006 11:34:26 -0400 To: categories@mta.ca From: Kreutzer + Schweikardt Subject: categories: FLoC'06 - Call for Papers Reply-To: floc@informatik.hu-berlin.de Date: Mon, 23 Jan 2006 20:03:04 +0100 (CET) Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 32 FLoC'06 - Call for Papers The 2006 Federated Logic Conference Seattle, Washington, USA August 10 -- August 22, 2006 http://research.microsoft.com/floc06/ In 1996, as part of its Special Year on Logic and Algorithms, DIMACS hosted the first Federated Logic Conference (FLoC). It was modeled after the successful Federated Computer Research Conference (FCRC), and synergetically brought together conferences that apply logic to computer science. The second Federated Logic Conference (FLoC'99) was held in Trento, Italy, in 1999, and the third (FLoC'02) was held in Copenhagen, Denmark, in 2002. The Fourth Federated Logic Conference (FLoC'06) will be held in Seattle, Washington, in August 2006, at the Seattle Sheraton (http://www.sheraton.com/seattle). The following conferences will participate in FLoC'06: Int'l Conference on Computer-Aided Verification (CAV) Int'l Conference on Rewriting Techniques and Applications (RTA) IEEE Symposium on Logic in Computer Science (LICS) Int'l Conference on Logic Programming (ICLP) Int'l Conference on Theory and Applications of Satisfiability Testing (SAT) Int'l Joint Conference on Automated Reasoning (IJCAR) In addition, FLoC'06 will host 42 workshops. Pre-conference workshops will be held on August 10-11. LICS, RTA, and SAT will be held in parallel on August 12-15, to be followed by mid-conference workshops and excursions on August 15-16. CAV, ICLP, and IJCAR will be held in parallel on August 16-21, to be followed by post-conference workshops on August 21-22. Plenary events involving all the conferences are planned. Calls for papers for the conferences and workshops are available at the conference website: http://research.microsoft.com/floc06/. We invite you to submit papers to FLoC'06 conferences and workshops. FLoC'06 Steering Committee Moshe Y. Vardi (General Chair) Jakob Rehof (Conference Chair) Edmund Clarke (CAV) Reiner Hahnle (IJCAR) Manuel Hermenegildo (ICLP) Phokion Kolaitis (LICS) Henry Kautz (SAT) Aart Middeldorp (RTA) Andrei Voronkov (IJCAR) From rrosebru@mta.ca Tue Jan 24 11:38:22 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 24 Jan 2006 11:38:22 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1F1Q9o-0005L3-Fr for categories-list@mta.ca; Tue, 24 Jan 2006 11:32:32 -0400 Message-ID: <43D4E02A.5010606@cs.stmarys.ca> Date: Mon, 23 Jan 2006 09:54:50 -0400 From: "Robert J. MacG. Dawson" User-Agent: Mozilla Thunderbird 1.0.2 (Windows/20050317) X-Accept-Language: en-us, en To: Categories List Subject: categories: Re: Fuzzy categories 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: 33 Steve Stevenson wrote: > This seems like a natural idea. But the American Math Soc web site > has no listings. What is a fundamental reference? Kelly's "Basic Concepts of Enriched Category Theory" http://www.tac.mta.ca/tac/reprints/articles/10/tr10.pdf Of course, the term "fuzzy categories" is never actually used there. (You can put the stockwhip down now, Max!) Moreover, it is not clear to me that "fuzzification" in its usual cottage-industry sense would be seen by many categorists as the right level of generality. But if you wanted to do it for some reason, that's probably where to start. -Robert Dawson From rrosebru@mta.ca Wed Jan 25 06:11:53 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 25 Jan 2006 06:11:53 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1F1ha4-0001Zm-J0 for categories-list@mta.ca; Wed, 25 Jan 2006 06:08:48 -0400 Subject: categories: Re: Fuzzy categories From: Graham White To: Categories@mta.ca In-Reply-To: <43D4E02A.5010606@cs.stmarys.ca> References: <43D4E02A.5010606@cs.stmarys.ca> Content-Type: text/plain Date: Tue, 24 Jan 2006 16:54:03 +0000 Message-Id: <1138121643.9030.30.camel@localhost.localdomain> Mime-Version: 1.0 X-Mailer: Evolution 2.4.1 Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 34 On Mon, 2006-01-23 at 09:54 -0400, Robert J. MacG. Dawson wrote: > Steve Stevenson wrote: > > This seems like a natural idea. But the American Math Soc web site > > has no listings. What is a fundamental reference? > > Kelly's "Basic Concepts of Enriched Category Theory" > > http://www.tac.mta.ca/tac/reprints/articles/10/tr10.pdf > > Of course, the term "fuzzy categories" is never actually used there. > (You can put the stockwhip down now, Max!) Moreover, it is not clear to > me that "fuzzification" in its usual cottage-industry