From: street@macadam.mpce.mq.edu.au (Ross Street) Date: Wed, 1 Jul 92 12:50:52 EST This is a hasty reply to David Yetter's question. The original Dold-Kan theorem is that the category of simplicial abelian groups is equivalent to the category of chain complexes of abelian groups. Dominique Bourn has studied this quite deeply. One of his results (all published in JPAA & Cahiers) is that the category of length n chain complexes of abelian groups is equivalent to the cat of abelian groups in n-Cat (= n-categories in Ab). Thus, looking at homs, we can relate differential graded categories (DG-categories are categories with homs in chain complexes of abelian groups) and (n+1)-categories. However, there is a need to look at the tensor products on these base monoidal categories. This is why David was led to his next question which Bourn has solved for all n in the additive case. In the non-additive situation, we need the tensor product of John Gray on 2-Cat, not the cartesian product. Categories enriched in this monoidal category are almost 3-categories except for a wobbly middle-4-interchange. Groupoid- like such are Joyal-Tierney homotopy 3-types. Higher dimensional cases are at various stages of completion in the non- additive case: Bourn has done the additive case: I have preprints of his papers "Un theoreme de Dold-Kan pour les groupes abeliens n-categoriques", "The tower on n-groupoids and the long cohomology sequence" JPAA 62 (1989) 137-183 "Produits tensoriels coherents de complexes de chaine" Bull soc Math de Belgique 41 (2) (1989) 219-248 "Another denormalization theorem for abelian chain complexes" JPAA Regards to all: sorry I won't get to Sussex this year. Ross Street ++++++++++++++++++++++++++++++++ Date: Wed, 1 Jul 92 16:46 GMT From: MAS013@VAXC.BANGOR.AC.UK Subject: Dave Yetter's query. The groupoid enriched category of chain complexes is explored in Gabriel and Zisman. Yes a three cat is possible as is a four .... or infinity cat version. Interesting ideas relating to this can be found in Grothendieck's cotangent complex lecture notes. Ronnie, Tim, Markus and Larrie(visiting); Bangor. ============================================================================== Subject: more in re: Yetter's question Date: Wed, 1 Jul 92 21:04:58 GMT-0400 From: jds@rademacher.math.upenn.edu In re: Yetter's weak middle interchange The analogies between Yetter's problems with cat of chain complexes and mine with the non-cat of H-spaces are several. All my H-spaces have strict units so modify your favorite definition of tensor cat accordingly. Question: when is the multiplication m: X x X --> X of an associative H-space an H-map? Answer: iff m is homotopy commutative the interchange for homotopy commutativity is the interchange of the middle two when the outside two are the unit Note also that the problem with the tensor product of chain homotopic maps is that a chain homotopy for that product must deform one factor first and then the otherr JUST as in the simplicial approximation to the diagonal map which gies rise to the homotpy commutativity of cup product ============================================================================== Subj: Re: the 2- (n-?) category of chain complexes From: street@macadam.mpce.mq.edu.au (Ross Street) Date: Thu, 2 Jul 92 10:02:02 EST Addendum to my reply to Yetter's letter: There were other things I meant to say but was short of time yesterday. 1) The work of Brown, Porter, Higgins deals with the non-additive groupoid case. Now I see that they have replied by referring to SLN 72. 2) Andre Joyal has a beautiful proof of the Dold-Kan theorem showing that it is a qualitative version of Isaac Newton's result that a list of data can be recaptured from the first column of iterated differences. I told Dold this while he was visiting Macquarie; he was delighted. 