From: Ross Street <ross.street@mq.edu.au>
To: Ronnie Brown <ronnie.profbrown@btinternet.com>
Cc: Ondrej Rypacek <ondrej.rypacek@gmail.com>, categories@mta.ca
Subject: Re: double 2-categories
Date: Thu, 9 Dec 2010 20:36:10 +1100 [thread overview]
Message-ID: <E1PQlYc-0003Bs-TG@mlist.mta.ca> (raw)
In-Reply-To: <E1PQ9wp-0006f3-VO@mlist.mta.ca>
I would also point to the papers by Andrée and Charles Ehresmann:
Multiple functors. II. The monoidal closed category of multiple
categories.
Cahiers Topologie Géom. Différentielle 19 (1978), no. 3, 295–333.
Multiple functors. III. The Cartesian closed category ${\rm Cat}_{n}$.
Cahiers Topologie Géom. Différentielle 19 (1978), no. 4, 387–443.
==Ross
On 08/12/2010, at 1:13 AM, Ronnie Brown wrote:
> I am not sure why there is the restriction to having 2-categories as
> edge arrows. They could be double categories, perhaps. Would this
> then
> be any more general than a 4-fold category?
>
> A definition of n-fold category is given in
>
> 34. (with P.J. HIGGINS), ``The equivalence of $\infty$-groupoids and
> crossed complexes'', {\em Cah. Top. G\'eom. Diff.} 22 (1981)
> 371-386.
>
> and this also contains a definition of what was later called a
> globular
> set, giving a notion of what we now call a strict globular n-category,
> though the emphasis in the paper is on the groupoid case.
>
> Ronnie
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
next prev parent reply other threads:[~2010-12-09 9:36 UTC|newest]
Thread overview: 6+ messages / expand[flat|nested] mbox.gz Atom feed top
2010-12-07 12:59 Ondrej Rypacek
2010-12-07 14:13 ` Ronnie Brown
2010-12-09 9:36 ` Ross Street [this message]
[not found] ` <4CFE4105.5020902@btinternet.com>
2010-12-07 16:08 ` Ondrej Rypacek
2010-12-07 18:35 ` Jeff Egger
[not found] ` <456981.42294.qm@web110605.mail.gq1.yahoo.com>
[not found] ` <16A709CA-BA0D-4E71-8994-F700356973D3@gmail.com>
2010-12-07 19:31 ` Ondrej Rypacek
Reply instructions:
You may reply publicly to this message via plain-text email
using any one of the following methods:
* Save the following mbox file, import it into your mail client,
and reply-to-all from there: mbox
Avoid top-posting and favor interleaved quoting:
https://en.wikipedia.org/wiki/Posting_style#Interleaved_style
* Reply using the --to, --cc, and --in-reply-to
switches of git-send-email(1):
git send-email \
--in-reply-to=E1PQlYc-0003Bs-TG@mlist.mta.ca \
--to=ross.street@mq.edu.au \
--cc=categories@mta.ca \
--cc=ondrej.rypacek@gmail.com \
--cc=ronnie.profbrown@btinternet.com \
/path/to/YOUR_REPLY
https://kernel.org/pub/software/scm/git/docs/git-send-email.html
* If your mail client supports setting the In-Reply-To header
via mailto: links, try the mailto: link
Be sure your reply has a Subject: header at the top and a blank line
before the message body.
This is a public inbox, see mirroring instructions
for how to clone and mirror all data and code used for this inbox;
as well as URLs for NNTP newsgroup(s).