sense would be > seen by many categorists as the right level of generality. But if you > wanted to do it for some reason, that's probably where to start. > > -Robert Dawson There has been quite a lot of work on fuzzy sets and topos theory: a Google search for "fuzzy sets topos", or "fuzzy logic topos", will turn up quite a lot of it. I find it a bit surprising that there is so much work, given the sociological characteristics of the communities involved. But it's there anyway. Graham White From rrosebru@mta.ca Wed Jan 25 06:11:53 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 25 Jan 2006 06:11:53 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1F1hYA-0001Wt-7x for categories-list@mta.ca; Wed, 25 Jan 2006 06:06:50 -0400 From: "Marta Bunge" To: categories@mta.ca Subject: categories: book and preprints available Date: Tue, 24 Jan 2006 11:51:29 -0500 Mime-Version: 1.0 Content-Type: text/plain; format=flowed Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: RO X-Status: X-Keywords: X-UID: 35 Dear colleagues, The following recent preprints (including a book) are available in my (updated) homepage http://www.math.mcgill.ca/bunge Marta Bunge and Jonathon Funk, Topos Distributions and Singular Coverings. Book. Submitted to Springer Lecture Notes in Mathematics. http://www.math.mcgill.ca/bunge/s.ps Marta Bunge and Jonathon Funk, "Quasicomponents in Topos Theory: the Hyperpure, Complete Spread Factorization". To appear in Mathematical Proceedings of the Cambridge Philosophical Society. http://www.math.mcgill.ca/bunge/mpcps.ps Marta Bunge and Jonathon Funk, "An Intrinsic Characterization of Branched Coverings". To appear in the Streetfest Proceedings, possibly in Contemporary Mathematics, AMS. http://www.math.mcgill.ca/bunge/intrinsic.ps Comments to either one of us (jfunk@uwichill.edu.bb, marta.bunge@mcgill.ca) are welcome. Greetings, Marta Bunge ************************************************ Marta Bunge Professor Emerita Dept of Mathematics and Statistics McGill University 805 Sherbrooke St. West Montreal, QC, Canada H3A 2K6 Office: (514) 398-3810 Home: (514) 935-3618 marta.bunge@mcgill.ca http://www.math.mcgill.ca/bunge/ ************************************************ From rrosebru@mta.ca Wed Jan 25 12:56:10 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 25 Jan 2006 12:56:10 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1F1np8-0007ZB-CH for categories-list@mta.ca; Wed, 25 Jan 2006 12:48:46 -0400 Subject: categories: CT 2006: student support and registration To: categories@mta.ca (Categories List) Date: Tue, 24 Jan 2006 17:29:58 -0400 (AST) X-Mailer: ELM [version 2.5 PL2] MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Message-Id: <20060124212958.28F2B1084A@sigma.mathstat.dal.ca> From: selinger@mathstat.dal.ca (Peter Selinger) Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 36 CALL FOR PARTICIPATION International Category Theory Conference CT 2006 June 25 - July 1, 2006 White Point, Nova Scotia http://www.mathstat.dal.ca/~selinger/ct2006/ * * * IMPORTANT NEWS CONTAINED IN THIS ANNOUNCEMENT: * invited speakers * graduate student support (application deadline Feb 15!) * submission of abstracts (deadline Feb 27!) * registration is now open * arrival and departure information * airport information The International Category Theory Conference (CT) covers all areas of pure and applied category theory. Topics of interest include, but are not limited to: higher dimensional categories, categorical logic, applications of categories in algebra, topology, combinatorics, and other areas of mathematics, applications of category theory to computer science, physics and other mathematical sciences. Previous meetings in this series were held in Vancouver (2004), Como (2000), Coimbra (1999), Vancouver (1997), Halifax (1995), Tours (1994), Isle of Thorns (1992), Montreal (1991), and Como (1990). CT 2006 will be held at White Point Beach Resort (http://www.whitepoint.com/), a seaside resort in Nova Scotia (Canada), about 100 minutes' drive from Halifax. It will be an active research-oriented conference, in something of an "Oberwolfach style". All those interested in category theory and its applications are welcome. INVITED SPEAKERS: ***NEW*** The scientific committee has chosen five invited speakers, of whom the following four have already confirmed their participation: Kathryn Hess (EPF Lausanne) Steve Lack (University of Western Sydney) Tom Leinster (University of Glasgow) Peter Selinger (Dalhousie University) GRADUATE STUDENT SUPPORT: ***NEW*** Please encourage your graduate students to attend this conference. A limited amount of funding will be available to support the participation of graduate students. Students wishing to apply for this money should contact the organizers at ct06@mathstat.dal.ca by FEBRUARY 15, and include the following information: 1. A one-page email letter stating your background as well as why you are interested in attending the conference. 