3) The generalisation of Gray's tensor product of 2-categories is performed as follows. Let me write G for the monoidal category 2-Cat with Gray's tensor product. Then G-Cat is the category of categories with homs enriched in G. The category 3-Cat of 3-categories is contained in G-Cat. Let O(I^n) denote the free n-category on the n-cube I^n (as per the work of Iain Aitchison, Mike Johnson, Richard Steiner and myself; in fact, "Parity complexes" has appeared in Cahiers XXXII-4 1991 315-343 and provides a simple model for O(I^n)). Let Q^n denote the 3-category obtained from O(I^n) by forcing all cells of dimension higher than 3 to be identities. Thus we have a full subcategory T of G-Cat consisting of the Q^n; furthermore, T is dense in G-Cat. We certainly know how to multiply cubes: Q^m (tensor) Q^n = Q^(m+n). This tensor product extends from T to G-Cat by Kan extension along the inclusion (Brian Day studied the general process of extending promonoidal structures along dense functors; his convolution structures are about extension along Yoneda). This is the third stage in a clear recursive construction. Regards, Ross ============================================================================== Subj: exposition Date: Sat, 4 Jul 92 11:18:39 GMT-0400 From: jds@rademacher.math.upenn.edu What would anyone recommend as a good EXPOSITORY account/introduction for: 1)the category of modules/reps of a Lie algebra as symmetric monoidal? 2) same but with an eye to generalizing to quantum groups?? 3)relevance of n-cats to computer science?? thanks jim stasheff (messages unsigned but from jds@math.unc.edu orjds@math.upenn.edu are from me) ============================================================================== Subj: Categories: Routine Posting This is the quarterly routine distribution for the categories mailing list. It was last updated on June 30, 1992. Subscribers should note that the From: field of a categories posting is categories@mta.ca (which is different from some other mailing lists). Thus, an automatic reply is redirected to the entire list (unless another intention is clearly detected by the moderator). Administrative items (address changes etc.) can be sent to categories-request@mta.ca, or directly to the moderator. Usually, items of this sort sent to categories@mta.ca will not be posted. The archives of postings on categories are held at the ftp site macc2.mta.ca in the directory [.categories]. Note that this is a Vax VMS system and so the cd command requires appropriate syntax i.e. cd [.new] moves one node down the directory tree to new cd [-] moves one node up the tree. The postings are filed in yearly subdirectories called [.90], [.91] etc. Within those subdirectories there are monthly files, and an annual list of dates and subjects of postings. In the [.categories] directory there is also a file called ftp.sites with information about ftp sites holding files of interest to subscribers. Several TeX diagram macro packages are in the subdirectory [.macro]. Contributions for these files are welcome. This ftp site will also archive files which represent preprints in category theory for persons without access to an ftp archive. It is preferred that these be in TeX, but other submissions will be considered. Submissions should be sent to the moderator by e-mail only, and should include a short abstract suitable for posting to the categories list. Submissions must be ascii files only (so TeX source code in any flavour is fine, but dvi files are not acceptable currently.) If you need detailed instructions on how to use ftp ask anyone knowedgable about networks at your site, or write to me. Bob Rosebrugh Phone: 1-506-364-2538 Department of Mathematics and Computer Science Fax: -364-2210 Mount Allison University Sackville, N. B. E0A 3C0 Email: rrosebrugh@mta.ca Canada ============================================================================== Subj: Re: exposition From: dyetter@math.ksu.edu (David Yetter) Date: Mon, 6 Jul 92 9:33:22 CDT Regarding Jim Stasheff's query: I regret that I don't know any extant good exposition on any of the topics (not surpising on 3) since that's out of my area). However, David Kazhdan and Serge Gelfand are apparently working on a book on tensor categories (i.e. monoidal categories, though possibly with some linearity or abelianness required), which may fit the bill on 1) and 2). Sorry I can't be more helpful. Best Thoughts, David Yetter ============================================================================== Subj: Re: WANTED: Topos Theory Date: Mon, 06 Jul 92 11:24:00 From: Steve Vickers [This message is mainly directed at the 36 people who told me they'd like to buy reprinted copies of "Topos Theory".] I've now written to Roger Hill at Academic Press as follows: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Dear Mr Hill, I recently advertised