From rrosebru@mta.ca Fri Feb 4 11:59:37 2000 -0400 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id KAA02619 for categories-list; Fri, 4 Feb 2000 10:29:40 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: 4 Feb 2000 11:59:16 +0200 Subject: categories: CatMAT2000 From: "CatMAT2000" To: CATEGORIES@mta.ca X-Mailer: Cyberdog/2.0 MIME-Version: 1.0 Message-Id: X-Fontfamily: Geneva X-Fontsize: 12 Content-Type: text/enriched; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: SECOND ANNOUNCEMENT for CatMAT2000 As announced earlier the conference "Categorical Methods in Algebra and Topology - Commemorating 25 years of Category Theory in Bremen" will take place at the University of Bremen, from August 21 to 25, 2000. This message contains some important information as well as a registration form. All information can also be obtained from the conference website at http://katmat.math.uni-bremen.de/catmat2000/ where you might register, too. 1. DATES Registration deadline is April 15, 2000. Later registrations will be considered, but no slot in the program will be guaranteed. Deadline for submission of abstracts: May 31, 2000. 2. FEES There will be a conference fee of DM 100,00 to be paid by April 15. The fee will be DM 150,00 if paid later than April 15. The conference fee covers refreshments during breaks, conference material and a volume of the proceedings. Please pay your fees to Recipient: Universit=E4t Bremen Bank : Bremer Landesbank Bank Code (BLZ) 290 500 00 Account-No: 1070 115000 Reference: 2538/01812-3 CatMAT2000 3. PROGRAM The program will consist of invited lectures of 40 minutes each, and of contributed talks of 20 minutes. 4. ABSTRACTS Abstracts should not exceed 1 page. They should be submitted electronically (preferrably as a (La)TeX file) not later than May 31. 5. PROCEEDINGS The proceedings of the conference will appear as a volume of the Bremen preprint series "Mathematik-Arbeitspapiere". Please indicate on registration whether you will contribute to the proceedings. Contributions should not exceed 10 pages. 6. ACCOMMODATION Participants should make reservations on their own. Please visit the conference website for assistance (as from February 15). For further information (as e.g. w.r.t. travel information, get-together-venue, possible excursions etc) please visit the conference website. -----------------------------------------------------------------------= --- REGISTRATION FORM NAME: __________________________________________ INSTIUTION:_____________________________________ ADDRESS:________________________________________ _________________________________________ E-MAIL:__________________________________________ TITLE OF TALK:_____________________________________ ______________________________________ I intend to contribute to the proceedings: YES/NO I am booked into the following hotel: _______________________ --------------------------------------------------------- Hans-E. Porst e-mail: porst@math.uni-bremen.de FB 3: Mathematik Phone: +49 421 2182276 University of Bremen Secr.: +49 421 2184971 D-28334 Bremen Fax: +49 421 2184856 http://www.informatik.uni-bremen.de/~porst/ --------------------------------------------------------- From rrosebru@mta.ca Fri Feb 4 12:00:58 2000 -0400 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id KAA30473 for categories-list; Fri, 4 Feb 2000 10:29:03 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-Id: <200002041115.KAA07942@math4.unice.fr> X-Mailer: exmh version 2.0.2 To: categories@mta.ca Subject: categories: facial sets Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Date: Fri, 04 Feb 2000 10:15:35 -0100 From: "Carlos.SIMPSON" Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: Since noone seems to have found an already-existing standard (the terminology ``Delta set'' suffers from the fact that the standard notation for the usual simplicial category (with degeneracies) is $\Delta$), here is a suggestion: ``facial sets''. This is somewhat like ``face complex'' but could apply to other objects eg ``facial groups'' etc... ---Carlos Simpson From rrosebru@mta.ca Mon Feb 7 10:00:35 2000 -0400 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id IAA06393 for categories-list; Mon, 7 Feb 2000 08:20:49 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-ID: <389EA1A4.294B55E2@uycdc.uninet.cm> Date: Mon, 07 Feb 2000 11:42:44 +0100 From: "Moustapha N. PEMY" Reply-To: pemy@uycdc.uninet.cm Organization: University of yaounde X-Mailer: Mozilla 4.07 [en] (X11; I; Linux 2.0.36 i686) MIME-Version: 1.0 To: categories@mta.ca Subject: categories: cartesian closed categories with one object. Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: Please could somebody tell me how to build a cartesian closed category with one object ? From rrosebru@mta.ca Mon Feb 7 11:24:37 2000 -0400 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id JAA23959 for categories-list; Mon, 7 Feb 2000 09:44:06 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f From: Paul Taylor Date: Mon, 7 Feb 2000 13:28:43 GMT Message-Id: <200002071328.NAA19700@koi-pc.dcs.qmw.ac.uk> To: categories@mta.ca Subject: categories: cartesian closed categories with one object Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: > how to build a cartesian closed category with one object ? By the letter of the law, a CCC has finite products, including a terminal object, which is therefore the only object, and its only morphism is the identity. By the spirit of the question, there is such a thing as a CCC with one interesting object D, and one boring one, the terminal object. What you want, therefore, is [a full subcategory of] a category with an object D such that D D x D = D = D where of course "=" denotes isomorphism, not equality, and the two maps that form this isomorphism encode a lot of interesting structure. This structure is known as "the untyped lambda calculus with surjective pairing", and Dana Scott famously showed how to construct such objects in the early 1970s. Joachim Lambek and *Philip* Scott ("Intro to higher order categorical logic") have a nice discussion that goes from the question of a two-object CCC to the lambda calculus. Any account of domain theory will tell how more ways than the world ever needed to know of constructing these models. Paul From rrosebru@mta.ca Mon Feb 7 13:31:00 2000 -0400 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id LAA27474 for categories-list; Mon, 7 Feb 2000 11:37:59 -0400 (AST) X-Authentication-Warning: muppet48.cs.chalmers.se: prasad owned process doing -bs Date: Mon, 7 Feb 2000 16:35:24 +0100 (MET) From: "K. V. S. Prasad" To: categories@mta.ca Subject: categories: New PhD positions at Chalmers Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=ISO-8859-1 X-MIME-Autoconverted: from 8bit to quoted-printable by animal.cs.chalmers.se id QAA07216 Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by mailserv.mta.ca id LAA24247 Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: Please pass on to interested students. Apologies for multiple copies. -------------------------------------------------------------------- New PhD Positions (DEADLINE 1 March 2000! See "How to apply" below.) Department of Computing Science, Chalmers University of Technology and Göteborgs University, Sweden The Department has about 60 researchers, half being faculty members and half PhD students. Our focus is on programming logic and type theory, functional programming, formal methods, distributed and concurrent systems, security, algorithms, and computational linguistics, but research is not restricted to these topics. For more information, see www.cs.chalmers.se/Cs/Research. PhD positions are for 5 years. There is no tuition fee. A PhD position is a regular job with social benefits; the salary amounts to 16200 SEK per month in the first year (the exact amount depends on teaching duties, usually 20% of your time), which offers a higher standard of living than for most PhD students elsewhere. Knowledge of Swedish is not a prerequisite for application. English is our working language for research. Both Swedish and English are used in undergraduate courses. Half of our researchers are native Swedes; the rest come from more than 20 different countries. Applicants must have an undergraduate degree in Computing Science or in a related subject with a strong Computing Science component. You may also apply if you expect to have such a degree by September 2000. The School especially welcomes female applicants. How to apply ------------ First, immediately register your intention to apply using the electronic application form on the WWW at http://www.md.chalmers.se/Jobs/PhD/phd-00-en.thtml The full application should give 1 name, age, gender, nationality, post and email address, tel/fax no. 2 transcripts of grades from your undergraduate degree(s); 3 a statement of research interests; 4 some letters of recommendation from your teachers or employers; 5 copies of any scientific papers you have written. Send it (paper mail) to Section for Mathematics and Computer Science Chalmers University of Technology 412 96 Gothenburg Sweden to arrive by 1 