2. The letter should also describe any other sources of funding available to you to attend. 3. An email letter of reference from your supervisor or an appropriate other person. TO GIVE A TALK: Prospective speakers should submit an abstract of up to one page. Abstracts should be sufficiently detailed to allow the scientific committee to assess the merits of the work. Submissions should be in plain text, Postscript, or PDF format, and must be sent to ct06@mathstat.dal.ca by FEBRUARY 27. Receipt of all submissions will be acknowledged by return email. Authors will be notified by March 30 of the acceptance of their talks. REGISTRATION: ***NEW*** Registration is now open. The registration fees for CT 2006 are as follows: If registering by March 1 (early registration): Regular -- $120 Reduced (*) -- $75 If registering after March 1 (late registration): Regular -- $150 Reduced (*) -- $100 (*) the reduced registration fee applies to students, postdocs, and researchers without grant. There are two easy methods to register for CT 2006. The preferred method is to use our secure online registration form, which allows you to pay the registration fee by credit card: https://sigma.mathstat.dal.ca/~selinger/ct2006/registration.php An alternate paper registration form is also available on the same website, for those who wish to fax or mail their registration and payment. Please remember that, in addition to registering, you also need to reserve your accomodations with White Point Beach Resort. See the conference website for details. ACCOMMODATIONS, ARRIVAL, DEPARTURE: ***IMPORTANT*** Please book your rooms at White Point Beach Resort as soon as possible. We encourage all participants to book this by the end of January; keep in mind that it can be canceled later for a $5 fee. The normal arrival date is Sunday, June 25, and the normal departure date is Saturday, July 1. There will be an informal opening reception / buffet dinner on June 25 from 6:30-10:30pm. The normal check-in time is 2pm and check-out time is 11am. If you need to make special arrangements for early arrival or late departure, please make them by contacting White Point directly. The conference venue offers a choice of accommodation, both in comfortable finished cabins and in "hotel-style" rooms. All meals are included in the price of the rooms. Subject to availability, White Point Beach Resort has agreed to extend the conference rates to the weeks before and after the conference in case any guests wish to stay longer. If you would like to arrange this, please contact White Point directly. For reservations, please contact White Point Beach Resort: Tel: 1-800-565-5068 (U.S. and Canada) Tel: +1-902-354-2711 (international) Fax: +1-902-354-7278 Email reservations: greatday@whitepoint.com AIRPORT TRANSPORTATION: ***NEW*** We will arrange for shared transportation between Halifax International Airport and White Point Beach Resort on the days of arrival and departure, at no extra charge to conference participants and their guests. To take advantage of this, please let us know, at ct06@mathstat.dal.ca, your arrival and departure times, airline, and flight numbers, as soon as you have this information. Please note that White Point Beach Resort is 100 minutes driving distance from the airport, and there is no convenient alternative transportation available except for renting a car. IMPORTANT DEADLINES: Jan 25, 2006: early booking of rooms Feb 15, 2006: application for graduate student support Feb 27, 2006: submission of abstracts Mar 1, 2006: early registration Mar 30, 2006: notification of authors Apr 20, 2006: registration SCIENTIFIC COMMITTEE: Jiri Adamek John Baez Michael Barr Eugenia Cheng Maria Manuel Clementino Marcelo Fiore Peter Freyd Jonathon Funk Peter Johnstone Steve Lack Susan Niefield Phil Scott Ross Street Walter Tholen (chair) Enrico Vitale ORGANIZERS: Robert Dawson (rdawson@cs.stmarys.ca) Dorette Pronk (pronk@mathstat.dal.ca) Peter Selinger (selinger@mathstat.dal.ca) CONFERENCE EMAIL AND WEBSITE: ct06@mathstat.dal.ca http://www.mathstat.dal.ca/~selinger/ct2006/ From rrosebru@mta.ca Thu Jan 26 11:06:03 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 26 Jan 2006 11:06:03 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1F28b8-0006ha-5a for categories-list@mta.ca; Thu, 26 Jan 2006 10:59:42 -0400 To: categories@mta.ca Subject: categories: An International Symposium Celebrating the 100th Birthday of Kurt = Message-Id: From: cat-dist@mta.ca Date: Thu, 26 Jan 2006 10:59:42 -0400 Status: RO X-Status: X-Keywords: X-UID: 37 G=F6del From: goedel2006@logic.at Message-Id: Sender: cat-dist@mta.ca Precedence: bulk Horizons of Truth Logics, Foundations of Mathematics, and the Quest for Understanding the Nature of Knowledge. G=F6del Centenary 2006 An International Symposium Celebrating the 100th Birthday of Kurt G=F6del 27.