for a second-hand copy of Topos Theory by Peter Johnstone, which you published in 1977 (London Mathematical Society Monographs no. 10). Instead of any offers, I received a number of commiserational messages saying how terrible it was that such a classic should have been allowed to go out of print. Im writing this letter to encourage you to consider reprinting the work. (You were suggested to me by Susan Overy as the most appropriate person to write to.) I am a research worker in topos theory. Johnstone's book is one of the tools of my trade and it is disappointing to me not to find it readily obtainable. Do you think there is any chance of a reprint, preferably in paperback? New books on toposes are in preparation, but to my mind the depth and authority of Johnstone's old book should give it a continuing place in the literature. The following people have told me that they will definitely buy a copy if the book is reprinted at not too high a price. Almost all of them responded within four days when I circularized an electronic mail message saying I was going to write to you. You will notice that many of them work (like myself) in computer science departments. The theory of toposes is now being enthusiastically embraced by quite a few workers in theoretical computer science, so the market for books on toposes is opening up. <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<< (Then I included the list of 36 names.) Steve Vickers. ============================================================================== Subj: TeX diagram macros Date: Mon, 6 Jul 92 08:54:05 +0200 From: dybkjaer@euler.ruc.dk (Hans Dybkjaer) Dear Bob, In your latest note on posting in categories@mta.ca you mentioned [.macro]. For diagrams in TeX I'm using XY-pic which is probably the most extensive diagram package available, and quite "user-friendly", too. Moreover, the author is supporting the package. It is listed in DM Jones' "styles-and-macros.Index" as: Name: xypic.tex Description: Macros for typesetting diagrams. Keywords: plain TeX, AMS-TeX, LaTeX, XY-pic, diagrams, graphics, commutative diagrams. Author: Kristoffer H. Rose Supported: yes Latest Version: v2.6, 24 Jun 1992 Note: Comes with extensive documentation (xypicman.doc) which requires AMS-TeX, xppt.tex, xfixed.tex and xrcs.tex to format. (The manual is also distributed preformatted.) XY-pic also requires several special fonts (xyatip10.mf, xybtip10.mf, xyline10.mf and xymisc10.mf) which are distributed with the package. Numerous other files are also included. Archives: aston, stuttgart, utrecht, shsu, ftp.diku.dk* [/pub/TeX/misc/xypic*] and is probably best available via ftp to diku.dk in TeX/misc/xypic. It has previously been announced on the news net. By the way, you might also consider including the "styles-and-macros.Index". I append the distribution message in the end of this mail. yours, Hans ------------------------------------------------------------------------------ From: dmjones@theory.lcs.mit.edu (David M. Jones) Date: Wed, 01 Jul 92 22:33:16 EDT To: dybkjaer@ruc.dk Subject: TeX Macro Index I'm mailing you a copy of this announcement because you are one of the authors whose packages are listed in the Index. Yours, David. *************************************************************************** I am happy to announce that the first edition of the TeX Macro Index is now available by anonymous ftp and/or mail server from the following sites: [1] archive.cs.ruu.nl [2] ftp.th-darmstadt.de [3] ftp.math.utah.edu [4] Niord.SHSU.edu [5] TeX.ac.uk [6] theory.lcs.mit.edu Full instructions for retrieving the Index from these machines are appended to the end of this message. All of the archives have identical copies of the Index. In order to minimize the burden on the net, please pick the archive closest to you. I am forwarding this announcement to all of the TeX-related mailing lists that I know of. If you belong to a list that does not receive a copy of the message, but which you think would be interested in the Index, please forward this announcement. If you do so, I would appreciate it if you would also tell me the name of the list. A brief description of the Index follows. David M. Jones =========================================================================== This is an index of TeX macros. Its scope includes all macros that are available