March 2000. You will know the result of your application by 1 June 2000. Formal papers might take time. Meanwhile, e-mail will do perfectly well for the information content of your application. Send it to prasad@cs.chalmers.se This will be of particular help should you be unable to send in complete information to the Section by 1 March. --------------------------------------------------------------- K. V. S. Prasad e-mail: prasad@cs.chalmers.se Dir of Graduate Studies URL: www.cs.chalmers.se Dept. of Computing Science Tel: 46-31-772 1021 Chalmers University 412 96 Gothenburg, Sweden Fax: 46-31-16 56 55 From rrosebru@mta.ca Mon Feb 7 18:08:22 2000 -0400 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id RAA26645 for categories-list; Mon, 7 Feb 2000 17:00:11 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-ID: <389F31FB.EF054924@yorku.ca> Date: Mon, 07 Feb 2000 15:58:45 -0500 From: jwpell X-Mailer: Mozilla 4.7 (Macintosh; U; PPC) X-Accept-Language: en MIME-Version: 1.0 To: categories@mta.ca Subject: categories: preprint: On the Quantisation of Points Content-Type: text/plain; charset=us-ascii; x-mac-type="54455854"; x-mac-creator="4D4F5353" Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: The final version of "On the Quantisation of Points" by Chrisopher J. Mulvey and Joan Wick Pelletier (to appear in the Journal of Pure and Applied Algebra) is now available on-line at the following addresses: pdf file: http://www.maths.sussex.ac.uk/Staff/CJM/research/pdf/quanpts.pdf ps file: http://www.maths.sussex.ac.uk/Staff/CJM/research/ps/quanpts.ps -- Dr. Joan Wick Pelletier Department of Mathematics and Statistics York University From rrosebru@mta.ca Mon Feb 7 20:22:05 2000 -0400 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id TAA00799 for categories-list; Mon, 7 Feb 2000 19:29:35 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-ID: <389EE9DA.3832DFD0@cea.fr> Date: Mon, 07 Feb 2000 16:50:50 +0100 From: Christophe Tabacznyj X-Mailer: Mozilla 4.7 [en] (X11; I; SunOS 5.6 sun4u) X-Accept-Language: fr MIME-Version: 1.0 To: categories@mta.ca Subject: categories: CFP: GETCO'00 (a satellite to CONCUR'00) Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Content-Transfer-Encoding: 7bit Content-Transfer-Encoding: 7bit Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: _________________________________________________________________________ PRELIMINARY ANNOUNCEMENT AND CALL FOR PAPERS GETCO'00 2nd Workshop on Geometric and Topological Methods in Concurrency Theory http://www.dmi.ens.fr/~goubault/getco.html a satellite to CONCUR'00 PennState, 21st of August 2000 (to coincide with EXPRESS'00, another satellite) _________________________________________________________________________ (apologies for multiple copies) This workshop follows last year's "Geometric and Topological Methods in Concurrency Theory" meeting held at Aalborg University. The aim is to bring together researchers that apply geometric, topological and algebraic topological methods to formalize and analyze dynamical, concurrent and distributed systems. The spirit of the meeting will be informal and will focus on exchange of information and discussion. It will consist of a number of tutorials, invited talks, together with accepted papers. Abstracts and work in progress reports are encouraged. The submission deadline is the 19th of may. For more information please see URLs GETCO'00 http://www.dmi.ens.fr/~goubault/getco.html CONCUR'00 http://www.cse.psu.edu/concur2000/ EXPRESS'00 http://www.docs.uu.se/~victor/Express/express00.shtml GETCO'99 http://www.math.auc.dk/~raussen/admin/workshop/workshop.html _________________________________________________________________________ From rrosebru@mta.ca Mon Feb 7 20:22:52 2000 -0400 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id TAA32529 for categories-list; Mon, 7 Feb 2000 19:28:54 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Sender: spreen@clapton Message-Id: Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Date: Mon, 7 Feb 2000 17:06:43 +0100 To: categories@mta.ca, types@cis.upenn.edu, comprox@doc.ic.ac.uk From: Dieter Spreen Subject: categories: Workshop on Domains IV, 1998 Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: The proceedings of the Workshop on Domains IV, Rolandseck, Germany, October 2-4, 1998 can be obtained electronically via http://www.informatik.uni-siegen.de/theo.html#pub Best regards, Dieter Spreen From rrosebru@mta.ca Tue Feb 8 10:14:47 2000 -0400 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id IAA16744 for categories-list; Tue, 8 Feb 2000 08:27:15 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-ID: <20000208075925.17402.qmail@hotmail.com> X-Originating-IP: [63.27.230.49] From: "Bill Halchin" To: categories@mta.ca Subject: categories: RFC Walters' "Categories and Computer Science" : Functional Specification Date: Mon, 07 Feb 2000 23:59:25 PST Mime-Version: 1.0 Content-Type: text/plain; format=flowed Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: In Chapter 5 "Categories of Functors", there is Section 5 entitled "The Specification of Functions". To me this is pretty interesting and neat stuff!! I have some thoughts, questions, etc. which I will now enumerate: 1) The method of specification defined in this section seems to be essentially a rewrite system, i.e. we do a series of rewrites or reductions on "data" (actually a certain kind of path in a Data graph) until we possibly terminate. Hence the finite set of Equation that Walters' describes is basically a set of rewrite rules, i.e. one-way rules in Rewriting Systems parlance. 2) We have two sets of Data paths that define the domain and codomain, respectively:: - The Domain is respresented by a set of paths starting at Data graph's "I" node and ending at "J" node - The Codomain is represented by a set of paths starting at the Data graph's "I" node and ending at the "K" node Question: I guess using "I" for both Domain and Codomain is just a clever way of partitioning some of the possible paths of the Data graph into one set of paths representing Domain and another set of paths representing the Codomain (of course these sets can be the same!)???? I.e. we could have chosen a different mechanism that I, J, K, yes??? 3) On pg. 118, there is a "Note" about work that Robie Gates did to show that we can achieve Turing completeness with this method of function specfication.i.e. we can compute all parial recursive functions from N to N. Hence the computation may not be terminating!!!! Otherwise, we would not have Turing completeness and could solve Halting problem. Also mentioned in this Note is that not only are we not guaranteed total functions (hence possibly partial functions), but we may also be computing a relation. - Question: what restrictions must we put on the finite set Equation to guarantee confluence???? I.e. computing a function and not computing a relation??? Probably the answer to this is in a book on Rewriting Systems or maybe Dershowitz paper. 4) Also it seems that Walters' approach of functional/relational specification, could be looked at in terms of equational reasoning. I.e. if we have a "specfied arrow" f: J -> K and lambda, a path from I to J and epsilon, a path belonging to I to K, then Equation |- (f.lambda, epsilon). Yes??? 5) Finally and important to me, has work been continued by anyone else in this area?? I don't see any papers in Walters' groups archive!! This approach to function (and relation) specification is pretty spiffy from a theoritcal viewpoint, but it seems it could be used as a basis to do functional programming or even logic programming (computing relations) by specifying the programs graphically!! Regards, Bill Halchin From rrosebru@mta.ca Wed Feb 9 12:28:33 2000 -0400 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id KAA30861 for categories-list; Wed, 9 Feb 2000 10:35:58 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Tue, 8 Feb 2000 15:45:58 +0100 (CET) To: categories@mta.ca From: Sebastiano Vigna Subject: categories: Re: RFC Walters' "Categories and Computer Science" : Functional Specification In-Reply-To: <20000208075925.17402.qmail@hotmail.com> Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: On Mon, 7 Feb 2000, Bill Halchin wrote: > 1) The method of specification defined in this section seems to be > essentially a rewrite system, i.e. we do a series of rewrites or > reductions on "data" (actually a certain kind of path in a Data graph) > until we possibly terminate. Hence the finite set of Equation that > Walters' describes is basically a set of rewrite rules, i.e. one-way > rules in Rewriting Systems parlance. Yes. Indeed as part of my Ph.D. dissertation I wrote a complete specification of the interpreter in ASF+SDF, a rewrite rule-based system for algebraic specifications used at the University of Amsterdam. It can execute programs of that kind. I can send it to you if you want so. The interpreter is partially described also in the following papers: Sebastiano Vigna. Specifying IMP(G) using ASF+SDF: A case study. In Proc. of the ASF+SDF95 workshop on generating tools from algebraic specifications. Technical