From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6406 Path: news.gmane.org!not-for-mail From: Ondrej Rypacek Newsgroups: gmane.science.mathematics.categories Subject: Re: double 2-categories Date: Tue, 7 Dec 2010 16:08:13 +0000 Message-ID: References: <4CFE4105.5020902@btinternet.com> Reply-To: Ondrej Rypacek NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1291776095 30012 80.91.229.12 (8 Dec 2010 02:41:35 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Wed, 8 Dec 2010 02:41:35 +0000 (UTC) Cc: categories@mta.ca To: Ronnie Brown Original-X-From: majordomo@mlist.mta.ca Wed Dec 08 03:41:31 2010 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.114]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1PQ9yD-0007oh-IK for gsmc-categories@m.gmane.org; Wed, 08 Dec 2010 03:41:29 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:46542) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1PQ9xt-0006kE-Gr; Tue, 07 Dec 2010 22:41:09 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1PQ9xo-0006h0-UC for categories-list@mlist.mta.ca; Tue, 07 Dec 2010 22:41:05 -0400 In-Reply-To: <4CFE4105.5020902@btinternet.com> Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6406 Archived-At: Thanks! I think a special case of a 4-fold category is precisely what I'm after, I just didn't know what are they called beyond the double case. Ondrej On 7 December 2010 14:13, Ronnie Brown wr= ote: > I am not sure why there is the restriction to having 2-categories as edge > arrows. They could be double categories, perhaps. =A0Would this then be a= ny > more general than a 4-fold category? > > A definition of n-fold category is given in > > 34. =A0(with P.J. HIGGINS), ``The equivalence of $\infty$-groupoids and > crossed =A0complexes'', {\em Cah. Top. G\'eom. Diff.} 22 (1981) > 371-386. > > and this also contains a definition of what was later called a globular s= et, > 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/ ]