-29. April 2006 Festsaal of the University of Vienna Organized by the Kurt G=F6del Society The Symposium will take place April 27- 29 in the Celebration Hall of the University of Vienna, famous for its architectural beauty and Gustav Klimt murals. More than 20 lectures by eminent scientists in the fields of logics, mathematics, philosophy, physics, cosmology, and theology will provide new insights into the life and work of Kurt G=F6del and their implications for future generations. A young researcher's competition will allow 10 young researchers to present their projects to an eminent audience, the awards being presented at Belvedere Palace on Friday, April 28, Kurt G=F6del's 100th birthday. The first prize in the amount 20 000 EUR will be awarded to the best project, followed by two additional prizes of 5000 EUR each. A poster session, containing presentations of selected posters will be held in the Small Celebration Hall, and the Senate Hall of the University of Vienna. The poster volume will be published by the Kurt G=F6del Society after the Symposium and sent to all authors. An exhibition on G=F6del life and work will be held in the old library of the University of Vienna throughout the Symposium. Honorary Chair: Gaisi Takeuti, University of Tsukuba, President of the Kurt G=F6del Society Invited Speakers: John D. Barrow, University of Cambridge Gregory J. Chaitin, IBM Thomas J. Watson Research Center, New York Paul Cohen, Stanford University Jack Copeland, University of Canterbury, New Zealand George Ellis, University of Cape Town Solomon Feferman, Stanford University Harvey Friedman, Ohio State University Ivor Grattan-Guinness, Middlesex University Petr Hajek, Academy of Sciences of the Czech Republic Juliette Kennedy, University of Helsinki Ulrich Kohlenbach, Darmstadt University of Technology Georg Kreisel, Royal Society Angus John Macintyre, Royal Society Piergiorgio Odifreddi, University of Turin Christos H. Papdimitiriou, University of California, Berkeley Roger Penrose, University of Oxford Hilary Putnam, Harvard University Wolfgang Rindler, University of Texas, Dallas Dana Scott, Carnegie Mellon University Avi Wigderson, Institute for Advanced Study, Princeton Hugh Woodin, University of California, Berkeley Invited Presentation: Andrei Voronkov, University of Manchester and Microsoft Web and registration: http://www.logic.at/goedel2006/ From rrosebru@mta.ca Sat Jan 28 18:03:37 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 28 Jan 2006 18:03:37 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1F2y1C-00054e-Nu for categories-list@mta.ca; Sat, 28 Jan 2006 17:54:02 -0400 Message-Id: <200601262109.k0QL9aq00157@math-cl-n03.ucr.edu> Subject: categories: universal algebra and diagrammatic reasoning To: categories@mta.ca (categories) Date: Thu, 26 Jan 2006 13:09:36 -0800 (PST) From: "John Baez" X-Mailer: ELM [version 2.5 PL6] 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: 38 Hi - I hope to see some of you in Marseille for Geocal06! I'll be talking about "universal algebra and diagrammatic reasoning", and there's a bunch of lecture notes here: http://math.ucr.edu/home/baez/universal/ Abstract: Since the introduction of category theory, the old subject of "universal algebra" has diversified into a large collection of frameworks for describing algebraic structures. These include "monads" (formerly known as "triples"), the "algebraic theories" of Lawvere, and the "PROPs" of Boardman and Vogt. We give an overview of these different frameworks, which are closely related, and explain how one can reason diagrammatically about algebraic structures defined using them. We focus on the bar construction and the relation between algebraic theories and PROPs. (I feel guilty for not talking about operads... I'll do it if there's time!) Best, jb From rrosebru@mta.ca Sat Jan 28 18:03:37 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 28 Jan 2006 18:03:37 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1F2y2I-00058M-5B for categories-list@mta.ca; Sat, 