Report P9504 of the University of Amsterdam, 1995. Sebastiano Vigna. Towards an efficient implementation of distributive programs. In Proc. of the 2nd International Workshop on the Theory and Practice of Algebraic Specifications ASF+SDF, Workshops in Comput. Springer-Verlag, 1998. > 3) On pg. 118, there is a "Note" about work that Robie Gates did to show > that we can achieve Turing completeness with this method of function > specfication.i.e. we can compute all parial recursive functions from N to > N. Hence the computation may not be terminating!!!! Otherwise, we would > not have Turing completeness and could solve Halting problem. Of course (the book is a bit confusing about this issue). Turing completeness is proved in Nicoletta Sabadini, Sebastiano Vigna, and Robert F.C. Walters. A note on recursive functions. Math. Struct. Comp. Sci., 6:127-139, 1996. and BSS (real numbers computability) completeness is proved in Sebastiano Vigna. On the relations between distributive computability and the BSS model. Theoret. Comput. Sci., 162:5-21, 1996. > 5) Finally and important to me, has work been continued by anyone else in > this area?? I don't see any papers in Walters' groups archive!! This Not to my knowledge, but you should ask Bob Walters directly. Greetings, Sebastiano Vigna From rrosebru@mta.ca Wed Feb 9 12:30:56 2000 -0400 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id LAA07104 for categories-list; Wed, 9 Feb 2000 11:16:01 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f From: John MacDonald Message-Id: <200002090122.RAA19880@viol.math.ubc.ca> Date: Tue, 8 Feb 2000 17:22:07 -0800 (PST) To: categories@mta.ca Subject: categories: FMCS2000 Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: First Announcement FMCS2000 Foundational Methods in Computer Science JUNE 1st - 4th, 2000 The Department of Mathematics at the University of British Columbia in cooperation with the Pacific Institute of Mathematical Sciences is hosting the Foundational Methods in Computer Science workshop on June 1st - 4th, 2000, on the University of British Columbia Campus in Vancouver, B.C., Canada The workshop is an informal meeting to bring together researchers in mathematics and computer science with a focus on the application of category theory in computer science. It is a three day meeting, that starts off with a day of tutorials aimed at students and newcomers to category theory, followed by a day and a half of research talks. There will be a series of invited presentations (TBA). The remaining research talks are solicited from the participants. Student participation is particularly encouraged at FMCS. To receive further information about FMCS2000 as it becomes available, including information about housing and registration, please send email to johnm@math.ubc.ca with subject heading FMCS2000. John MacDonald Local organizer, FMCS2000 From rrosebru@mta.ca Wed Feb 9 17:44:40 2000 -0400 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id QAA03872 for categories-list; Wed, 9 Feb 2000 16:57:39 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-ID: <38A194DB.754BD315@acsu.buffalo.edu> Date: Wed, 09 Feb 2000 11:25:00 -0500 From: Marie Bennett X-Mailer: Mozilla 4.51 [en] (Win95; U) X-Accept-Language: en,pdf MIME-Version: 1.0 To: categories@mta.ca Subject: categories: Regarding John Isbell Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: Hi, As you know John Isbell is still recovering from the major illness he suffered last year. He is in a rehab center and has made remarkable progress. There is still a long way to go before he will be released. There is very little mental stimulation in these facilities. If you can spare the time, a visit would be wonderful. If that is not possible, I'm sure a note would be welcome. Anything to break up the sameness of the days. The address is: Harris Hill Nursing Facility 2699 Wehrle Dr. Williamsville NY 14221 From rrosebru@mta.ca Wed Feb 9 20:13:20 2000 -0400 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id TAA18885 for categories-list; Wed, 9 Feb 2000 19:28:10 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-ID: <20000209232044.66573.qmail@hotmail.com> X-Originating-IP: [207.46.125.17] From: "Bill Halchin" To: categories@mta.ca Subject: categories: re: RFC Walters' "Categories and Computer Science": Function Spec Date: Wed, 09 Feb 2000 15:20:43 PST Mime-Version: 1.0 Content-Type: text/plain; format=flowed Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: Hello, I'm sorry if this a multiple posting. My mailbox was full so I am afraid that some replies to me were bounced back to senders. If you replied to my post, kindly send again. Much thanks, Bill Halchin From rrosebru@mta.ca Wed Feb 9 20:13:30 2000 -0400 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id TAA15193 for categories-list; Wed, 9 Feb 2000 19:32:36 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Received: from zent.mta.ca (zent.mta.ca [138.73.101.4]) by mailserv.mta.ca (8.9.3/8.9.3) with SMTP id MAA06649 for ; Wed, 9 Feb 2000 12:35:01 -0400 (AST) X-Received: FROM resu1.ulb.ac.be BY zent.mta.ca ; Wed Feb 09 12:55:06 2000 X-Received: from mach.vub.ac.be (mach.ulb.ac.be [164.15.128.3]) by resu1.ulb.ac.be (8.8.8/3.17.0.ap (resu)) id RAA23864; Wed, 9 Feb 2000 17:31:20 +0100 (MET) for X-Received: (bocoecke@localhost) by mach.vub.ac.be (8.9.3/%I%.1.ap (mach.test)) id RAA14063; Wed, 9 Feb 2000 17:30:55 +0100 (MET) for From: bocoecke@vub.ac.be (Coecke Bob) Message-Id: <200002091630.RAA14063@mach.vub.ac.be> Subject: categories: Category Theory Symposium To: categories@mta.ca Date: Wed, 9 Feb 2000 17:30:55 +0100 (MET) X-Mailer: ELM [version 2.4ME+ PL66 (25)] MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 X-MIME-Autoconverted: from 8bit to quoted-printable by resu1.ulb.ac.be id RAA23864 Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by mailserv.mta.ca id MAA06649 Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: (This mail has been sent to category theorists visiting Louvain-La-Neuve in April this year, participants of the "Workshop on categorical methods in algebra and topology" in Nassogne, organized last year by F. Borceux, and participants of the recent "PSSL 71" at Louvain-La-Neuve --- please feel free to forward it to anyone that might be interested.) The research unit Foundations of Exact Sciences of the Free University of Brussels, active in axiomatic quantum theory/logic, organizes its annual workshop on "Operational Quantum Logic" the week of April 10-14. This year's main theme will be the role of quantales in, and categorical aspects of quantum logic. Motivated by the large number of visiting category theorists in Louvain-La-Neuve and workshop participants in Brussels in that period, and the non-empty intersection of their research domains, we have, after consulting Francis Borceux, decided to organize a "Category Theory Symposium" in Brussels, the weekend of April 8-9, 2000 as a satellite of our workshop on quantum logic. The style of the meeting will be essentially inspired by the PSSL meetings, although we don't use that name since there has been an earlier announcement of a "PSSL" in Braunschweig taking place later in April. We would very much appreciate your participation in the "Category theory symposium", convinced as we are of the benefit of interaction between the researchers of our respective domains! As location for the "Category theory symposium" we have chosen for the homebase of an artists-collective, which is a actually a 'swimming pool with no water' in Vorst (Fôret), Brussels - the artists are looking forward to the encounter with mathematicians and are (allready now) showing signs of inspiration. As provisional program we propose the following: - Saturday (April 8): 9.30h Welcome in Vorst (F™ret), Brussels; 10.00h Start lectures; 13.00h Lunch offered by us; 14.30h Some more lectures; 19.30h Dinner offered by us. - Sunday (April 9): 10.00h Lectures; 13.00h Lunch, outing and tourism in Brussels. Please let us know if you are interested in: attending and/or giving a talk at the "Category Theory Symposium" (or if you might want to participate in the workshop on "Operational Quantum Logic: quantum logic/quantales/categories'', the week after), by mailing to any of the following: - The organizers: Bob Coecke; bocoecke@vub.ac.be Steven Sourbron; ssourbro@vub.ac.be Frank Valckenborgh; fvalcken@vub.ac.be - Their "partner in crime" in Louvain-La-Neuve: Isar Stubbe; i.stubbe@agel.ucl.ac.be This meeting and the quantum logic/quantale workshop is supported by FWO Research Network WO.011.96N: fundamentele methodes en thechnieken in de wiskunde. --- Bob Coecke, Foundations of Exact Sciences (FUND), Department of Mathematics, Free University of Brussels, Tel: ++32/2/629.34.99; Fax: ++32/2/629.34.95 http://www.vub.ac.be/CLEA/BobCoecke.html From rrosebru@mta.ca Wed Feb 9 20:16:32 2000 -0400 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id TAA09750 for categories-list; Wed, 9 Feb 2000 19:21:13 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f From: Jiri Rosicky Message-Id: <200002091308.OAA24141@bart.math.muni.cz> Subject: categories: flat covers To: categories@mta.ca Date: Wed, 9 Feb 2000 14:08:06 +0100 (CET) X-Mailer: ELM [version 2.4ME+ PL69 (25)] 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: The flat cover conjecture was formulated by E. Enochs in 1981 and asks whether every module has a flat cover. In his paper, he also showed that it is equivalent to weak coreflectivity of flat modules in modules. In 1995, J. Xu has proved that it is true over commutative noetherian rings of finite Krull dimension. The flat cover conjecture has been recently proved (over an arbitrary ring) by L. Bican, R. El Bashir and E. Enochs. In a paper "Flat covers and factorizations", I am giving a purely categorical proof based on the theorem of J. Smith about weak factorization systems. Jiri Rosicky From rrosebru@mta.ca Fri Feb 11 16:27:56 2000 -0400 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id PAA00268 for categories-list; Fri, 11 Feb 2000 15:05:51 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f To: categories@mta.ca Subject: categories: PhD positions available, please advertise Message-Id: From: Fairouz Kamareddine Date: Fri, 11 Feb 2000 17:34:22 +0000 Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: PhD positions in Logics, Types, Rewriting The ULTRA group Heriot-Watt University, Edinburgh, Scotland We have many PhD openings within the ULTRA group. See http://www.cee.hw.ac.uk/ultra/index.html The ULTRA group works on the applications of logics, type theories, and rewriting theory to the design and implementation of programming languages, the formalization of mathematics, and theorem proving. The ULTRA group is located in the Department of Computing and Electrical Engineering at Heriot-Watt University, Edinburgh, Scotland. The department of Computing and Electrical at Heriot-Watt is a very lively, active and friendly place with a supportive spirit. The department is committed to excellence and is investing a lot in the future. Heriot-Watt is located in beautiful parklands on the outskirsts of Edinburgh, the capital of Scotland and a beautiful and historic city. We are looking for active, energetic and committed people. If you are interested, send your c.v. to Professor Fairouz Kamareddine of Dr Joe Wells by e-mail (fairouz@cee.hw.ac.uk or jbw@cee.hw.ac.uk) or post (Heriot-Watt University, Department of Computing and Electrical Engineering, Riccarton, Edinburgh EH14 4AS, Scotland) and arrange for three letters of recommendation. From rrosebru@mta.ca Fri Feb 11 16:28:37 2000 -0400 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id PAA02752 for categories-list; Fri, 11 Feb 2000 15:06:24 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f To: categories@mta.ca Subject: categories: Tenured posts, please advertise thanks Message-Id: From: Fairouz Kamareddine Date: Fri, 11 Feb 2000 17:53:14 +0000 Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: Tenured Posts in Computer Science Heriot-Watt University, Edinburgh, Scotland Posts at the level of lecturer (assistant professor), senior lecturer and reader (associate professor) are available at the department of Computing and Electrical Engeneering at Heriot-Watt University, Edinburgh Scotland. The posts are in a number of areas of Computer Science. I would strongly encourage applications from academics whose research area is on type theory, term rewriting, logic, and the foundations of programming languages and theorm proving. Look at the web pages of the ULTRA group http://www.cee.hw.ac.uk/ultra/ for information on the areas we are involved in. The department of Computing and Electrical at Heriot-Watt is a very lively, active and friendly place with a supportive spirit. The department is expanding fast and is committed to excellence and is investing a lot in the future. So, if you can contribute to this excellence and you want to play an influential role in a supportive environment, send your application. Heriot-Watt is located in beautiful parklands on the outskirsts of Edinburgh, the capital of Scotland and a beautiful and historic city. Further details about the Department are available on http://www.cee.hw.ac.uk/ Informal enquiries to Prof. R.J. Clarke, Head of Department {email rjc@cee.hw.ac.uk}. If your questions are related to the above areas, contact Fairouz Kamareddine (fairouz@cee.hw.ac.uk). For application details please contact the Personnel Office, Heriot-Watt University, Edinburgh EH14 4AS, Tel. 0131 451 3475 (24 hrs), quoting Reference No (Ref. 19/00) for Reader/Senior Lecturer and Reference No (Ref. 20/00) for the Lecturer. Salary for the lectureship is on the scale: 17,238-30,065 UK pounds Salary for the reader/senior lectureship is between: 31,563-35,670 UK pounds Closing date: 3 March 2000. Fairouz Kamareddine From rrosebru@mta.ca Sat Feb 12 14:21:30 2000 -0400 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id NAA18377 for categories-list; Sat, 12 Feb 2000 13:28:39 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Sat, 12 Feb 2000 12:23:31 -0500 (EST) From: James Stasheff X-Sender: jds@gandalf To: dmd1@lehigh.edu, categories@mta.ca Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: As of some notes from 1996, it was an open question as to how to make a closed model category from coalgebras which as dg modules are flat over the ground ring one problem: the naive cokernel is no longer flat .oooO Jim Stasheff jds@math.unc.edu (UNC) Math-UNC (919)-962-9607 \ ( Chapel Hill NC FAX:(919)-962-2568 \*) 27599-3250 http://www.math.unc.edu/Faculty/jds From rrosebru@mta.ca Sat Feb 12 15:34:30 2000 -0400 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id OAA06360 for categories-list; Sat, 12 Feb 2000 14:48:54 -0400 (AST) X-Authentication-Warning: triples.math.mcgill.ca: barr owned process doing -bs Date: Sat, 12 Feb 2000 13:46:44 -0500 (EST) From: Michael Barr X-Sender: barr@triples.math.mcgill.ca To: Categories list Subject: categories: A curiosity Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: You may be amused trying to prove it (it is not easy), but a category in which every morphism has a unique quasi-inverse (AfE!g fgf=f) is a groupoid. It is actually a theorem about semigroups, but the proof works just as well for categories. (You can add an identity without affecting the hypothesis.) Michael From rrosebru@mta.ca Sun Feb 13 10:35:30 2000 -0400 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id JAA08336 for categories-list; Sun, 13 Feb 2000 09:48:34 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Sat, 12 Feb 2000 16:14:25 -0500 From: glenn Subject: categories: RE: A curiosity To: Categories list , Michael Barr Message-id: <38A37CC5@cuasenti> MIME-version: 1.0 X-Mailer: WebMail (Hydra) SMTP v3.60 Content-type: text/plain; charset="ISO-8859-1" Content-transfer-encoding: 7bit X-WebMail-UserID: glenn X-EXP32-SerialNo: 00002987 Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: >===== Original Message From Michael Barr ===== >You may be amused trying to prove it (it is not easy), but a category in >which every morphism has a unique quasi-inverse (AfE!g fgf=f) is a >groupoid. It is actually a theorem about semigroups, but the proof works >just as well for categories. (You can add an identity without affecting >the hypothesis.) > >Michael Dear category list, Mike's exercise: Suppose C is a category with the following property. For all f there exists a unique g such that fgf=f. Prove: C is a groupoid. Here's a short argument: Note that fgf=f implies we have two idempotents, namely gfgf=gf and fgfg=fg. So as a special case, suppose ff = f. The uniqueness of g such that fgf=f together with the fact that fff=ff=f and f1f=ff=f implies that f=g=1. So the only idempotents are the identity maps. Therefore, also, gf=1 and fg=1. Paul Glenn Dept of Mathematics Catholic Univ. of America Washington, DC 20064 From rrosebru@mta.ca Sun Feb 13 10:36:08 2000 -0400 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id JAA09642 for categories-list; Sun, 13 Feb 2000 09:47:44 -0400 (AST) X-Authentication-Warning: triples.math.mcgill.ca: barr owned process doing -bs Date: Sat, 12 Feb 2000 19:20:46 -0500 (EST) From: Michael Barr X-Sender: barr@triples.math.mcgill.ca To: Categories list Subject: categories: My posting Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: >From Todd Wilson, I learned that adding identities is not so harmless. So suppose only that there are objects, arrows, source and target and arrows that compose associatively only when source matches target. With identities, you can conclude, for any idempotent e, from eee = e1e, that e = 1 and that makes it trivial. Michael From rrosebru@mta.ca Wed Feb 16 14:16:53 2000 -0400 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id MAA07153 for categories-list; Wed, 16 Feb 2000 12:18:31 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Wed, 16 Feb 2000 16:10:13 +0100 (MET) Message-Id: <200002161510.QAA24398@brehat.haiti.cs.uni-potsdam.de> From: Torsten Schaub To: categories@mta.ca Subject: categories: Position: Research (2) University of Potsdam, Germany Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: [Please forward the following to anybody who you