via anonymous ftp or mail-server or some similar mechanism. Commercial packages will be included only if a full Index entry is supplied to me by the vendor. Since the Index is devoted to macros, fonts and special-purpose programs are mentioned only when they are necessary to explain the purpose of a set of macros. Each entry is divided into several fields with the following functions: Name: The name of the macro package. Description: A short (usually 1-3 line) description of the package. Keywords: A list of keywords to facilitate searching for special-purpose macros, as well as to help describe the macros. A glossary of keywords can be found at the end of the file. Archives: A list of archives where the package can be found. Whenever known, the primary distribution site is marked with an asterisk. Author: The name and address (preferably electronic) of the author of the package. Latest Version: The date and/or version number of the latest release of the package. Supported: Whether or not the package is supported, that is, whether the author wants to receive bug reports and/or comments on the package. See also: A list of other packages with similar features. Note: Any additional information that seems pertinent. In addition to the list of packages, the Index also contains a brief list of TeX Archives with descriptions of the services they offer. =========================================================================== HOW TO RETRIEVE THE TEX MACRO INDEX First, here are some general instructions on anonymous ftp for those who haven't used it before. After deciding which archive you want to use, read the instructions below to find out the following three things: 1) the full name of the machine containing the archive 2) the name of the directory where the TeX Index is located 3) the name of the file containing the Index In addition, you should check the name of the file to see if it ends in ".Z", ".zoo", or ".zip". If so, it is a binary file and you will have to perform an extra step below. Once you have all of this information, you should type the following command: ftp name_of_machine When you are asked for a user name, type "anonymous". When you are asked for a password, type in your email address. Next, type cd name_of_directory If the file you are retrieving is a binary file, then you must now type the command binary Finally, retrieve the file by typing the command get name_of_file Once the transfer is complete, type bye to end the ftp session. [1] archive.cs.ruu.nl (Netherlands) How to get TeX-index.Z from the archive at Dept. of Computer Science, Utrecht University: NOTE: In the following I have assumed your mail address is john@highbrow.edu. Of course you must substitute your own address for this. This should be a valid internet or uucp address. For bitnet users name@host.BITNET usually works. by FTP: (please restrict access to weekends or evening/night (i.e. between about 20.00 and 0900 UTC)). ftp archive.cs.ruu.nl [131.211.80.5] user name: anonymous or ftp password: your own email address (e.g. john@highbrow.edu) Don't forget to set binary mode if the file is a tar/arc/zoo archive, compressed or in any other way contains binary data. get TEX/DOC/TeX-index.Z by mail-server: send the following message to mail-server@cs.ruu.nl (or uunet!mcsun!hp4nl!ruuinf!mail-server): begin path john@highbrow.edu (PLEASE SUBSTITUTE *YOUR* ADDRESS) send TEX/DOC/TeX-index.Z end NOTE: *** PLEASE USE VALID INTERNET ADDRESSES IF POSSIBLE. DO NOT USE ADDRESSES WITH ! and @ MIXED !!!! BITNETTERS USE USER@HOST.BITNET *** The path command can be deleted if we receive a valid from address in your message. If this is the first time you use our mail server, we suggest you first issue the request: send HELP ------------------------- [2] ftp.th-darmstadt.de (Germany) The TeX Macro Index is available via anonymous ftp from ftp.th-darmstadt.de [130.83.55.75] directory pub/tex/documentation file styles-and-macros.Index.Z ------------------------- [3] ftp.math.utah.edu (USA) The TeX Macro Index is available via anonymous ftp from ftp.math.utah.edu [128.110.198.2] in the file pub/tex/tex-index. To retrieve it by e-mail server, send a message to tuglib@math.utah.edu with the subject or body "send tex-index from tex". ------------------------- [4] Niord.SHSU.edu (USA) To retrieve the Index in 8 parts suitable for