28 Jan 2006 17:55:10 -0400 Date: Fri, 27 Jan 2006 11:17:42 -0500 (EST) From: Susan Niefield To: categories@mta.ca Subject: categories: horizontal composition 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: 39 Does anyone know of a reference for the following definition of a bicategory? The primitive composites are: gf for composable 1-cells GF for vertically composable 2-cells f*G and F*g for horizontally composable pairs of each with appropriate axioms including (G*f')(g*F)=(g'*F)(G*f), for F:f->f':X->Y and G:g->g':Y->Z. The horizontal composite G*F is defined to be the common value of the two vertical composites. -Susan From rrosebru@mta.ca Tue Jan 31 10:19:56 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 31 Jan 2006 10:19:56 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1F3wF4-0005hx-OY for categories-list@mta.ca; Tue, 31 Jan 2006 10:12:22 -0400 From: mgs2006@mcs.le.ac.uk To: categories@mta.ca Subject: categories: Midlands Graduate School Date: 30 Jan 2006 11:12:57 +0000 Message-ID: Mime-Version: 1.0 Content-Type: text/plain; format=flowed; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 40 [Apologies for multiple copies] ************************************************************* Midlands Graduate School 2006 in the Foundations of Computing ************************************************************* http://www.cs.le.ac.uk/~mgs2006 The Midlands Graduate School is taking place 8 - 12 April 2006 at the University of Leicester, UK. The School provides an intensive course of lectures on the Foundations of Computing. It is very well established, having run annually for the past six years, and has always proved a popular and successful event. This year we have Luke Ong, Oxford University and Thomas Streicher, Darmstadt University as guest lecturers. The lectures are aimed at graduate students, typically in their first or second year of study for a PhD. However, the school is open to anyone who is interested in learning more about mathematical computing foundations, and we especially invite participants from UK universities and from sites participating in the APPSEM working group. Foundational courses: R Crole Leicester Operational Semantics =09 P Levy Birmingham Typed Lambda Calculus =09 D Pattinson Leicester Category Theory =09 Advanced courses: T Altenkirch Nottingham Quantum Programming M Escardo Birmingham Operational Domain Theory & Topology H Nilsson Nottingham Advanced Functional Programming L Ong Oxford Game Semantics T Streicher Darmstadt Constructive Logic E Tuosto Leicester Concurrency We expect to have some grants for UK students, while APPSEM funds can be used to support students from APPSEM affiliated sites. For further details and registration please visit http://www.cs.le.ac.uk/~mgs2006 Please register soon! Places and accommodation will be allocated on a first-come, first-serve basis. Roy Crole Alexander Kurz Dirk Pattinson From rrosebru@mta.ca Tue Jan 31 10:19:56 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 31 Jan 2006 10:19:56 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1F3wHs-000600-AH for categories-list@mta.ca; Tue, 31 Jan 2006 10:15:16 -0400 Message-ID: <1138712024.43df5dd8f133d@webmail.unige.it> Date: Tue, 31 Jan 2006 13:53:44 +0100 From: grandis@dima.unige.it To: categories@mta.ca Subject: categories: Re: horizontal composition MIME-Version: 1.0 Content-Type: text/plain; charset=iso-8859-15 User-Agent: Internet Messaging Program (IMP) 3.2.8 X-Virus-Scanned: by amavisd-new at dima.unige.it Content-Transfer-Encoding: quoted-printable Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 41 You can find the strict version of that result in Prop. 1.4 of - M. Grandis, Homotopical algebra in homotopical categories, Appl. Categ= . Structures 2 (1994), 351-406. I do not know if it has been written down elsewhere. For sure, whiskering of natural transformations with functors is used in= : - R. Street, Categorical structures, in: Handbook of Algebra, Vol. 1, 52= 9-577, North Holland, Amsterdam 1996. where you can find the notion of a sesqui-category (which does not assum= e the "reduced interchange axiom" you are mentioning). With best regards M. Grandis > > Does anyone know of a reference for the following definition of a > bicategory? The primitive composites are: > > gf for composable 1-cells > GF for vertically composable 2-cells > f*G and F*g for horizontally composable pairs of each > > with appropriate axioms including (G*f')(g*F)=3D(g'*F)(G*f), for > F:f->f':X->Y and G:g->g':Y->Z. The horizontal composite G*F is define= d to > be the common value of the two vertical