think may be interested. Apologies if you have already seen this.] ========================================================================= Two Research Positions Available Department of Informatics, University of Potsdam, Germany The Knowledge Representation and Reasoning Group at the University of Potsdam offers two research positions within the project ``Nonmonotonic inference systems for reasoning with conflictual rules''. Apart from the development and implementation of corresponding reasoning techniques, a particular emphasis lies on the integration of flexible conflict resolution mechanisms that are in turn applied to modeling conflictual knowledge bases found in linguistics. The project is part of the Research Group ``Conflictual rules'' (in German: Forschergruppe ``Konfligierende Regeln''), funded by the German Science Foundation (DFG). This research group offers an interdisciplinary context comprising adjacent research projects from Linguistics, Psychology, Physics, and Informatics. Applicants must hold a master's degree (Diplom, DEA, or equivalent) and should preferably have a PhD in Informatics/Computer Science or Mathematics, although a PhD project is also conceivable. A suitable candidate is expected to have good communication skills (though fluency in German is not required) and research experience in at least one area, relevant to logic-based knowledge representation and reasoning, eg. nonmonotonic reasoning, logic programming, automated deduction, argumentation systems, deductive databases, etc. However, highly motivated and academically strong applicants interested in getting into nonmonotonic reasoning/logic programming are also encouraged to apply. The positions are available immediately; they will be filled for a period of up to 24+12 months in the first instance, with a likely extension by three additional years. Salary is according to the German BAT scale (Bat-O IIa), depending on age and family status. Candidates should send a curriculum vitae, a list of publications, references, and a statement of research interests to: Prof. Torsten Schaub phone (+49) 331 977 1163/1057 Universität Potsdam fax (+49) 331 977 1720 Institut für Informatik mail torsten@cs.uni-potsdam.de Am Neuen Palais 10 url http://www.cs.uni-potsdam.de/~torsten D-14469 Potsdam An hyperlinked version of this offer is available at http://www.cs.uni-potsdam.de/~torsten/jobs. If you need more information just give me a call or send me an email. Torsten Schaub 2000-02-15 ============================================================ From rrosebru@mta.ca Sat Feb 19 14:42:15 2000 -0400 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id NAA00537 for categories-list; Sat, 19 Feb 2000 13:41:25 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Sat, 19 Feb 2000 09:02:11 -0500 (EST) From: Michael Barr To: Categories list Subject: categories: triples down Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: The disk on triples died yesterday. If you send mail to barr@barrs.org or to barr@math.mcgill.ca, it should arrive normally. However, any mail sent between 9AM and about 5PM yesterday will have been lost. As will the 199 messages that were waiting for me to act on. Included was at least one referee's report and one journal submission that arrived while I was away and I had left there to deal with when I got back. Which I did Thursday night, but I hadn't done anything by Friday at 9. So if you sent me anything important like that recently, please resend it. We should have triples back in service by Monday or so, but whether we can recover the information on the disk is not clear. Michael From rrosebru@mta.ca Sat Feb 19 14:42:15 2000 -0400 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id NAA00132 for categories-list; Sat, 19 Feb 2000 13:38:17 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f From: Koslowski Message-Id: <200002181315.OAA09875@lisa.iti.cs.tu-bs.de> Subject: categories: PSSL 73, First Announcement To: categories@mta.ca (categories list) Date: Fri, 18 Feb 2000 14:15:12 +0100 (MET) 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 Status: O X-Status: PERIPATETIC SEMINAR ON SHEAVES AND LOGIC 73rd meeting - first announcement The 73rd meeting of the seminar will be held at the Department of Theoretical Computer Science of the Technical University in Braunschweig, Germany, over the weekend of April 29-30, 2000. Notice that Monday, May 1, is a holiday in Germany. The seminar welcomes talks using or addressing category theory or logic, either explicitly or implicitly, in the study of any aspect of mathematics or science. Braunschweig is located about 60 km East of Hannover and can easily be reached by car or train. The closest airport is in Hannover; the airport bus to the Hannover train station takes about 20 minutes, and the train from there to Braunschweig takes about 40 minutes or less. We will send further information on the location of the seminar, along with details on local travel and accommodation to those who register, at least a week before the meeting. Jiri Adamek J"urgen Koslowski ------------------------------------------------------------------------------- Please return to J"urgen Koslowski (or , if you have problems with the first address), preferably before April 1. Postal address: Institut f"ur Theoretische Informatik TU Braunschweig Postfach 3329 D-38023 Braunschweig Germany ====================================================================== I intend to come to the 73rd meeting of the PSSL in Braunschweig * I intend to give a talk entitled ..................................... * Please reserve accommodation for Thursday/Friday/Saturday/Sunday night(s) Name : Address: Email : Phone : *Delete if inapplicable ======================================================================= -- J"urgen Koslowski \ If I don't see you no more on this world ITI, TU Braunschweig \ I'll meet you on the next one koslowj@iti.cs.tu-bs.de \ and don't be late! http://www.iti.cs.tu-bs/~koslowj \ Jimi Hendrix (Voodoo Child, SR) From rrosebru@mta.ca Sat Feb 19 14:44:23 2000 -0400 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id NAA00344 for categories-list; Sat, 19 Feb 2000 13:40:01 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Sender: ecooper@pop.iis.varian.com X-Mailer: QUALCOMM Windows Eudora Pro Version 4.0.2 Date: Fri, 18 Feb 2000 17:09:51 -0500 To: categories@mta.ca From: Ellis Cooper Subject: categories: The Category of all Smooth Manifolds a la Lawvere Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Message-ID: <20000218221004326.AAA493@sx1.iis.varian.com@salish> Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: Hello, In his paper "Qualitative distinctions between some toposes of generalized graphs" (Contemporary Mathematics Volume 92, 1989, pp. 261-299) Lawvere mentions a "powerful theorem" that "justifies bypassing the complicated considerations" usually associated with defining a smooth manifold (charts, atlases, etc.). This is in the context of something called "closed under splitting of idempotents" and the kind of idempotent he is talking about, I think, is what you get if you embed a manifold in a sufficiently high-dimensional space, wrap it inside and out with foam, call that foamy thing an open set, and then the idempotent is the projection of the foam back onto the embedded manifold. What I would like is a carefully written, fully spelled out statement and proof of his theorem. Please advise. In fact, I would be even more delighted by a more standard (motivation, definition, theorem, proof) version of his entire paper, but I suppose that is too much to ask. Please reply directly to me, at Ellis D. Cooper Senior Software Engineer Varian Semiconductor Equipment Associates, Inc. ellis.cooper@vsea.com From rrosebru@mta.ca Sat Feb 19 14:52:32 2000 -0400 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id NAA00040 for categories-list; Sat, 19 Feb 2000 13:36:57 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Fri, 18 Feb 2000 13:51:31 GMT From: Marta Z Kwiatkowska Message-Id: <200002181351.NAA02323@chip.cs.bham.ac.uk> To: categories@mta.ca Subject: categories: Research scholarships available at Birmingham Cc: M.Z.Kwiatkowska@cs.bham.ac.uk X-Sun-Charset: US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: Please bring this to the attention of potential applicants. Apologies for duplicate mailing. Thanks Marta _____ ========================================================================= The University of Birmingham School of Computer Science Research scholarships in Computer Science and Artificial Intelligence ========================================================================= The School of Computer Science has research strengths in the areas of Theoretical Computer Science, Artificial Intelligence and Cognitive Science, and Software Engineering. The Theory of Computation group concentrates on the development of logics and semantics for programming languages. The overall aim is to provide intuitive conceptual tools for the everyday practice of programming. Within this framework, the activities range from abstract mathematics to issues