July 1992 - Categories - categories.org.au

Topos Theory
by Steve Vickers 21 Jul '92

21 Jul '92

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.

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SYDNEY CATEGORY THEORY ftp SITE
by walters_b＠maths.su.oz.au 09 Jul '92

09 Jul '92

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" ==============================================================================

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exposition
by jds＠rademacher.math.upenn.edu 07 Jul '92

07 Jul '92

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(a)math.unc.edu orjds(a)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(a)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(a)mta.ca, or directly to the moderator. Usually, items of this sort sent to categories(a)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(a)mta.ca Canada ==============================================================================

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WANTED: Topos Theory
by Steve Vickers 06 Jul '92

06 Jul '92

Can anyone in Britain sell me a copy of Peter Johnstone's "Topos Theory"? Name your price. Steve Vickers. ==========================================================================

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TeX diagram macros
by dybkjaer＠euler.ruc.dk 06 Jul '92

06 Jul '92

<note from moderator: Thanks to Hans for mentioning xypic. The tar files for it are now located in the [anonymous.categories.macro] directory at macc2.mta.ca. So are the TeX source files and documentation for Mike Barr's, Francis Borceux' and Paul Taylor's diagram macros. A pointer to David Jones TeX macro index is included in the ftp site list. Bob> Dear Bob, In your latest note on posting in categories(a)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 <kris(a)diku.dk> 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 ------------------------------------------------------------------------------

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the 2- (n-?) category of chain complexes
by dyetter＠math.ksu.edu 03 Jul '92

03 Jul '92

Surely this must be known, but where is there a reference? If one considers any abelian category A, one can from a 2-category as follows: objects: differential graded objects in A (i.e. chain complexes) 1-arrows: chain maps 2-arrows: equivalence classes of chain homotopies where two chain homotopies a,b:F--->G are equivalent if there exits a map x of degree -2 from the common source of F and G to the common target of F and G such that a - b = xd - dx. The two dimensional composition of chain homotopies is addition, the one dimensional is given by if a:F--->G, b:H--->K (source(H)=target(G)) then a *1 b = aH + Gb (composites in diagrammatic order). Also, can one play the game again, and get a 3-category, etc.? A related question: does anyone know of a notion of "weak n-category" in which associativities are strict, but the middle-four-interchange holds only up to higher dimensional data? (That's what happens here if one uses chain homotopies instead of equivalence classes.) --David Yetter ==========================================================================

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None
by dmjones＠theory.lcs.mit.edu 02 Jul '92

02 Jul '92

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(a)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(a)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(a)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(a)cs.ruu.nl (or uunet!mcsun!hp4nl!ruuinf!mail-server): begin path john(a)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(a)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(a)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(a)SHSU.BITNET (FILESERV(a)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(a)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(a)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(a)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 ==============================================================================

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more in re: Yetter's question
by jds＠rademacher.math.upenn.edu 02 Jul '92

02 Jul '92

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 ==============================================================================

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None
by street＠macadam.mpce.mq.edu.au 02 Jul '92

02 Jul '92

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 ++++++++++++++++++++++++++++++++

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Dave Yetter's query.
by MAS013＠VAXC.BANGOR.AC.UK 02 Jul '92

02 Jul '92

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. ==============================================================================

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