From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6413 Path: news.gmane.org!not-for-mail From: Ross Street Newsgroups: gmane.science.mathematics.categories Subject: Re: double 2-categories Date: Thu, 9 Dec 2010 20:36:10 +1100 Message-ID: References: Reply-To: Ross Street NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 (Apple Message framework v936) Content-Type: text/plain; charset=WINDOWS-1252; format=flowed; delsp=yes Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1291920611 20414 80.91.229.12 (9 Dec 2010 18:50:11 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Thu, 9 Dec 2010 18:50:11 +0000 (UTC) Cc: Ondrej Rypacek , categories@mta.ca To: Ronnie Brown Original-X-From: majordomo@mlist.mta.ca Thu Dec 09 19:50:06 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 1PQlZ8-0003qY-Fb for gsmc-categories@m.gmane.org; Thu, 09 Dec 2010 19:50:06 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:50427) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1PQlYg-00082F-AG; Thu, 09 Dec 2010 14:49:38 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1PQlYc-0003Bs-TG for categories-list@mlist.mta.ca; Thu, 09 Dec 2010 14:49:35 -0400 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6413 Archived-At: I would also point to the papers by Andr=E9e and Charles Ehresmann: Multiple functors. II. The monoidal closed category of multiple =20 categories. Cahiers Topologie G=E9om. Diff=E9rentielle 19 (1978), no. 3, 295=96333. Multiple functors. III. The Cartesian closed category ${\rm Cat}_{n}$. Cahiers Topologie G=E9om. Diff=E9rentielle 19 (1978), no. 4, 387=96443. =3D=3DRoss 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 =20 > 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 =20 > 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/ ]