of implementation and software development. For an overview of past research activities of the group, including funded research projects and publications, see the URL: http://www.cs.bham.ac.uk/research/research.html Current academic and research members of the Theory group are: Dr Christoph Benzmueller Mr Carsten Fuhrman Dr Mateja Jamnik Professor Achim Jung Dr Manfred Kerber Dr Marta Kwiatkowska Dr Gethin Norman Professor Uday Reddy Dr Eike Ritter Dr Mark Ryan Dr Andrea Schalk Dr Hayo Thielecke (from September 2000). There are also 11 PhD students associated with the group, of the total of 40 in the School. Possible topics for research include, but are not restricted to: Software verification and model checking Verification of probabilistic systems (theory and implementation) Verification of probabilistic real-time systems Probabilistic and stochastic calculi Semantics for concurrency Temporal and modal logics Domain theory Extensions to the relational database model (theory and implementation) Parametricity and foundations of data abstraction Type systems for imperative and OO programming Semantics and formal methods for OO programming Continuations and control Categorical models of programming languages Linear logic, type theory and corresponding categorical semantics Linear abstract machines Category theory and games models Agent based mathematical reasoning Machine-assisted reasoning Diagrammatic reasoning Theorem proving and proof planning Applicants must have or be about to gain at least an upper second class honours degree or an overseas equivalent in Computer Science or a related degree title. Successful applicants will be offerred an opportunity to join The Midlands Graduate School in the Foundations of Computing Science, a recent initiative between the Universities of Birmingham, Leicester, Nottingham and Warwick aiming to provide broader educational experience for doctoral students. For more information see URL: http://www.cs.nott.ac.uk/MGS/ The School has a number of EPSRC Studentships, School Studentships and Teaching Assistantships available to UK and European Union applicants. School Studentships and Teaching Assistantships cover tuition fees and maintenance for UK and European Union students. EPSRC studentships do not pay maintenance costs for non-UK students. Further details of these studentships and also of studentships for international students are given in: http://www.cs.bham.ac.uk/~pjh/prospectus/funding/research.html The School's research student prospectus and application form are available from: http://www.cs.bham.ac.uk/studentinfo/form_mailer.html Informal enquiries can be directed to any member of the group (see URL http://www.cs.bham.ac.uk/system/auto-gen/staff.html http://www.cs.bham.ac.uk for contact information), or *in the first instance* to Marta Kwiatkowska Email M.Z.Kwiatkowska@cs.bham.ac.uk Tel +44 121 414 7264 FAX +44 121 414 4281 ========================================================================= From rrosebru@mta.ca Sat Feb 19 14:55:35 2000 -0400 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id NAA00196 for categories-list; Sat, 19 Feb 2000 13:38:49 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f From: Koslowski Message-Id: <200002181335.OAA14685@lisa.iti.cs.tu-bs.de> Subject: categories: preprint + CT99 photos To: categories@mta.ca (categories list) Date: Fri, 18 Feb 2000 14:35:42 +0100 (MET) 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 Status: O X-Status: Dear Colleagues, Together with Robin Cockett and Robert Seely I would like to announce the availablility of a preprint Morphisms and modules for linear bicategories that has been submitted for the CT99 proceedings. You can get it from . Those interested in some of the pictures I took at that meeting may want to look at . If anybody wants his or her picture removed, or wants to order a print or a larger version of a picture, please let me know. -- J"urgen Koslowski Abstract: Linear bicategories are a generalization of bicategories, in which the horizontal composition of 1-cells is replaced by two (coherently linked) horizontal compositions. This notion combines and integrates compositional features typical of bicategories with those arising from linear logic. Linear bicategories, therefore, provide a natural categorical semantics and interpretation for (relational) non-commutative linear logic. In particular, the logical notion of negation (or complementation) turns into a linear notion of adjunction, with involutive negations corresponding to cyclic linear adjunctions. The latter are crucial for the construction of a tricategory of linear bicategories, linear functors, linear transformations and linear modifications. This paper first develops the structure of the afore-mentioned tricategory and describes how the various components have a natural interpretation using the diagrammatic calculus of circuits. Then we transfer the module construction to the linear setting, which leads to a new linear bicategory of linear monads, linear modules, and module transformations over a given linear bicategory. This lives in a tricategory where the 1-cells are given by linear functors that are strict on units. The connections of this construction with the nucleus construction for linear bicategories are indicated at the end. The present paper is primarily expository, setting out the notions necessary for the development of category theory enriched in a linear bicategory. -- J"urgen Koslowski \ If I don't see you no more on this world ITI, TU Braunschweig \ I'll meet you on the next one koslowj@iti.cs.tu-bs.de \ and don't be late! http://www.iti.cs.tu-bs/~koslowj \ Jimi Hendrix (Voodoo Child, SR) From rrosebru@mta.ca Tue Feb 22 21:05:10 2000 -0400 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id TAA27969 for categories-list; Tue, 22 Feb 2000 19:40:58 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Tue, 22 Feb 2000 18:17:00 -0500 (EST) From: Robert Seely To: Categories List Subject: categories: Montreal Seminar announcement list Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: Due to the recent hard disk failure on triples, I have lost the current electronic mailing list for notices of seminars of the Montreal Category Theory group. The seminar schedule is (as always) available on the triples home page http://www.math.mcgill.ca/triples so anyone interested in what talks are being given at McGill may check there. I will reconstruct the local mailing list, but if anyone wants me to add their names to that list, and they are not presently in Montreal, please email me, and I will do so. This might be a good time to remind people that if emailing folks at McGill, it is always best to use the format user@math.mcgill.ca rather than any variant using "triples" in the email address. This allows us to move things around as necessary, when crises strike. It may also be a good time to remind folks that all urls (including ftp) that began "http://triples.math.mcgill.ca/" have been replaced by more generic "http://www.math.mcgill.ca/triples/" (for ftp, the standard url is "ftp://ftp.math.mcgill.ca/pub/"). If you haven't updated your links and bookmarks, please do so, since the old formats are no longer supported. If a McGill link fails to work, check to see if this is the reason. -= rags =- =================================== RAG Seely =================================== From rrosebru@mta.ca Thu Feb 24 10:29:01 2000 -0400 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id IAA16144 for categories-list; Thu, 24 Feb 2000 08:58:54 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f From: Paul Taylor Date: Thu, 24 Feb 2000 11:18:52 GMT Message-Id: <200002241118.LAA18173@koi-pc.dcs.qmw.ac.uk> To: categories@mta.ca Subject: categories: 1970s programmable calculators Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: OK, I admit, this has nothing to do with category theory, but maybe one of my mates out there can help me ... Did any of the readers of "categories" own (or use) a programmable calculator in the 1970s? I'm looking for something that would have done about 100 to 1000 instructions per second, with conditional instructions, loops and indexed access to numbered memories. The reason s that I want to set a exam question about elementary ideas of complexity along the lines of "The XY99 calculator could execute this algorithm for a problem size up to nnnn - how big a problem could you solve today with your million-times faster computer?". Info about performance, price, the year it went on the market, etc please, by direct email to me. (OK, I'll summarise the responses I get in another message to "categories".) Paul From rrosebru@mta.ca Thu Feb 24 10:41:18 2000 -0400 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id JAA17895 for categories-list; Thu, 24 Feb 2000 09:00:47 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-Id: <200002241200.NAA20043@math.u-strasbg.fr> Date: Thu, 24 Feb 2000 13:00:54 +0100 (MET) From: Philippe Gaucher Reply-To: Philippe Gaucher Subject: categories: preprint: About the globular homology of higher dimensional automata To: categories@mta.ca