composites. > > -Susan From rrosebru@mta.ca Tue Jan 31 10:19:56 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 31 Jan 2006 10:19:56 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1F3wGt-0005s4-AY for categories-list@mta.ca; Tue, 31 Jan 2006 10:14:15 -0400 Content-Disposition: inline Content-Transfer-Encoding: quoted-printable Content-Type: text/plain; charset="iso-8859-1" MIME-Version: 1.0 From: "Dr. Cyrus F Nourani" To: categories@mta.ca Date: Mon, 30 Jan 2006 14:13:00 -0500 Subject: categories: re: universal algebra and diagrammatic reasoning Message-Id: <20060130191300.E33C13384C@ws7-3.us4.outblaze.com> Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 42 Hello, might be interested that my Morph Gentzen project since 1995, Virtual Geometry, ADG Zurich 2003, and two books published 1999 http://www.lulu.com/CrisFN,=20 2005 http://www.aspbs.com/mutlimedia.html are on a diagrammatic,categorial initial algebras, and structures on Lw1,w. Cyrus=20=20 > ----- Original Message ----- > From: "John Baez" > To: categories@mta.ca=20 > Subject: categories: universal algebra and diagrammatic reasoning > Date: Thu, 26 Jan 2006 13:09:36 -0800 (PST) >=20 >=20 > Hi - >=20 > I hope to see some of you in Marseille for Geocal06! I'll be > talking about "universal algebra and diagrammatic reasoning", > and there's a bunch of lecture notes here: >=20 > http://math.ucr.edu/home/baez/universal/ >=20 > Abstract: >=20 > Since the introduction of category theory, the old subject of > "universal algebra" has diversified into a large collection of > frameworks for describing algebraic structures. These include > "monads" (formerly known as "triples"), the "algebraic theories" > of Lawvere, and the "PROPs" of Boardman and Vogt. We give an > overview of these different frameworks, which are closely > related, and explain how one can reason diagrammatically about > algebraic structures defined using them. We focus on the bar > construction and the relation between algebraic theories and PROPs. >=20 > (I feel guilty for not talking about operads... I'll do it if > there's time!) >=20 > Best, > jb > --=20 _______________________________________________ Search for businesses by name, location, or phone number. -Lycos Yellow Pa= ges http://r.lycos.com/r/yp_emailfooter/http://yellowpages.lycos.com/default.as= p?SRC=3Dlycos10 From rrosebru@mta.ca Wed Feb 1 12:28:37 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 01 Feb 2006 12:28:37 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1F4Kha-0001oY-80 for categories-list@mta.ca; Wed, 01 Feb 2006 12:19:26 -0400 Date: Tue, 31 Jan 2006 20:22:16 +0100 Mime-Version: 1.0 (Apple Message framework v543) Content-Type: text/plain; charset=ISO-8859-1; format=flowed Subject: categories: Re: horizontal composition From: jean benabou To: Categories Content-Transfer-Encoding: quoted-printable Message-Id: Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 43 I thought I had invented bicategories in 1967, and that, at the very=20= beginning of the paper, in =A71, I had defined the two composition laws=20= and drawn pictures to explain them. Of course I denoted by capital=20 letters the 1-cells, thinking of functors, and by small letters the=20 2-cells, thinking of natural transformations. That certainly makes a=20 tremendous difference with Susan Niefield's notation who uses the=20 converse convention and amply justifies Marco Grandis in giving=20 references dated 1994 and 1996, i.e. more than 25 years posterior to my=20= original paper. With best regards > > You can find the strict version of that result in Prop. 1.4 of > > - M. Grandis, Homotopical algebra in homotopical categories, Appl.=20 > Categ. > Structures 2 (1994), 351-406. > > I do not know if it has been written down elsewhere. > > For sure, whiskering of natural transformations with functors is used=20= > in: > > - R. Street, Categorical structures, in: Handbook of Algebra, Vol. 1,=20= > 529-577, > North Holland, Amsterdam 1996. > > where you can find the notion of a sesqui-category (which does not=20 > assume the > "reduced interchange axiom" you are mentioning). > > With best regards > > M. Grandis > >> >> Does anyone know of a reference for the following definition of a >> bicategory? The primitive composites are: >> >> gf for composable 1-cells >> GF for vertically composable 2-cells >> f*G and F*g for horizontally composable pairs of each >> >> with appropriate axioms including (G*f')(g*F)=3D(g'*F)(G*f), for >> F:f->f':X->Y and G:g->g':Y->Z. The horizontal composite G*F is=20 >> defined to >> be the common value of the two vertical composites. >> >> -Susan > > >