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 <sjv@doc.imperial.ac.uk>

[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)

<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@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@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

------------------------------------------------------------------------------
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 <sjv@doc.imperial.ac.uk>

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.