electronic mail handling, include the command: SENDME TEX-INDEX in the body of a mail message to FILESERV@SHSU.BITNET (FILESERV@SHSU.edu). To retrieve the latest set of FAQ-related documents (Bobby Bodenheimer's "TeX, LaTeX, etc.: Frequently Asked Questions with Answers", Guoying Chen's "Supplement to the Frequently Asked Questions" and Liam R. E. Quin's "Complete list of all metafont-format fonts in the world"), include the command: SENDME FAQ in your mail request to FILESERV. For anonymous ftp retrieval from Niord.SHSU.edu (192.92.115.8), the complete Index may be found in the file [FILESERV.TEX-INDEX]TEX.INDEX and all FAQ-related documents may be found in the directory [FILESERV.FAQ]. ------------------------- [5] TeX.ac.uk (UK) The TeX Macro Index is available via anonymous ftp, JANET NIFTP and mail server from the UK TeX Archive, TeX.ac.uk [134.151.40.18] in the file [tex-archive.doc]TeX-index.txt. To retrieve it by mail server, send a message to TeXserver@tex.ac.uk containing the following lines FILES [tex-archive.doc]TeX-index.txt ------------------------- [6] theory.lcs.mit.edu (USA) The TeX Macro Index is available via anonymous ftp and mail server from theory.lcs.mit.edu [18.52.0.92] in the file TeX-index in the directory pub/tex. To retrieve it by mail server, send a message to archive-server@theory.lcs.mit.edu containing the following line send tex TeX-index The Index is also available in compressed, zip'ed and zoo'ed format in the files TeX-index.Z, TeX-index.zip and TeX-index.zoo, respectively. Note that if you want to request one of the compressed files by mail server, you'll have to specify a method of ASCII encoding by including one of the following lines in your mail message: encoder btoa encoder uuencode encoder rscs ------------------------------------------------------------------------------- Hans Dybkj{\ae}r Centre for Cognitive Informatics, Roskilde University Email: dybkjaer@ruc.dk P.O. Box 260, DK-4000 Roskilde, Denmark Phone: +45 46 75 77 11 Direct: +45 46 75 77 81 ... 2219 Fax: +45 46 75 53 13 ============================================================================== Subj: SYDNEY CATEGORY THEORY ftp SITE Date: Thu, 9 Jul 92 22:45:07 +1000 From: walters_b@maths.su.oz.au (Bob Walters) SYDNEY CATEGORY THEORY ftp SITE maths.su.oz.au directory sydcat Some recent additions: ---------------------- papers/phoa/tech.ps Replacing fibs.ps, topoi.ps, eff.ps, these notes provide an introduction to (aspects of) a) fibrations and polymorphic lambda calculus b) constructive logic, categorical logic and topos theory c) Kleene realizability; PERs and omega-sets d) the effective topos; modest sets and how they model polymorphism They assume some basic knowledge of category theory, logic and typed lambda calculus. No familiarity with indexed categories or with categorical logic or topos theory is required. The notes do not attempt to be comprehensive, but simply try to give a reasonably relaxed account of the material. They are about 150pp including the index and appendixes. There are plenty of exercises. papers/kelly/kan Dvi file for G.M. Kelly, S. Lack, "Finite-product-preserving functors, Kan extensions, and strongly-finitary monads" papers/walters/ccs Information about R.F.C. Walters' book "Categories and Computer Science" published by Carslaw Press in Australia (1991) and to be published in August 1992 by Cambridge University Press papers/walters/coinv Dvi file for G.M. Kelly, S. Lack, R.F.C. Walters, "Coinverters and categories of fractions for categories with structure" ============================================================================== Subj: Topos Theory Date: Mon, 20 Jul 92 14:51:33 From: Steve Vickers Following my letter to Academic Press enquiring about the possibility of their reprinting Johnstone's "Topos Theory", I've had the following reply from Andrew Carrick at the London Office. >>>>>>>>>>>>>>>>>>>>>>>> Many thanks for your letter concerning Johnstone's "Topos Theory", which made interesting reading. The situation viz a viz LMS Monographs and Academic Press is a complex one since we no longer publish with them. I will look into the possibility of a reprint and in the meantime see if we can find you a dusty old copy from our office - this is a long shot! <<<<<<<<<<<<<<<<<<<<<<<< Fingers crossed (at least for the dusty old copy), Steve Vickers.