MIME-Version: 1.0 Content-Type: TEXT/plain; charset=us-ascii Content-MD5: 0P0rDBcHOTXWozUVcpxhjA== X-Mailer: dtmail 1.3.0 CDE Version 1.3 SunOS 5.7 sun4u sparc Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: Bonjour, Here is a short note about the globular homology. Title : About the globular homology of higher dimensional automata Abstract : In this short note, we introduce a new simplicial nerve of higher dimensional automata whose homology groups yield a new definition of the globular homology. With this new definition, the drawbacks noticed with the construction of [Gau99] disappear. Comments : 20 pages Url : http://www-irma.u-strasbg.fr/~gaucher/sglob.ps.gz Cordialement, Philippe Gaucher. From rrosebru@mta.ca Thu Feb 24 17:55:59 2000 -0400 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id QAA06964 for categories-list; Thu, 24 Feb 2000 16:41:36 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Tue, 22 Feb 2000 14:47:04 -0800 Message-Id: <200002222247.OAA10085@lannion.ise> From: "TOOLS Conferences" To: categories@mta.ca Subject: categories: TOOLS USA 2000 Call for contributions Reply-to: announce@tools.com Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: Dear Colleague: This is the abbreviated call for contributions for TOOLS USA 2000. The full information is at http://www.tools-conferences.com/usa Please post or forward this information to any other colleague who think might be interested. With best regards, -- TOOLS Conference organization ************************************************************************* TOOLS USA 2000 "Software Serving Society" Santa Barbara, California July 30 - August 3, 2000 http://www.toolsconferences.com/usa CALL FOR CONTRIBUTIONS (deadline 10 March 2000) TOOLS is the major international conference series devoted to applications object technology, component technology and other advanced approaches to software development. TOOLS USA 2000 will be held in Santa Barbara, CA at the Fess Parker Double Tree Resort, one of the most beautiful resorts on the West Coast and will continue the commitment to excellence of earlier TOOLS conferences in Europe, Australia, Asia and the USA since 1989. The proceedings will be published world-wide by the IEEE Computer Society. PAPERS ------ TOOLS USA 2000 is now soliciting papers on all aspects of object and component technology. All submitted papers will be refereed and assessed for technical quality and usefulness to practitioners and applied researchers. TOOLS USA particularly welcomes papers that present general findings based upon industrial experience. Such papers will be judged by the quality of their contribution to industrial best-practice. TUTORIALS, WORKSHOPS AND PANELS ------------------------------- Tutorials, workshops, and panels form an important part of the TOOLS conferences. TOOLS USA 2000 is welcoming proposals for tutorials, workshops and panels on topics related to the theme of the conference. FOR MORE DETAILS AND REGISTRATION INFORMATION PLEASE VISIT THE CONFERENCE WEBSITE AT http://www.tools-conferences.com/usa From rrosebru@mta.ca Sat Mar 4 02:37:31 2000 -0400 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id CAA19627 for categories-list; Sat, 4 Mar 2000 02:04:00 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Tue, 29 Feb 2000 13:58:30 -0500 (EST) From: Peter Freyd Message-Id: <200002291858.NAA09396@saul.cis.upenn.edu> To: categories@mta.ca Subject: categories: Johnstone review of Clark/Davey Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: I am chagrined to find myself as one of two category people in the bibliography of the work reviewed below and -- worse -- Peter says that they ascribed schizophrenic objects "not altogether appropriately" to me. He's right. CMP 1 663 208 (99:06) 18-02 (03G25 06D05 08C15 18A40) Clark, David M.(1-SUNYP); Davey, Brian A.(5-LTRB) Natural dualities for the working algebraist. (English. English summary) Cambridge Studies in Advanced Mathematics, 57. Cambridge University Press, Cambridge, 1998. xii+356 pp. $64.95. ISBN 0-521-45415-8 I began reading this book (conventionally enough) with the first two paragraphs of the Preface: "In 1936 Marshall Stone published a truly novel theorem ... What Stone discovered was a representation for all Boolean algebras which gave algebraists a usable understanding of their structure, using topological spaces to construct the representations ... In fact, Stone proved much more than a representation theorem ... In modern language, he proved that the category of Boolean algebras is dually equivalent to the category of Boolean spaces ...". Finding in these words what I presumed to be a conscious echo of the words: "This book is about a particular theorem -- the Stone representation theorem for Boolean algebras -- and some of the mathematical consequences which have developed from it ... Stone's key idea was the introduction of topology ... this was a really bold idea ... Moreover, [Stone's representation formed] one of the earliest nontrivial examples of an equivalence of categories ..." with which I had begun the Introduction to my own book Stone spaces, published in the same C.U.P. series in 1982 [Cambridge Univ. Press, Cambridge, 1982; MR 85f:54002], I naturally turned next to the Bibliography to check that my book was listed there. After all, though my book dealt with other subjects besides duality, it did have a whole chapter devoted to dualities of the type studied by Clark and Davey, and so it ought to be one of their standard references. My name does not appear in the Bibliography. Indeed, its only occurrence in the entire book is in the list of previous volumes in the series which appears opposite the title page. I mention this at the outset of this review, in order to give the reader a fair chance to make allowance for what he may construe as "sour grapes" on my part. For a related reason, I have departed from Mathematical Reviews tradition by writing the review in the first person; I cannot pretend to have achieved the standards of objectivity and dispassionateness that would be implied by a third-person review. However, it is not only the works of Johnstone which have been overlooked by Clark and Davey. I looked next in the Bibliography for John Isbell's ground-breaking 1972 paper on general functorial semantics [Amer. J. Math. 94 (1972), 535--596; MR 53 #580], and his later work characterizing concrete dualities in terms of commuting subtheories of a ruled theory: neither is present, and Isbell is represented only by a much less important 1980 paper on median algebra. Again, the 1982 paper in which Harold Simmons coined the term "schizophrenic object" [Topology Appl. 13 (1982), no. 2, 201--223; MR 83f:18006], for a set with two commuting algebraic structures, is not there, although Clark and Davey freely use this term in their text. Having discovered this, I began studying the Bibliography more systematically, and soon realized its salient feature: all works written by category-theorists, or making serious use of categorical ideas, are excluded from it -- with the twin exceptions of Saunders Mac Lane's classic Categories for the working mathematician [Springer, New York, 1971; MR 50 #7275] (which, after all, the authors could hardly have left out, given their indebtedness to his title), and of Peter Freyd's 1966 paper on algebra-valued functors [Colloq. Math. 14 (1966), 89--106; MR 33 #4116] (to which I shall return below). This, then, is a book on a categorical subject -- duality -- by authors who are not category theorists, and presumably intended for such a readership. However, the editors of Mathematical Reviews have asked a category-theorist to review it, so the review is written from that point of view. The subject of the book is the construction of dual equivalences, or more generally contravariant adjunctions, between algebraic categories $\scr A$ and categories $\scr X$ whose objects are compact topological spaces equipped with compatible algebraic and/or relational structure. Here one encounters the first restrictive feature of the authors' outlook: for them "algebraic" means "finitary algebraic" (an attitude already debunked by Marshall Stone in 1947), and so the idea of a compact topology as a kind of algebraic structure (indeed, the universal example of a structure which commutes with all finitary structures) cannot be expressed. Nor can the concomitant "unity of opposites" idea that $\scr A$ and $\scr X$ are two categories of the same kind -- they are doomed to remain forever separate, like the lovers on Keats's Grecian urn. Clark and Davey follow the common tradition in universal algebra that the underlying set of an algebra is not allowed to be empty. Having thus amputated the initial objects from many of their categories $\scr A$, they are forced to amputate the terminal objects from the dual categories $\scr X$, leading to unnecessary complications in the descriptions of these categories as quasivarieties. Since they have not amputated the terminal object from $\scr A$, they are forced (in appropriate cases) to allow the empty space as a member of $\scr X$. Thus, for them, a topological algebra does not necessarily have an underlying discrete algebra! As already mentioned, Clark and Davey make heavy use of schizophrenic objects. However, as far as most of the book is concerned, schizophrenic objects are simply a convenient ad hoc way of constructing a contravariant adjunction; the fact that every contravariant adjunction between categories of the type they consider is induced by mapping into a schizophrenic object is not mentioned until page 162, where it is ascribed (not altogether appropriately) to the paper of Freyd mentioned earlier, and stated in such a convoluted way as to be almost unrecognizable. Again, all the schizophrenic objects the authors consider are finite (and topologically discrete); thus, although they refer to Pontryagin duality in their Preface (and Pontryagin appears, along with Birkhoff and Stone, as one of the three mathematicians to whose memory the work is dedicated), they are able to describe only the special case of Pontryagin duality for abelian groups of some fixed finite exponent. All the above criticisms are, in a sense, trivial ones; but their cumulative effect is nontrivial. Category theory is often criticized for consisting entirely of trivialities; but, as Freyd long ago observed, its real function is to demonstrate that the trivial parts of mathematics are trivial for trivial reasons, and that is a valuable service which it performs for the mathematical community. Reading Clark and Davey's book, anyone new to the field would find it difficult or impossible to distinguish between the trivialities and the results with genuine content, since the former are so often presented in ad hoc ways that obscure the underlying pattern. This is not a book that I would recommend a graduate student to read. One might argue that the book's shortcomings are not of major importance in relation to its declared purpose. After all, it contains a wealth of detailed information on particular techniques for establishing duality theorems, and "working algebraists" (read: working universal-algebraists) will undoubtedly find it immensely useful to have all these techniques collected together in one place. I admit the force of that argument; but I also find it seriously worrying, for it carries the implication that universal-algebraists have given up the attempt to engage in dialogue with the rest of the mathematical community. As the authors remark at the end of their Preface, there is much that remains to be done in studying and classifying concrete dualities; but this book is not likely to inspire anyone outside the closed circle of universal-algebraists to take up the task. Reviewed by Peter Johnstone Copyright American Mathematical Society 2000 From rrosebru@mta.ca Sat Mar 4 02:37:53 2000 -0400 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id BAA20993 for categories-list; Sat, 4 Mar 2000 01:50:03 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-ID: <002001bf81a9$2138f420$c238af83@tmp-sabadini.fis.unico.it> From: "walters" To: Subject: categories: CFP Category Theory 2000 Date: Mon, 28 Feb 2000 06:03:17 +0100 MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 4.72.3110.5 X-MimeOLE: Produced By Microsoft MimeOLE V4.72.3110.3 X-MIME-Autoconverted: from 8bit to quoted-printable by grus.promo.it id GAA05392 Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by mailserv.mta.ca id BAA28091 Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: SECOND CALL FOR PAPERS CATEGORY THEORY 2000 (CT 2000) July 16-22, 2000 Centro di Cultura Scientifica "Alessandro Volta" di Villa Olmo Como, Italy The next international summer conference in category theory will be held at Villa Olmo from Sunday 16th July to Saturday 22nd July 2000. We invite submissions in all areas of category theory and its applications, but particularly in the following areas: * algebraic topology and homological algebra, * categorical logic, * categories and computer science, * enriched category theory and 2-dimensional universal algebra, * galois theory and descent, * general category theory. * higher dimensional category theory and quantum algebra, * topos theory and synthetic differential geometry, The web page for the conference is http://www.disi.unige.it/conferences/ct2000/ Electronic submissions are preferred but authors may instead mail 4 copies of an extended abstract, in either case to arrive by 15th March, 2000. Email address for electronic submissions ct2000@disi.unige.it Mail address for hardcopy submissions RFC Walters (CT 2000) Dipartimento di Scienze CC., FF., MM., Università degli studi dell'Insubria 22100 Como, Italy Important Dates 15 March, 2000: Papers due 15 May, 2000: Notification of acceptance or rejection of papers 16-22 July, 2000: Conference Papers should be submitted in the form of an extended abstract. Papers should begin with the title of the paper, each author's name, affiliation, and e-mail address, followed by a statement as to which of the areas of category theory mentioned above the paper belongs, a succinct statement of the problems and goals that are considered in the paper, the main results achieved, the significance of the work in the context of previous research, and a comparison to past research. The abstract should provide sufficient detail to allow the program committee to evaluate the validity, quality, and relevance of the contribution. The entire extended abstract should not exceed 10 pages. Authors will be notified of acceptance or rejection by 15 May, 2000. Program Committee S.L. Bloom (Stevens Institute, USA) J.M.E. Hyland (Cambridge, U.K.) G. Janalidze (Tbilisi, Georgia) G.M. Kelly (Sydney, Australia) A. Kock (Aarhus, Denmark) I. Moerdijk (Utrecht, The Netherlands) R. Paré (Dalhousie, Canada) R.H. Street (Macquarie, Australia) Organizing Committee A. Carboni (Insubria) G. Rosolini (Genova) R.F.C. Walters (Insubria and Sydney) REGISTRATION Registration for the conference is now possible by consulting the web page http://www.disi.unige.it/conferences/ct2000/. The registration fee is Lit.250000, reduced to Lit.180000 for students. Also consider that the conference dinner will be on Wednesday, July 19, and the cost of a dinner ticket is Lit.70000. 28th February 2000 From rrosebru@mta.ca Sat Mar 4 02:38:20 2000 -0400 Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id BAA21033 for categories-list; Sat, 4 Mar 2000 01:55:00 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Subject: categories: Weak algebraic structures To: categories@mta.ca Date: Mon, 28 Feb 2000 14:20:46 +0000 (GMT) Cc: T.Leinster@dpmms.cam.ac.uk (Tom Leinster) X-Mailer: ELM [version 2.5 PL1] MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Message-Id: From: Tom Leinster Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: The following two papers on homotopy-algebraic structures - or "weakened" algebraic structures, if you prefer - are now available. The first one, "Up-to-Homotopy Monoids", is 8 pages long and is essentially a set of notes for the talk I gave at the Louvain-la-Neuve PSSL in October. It can serve as an introduction to the second one, "Homotopy Algebras for Operads" (100 pages, but don't let that scare you: it should be easy for category theorists). Abstracts are below. Tom Leinster * * * "Up-to-Homotopy Monoids" Informally, a homotopy monoid is a monoid-like structure in which properties such as associativity only hold `up to homotopy' in some consistent way. This short paper comprises a rigorous definition of homotopy monoid and a brief analysis of some examples. It is a much-abbreviated version of the paper `Homotopy Algebras for Operads', and does not assume any knowledge of operads. Available on the mathematics archive: http://xxx.lanl.gov/abs/math.QA/9912084 * * * "Homotopy Algebras for Operads" We present a definition of homotopy algebra for an operad, and explore its consequences. The paper should be accessible to topologists, category theorists, and anyone acquainted with operads. After a review of operads and monoidal categories, the definition of homotopy algebra is given. Specifically, suppose that M is a monoidal category in which it makes sense to talk about algebras for some operad P. Then our definition says what a homotopy P-algebra in M is, provided only that some of the morphisms in M have been marked out as `homotopy equivalences'. The bulk of the paper consists of examples of homotopy algebras. We show that any loop space is a homotopy monoid, and, in fact, that any n-fold loop space is an n-fold homotopy monoid in an appropriate sense. We try to compare weakened algebraic structures such as A_infinity-spaces, A_infinity-algebras and non-strict monoidal categories to our homotopy algebras, with varying degrees of success. We also prove results on `change of base', e.g. that the classifying space of a homotopy monoidal category is a homotopy topological monoid. Finally, we reflect on the advantages and disadvantages of our definition, and on how the definition really ought to be replaced by a more subtle infinity-categorical version. Available on the mathematics archive: http://xxx.lanl.gov/abs/math.QA/0002180