From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6430 Path: news.gmane.org!not-for-mail From: Ronnie Brown Newsgroups: gmane.science.mathematics.categories Subject: Re: fibrations_in_2-Cat Date: Sun, 19 Dec 2010 14:58:16 +0000 Message-ID: References: Reply-To: Ronnie Brown NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit X-Trace: dough.gmane.org 1293380902 15023 80.91.229.12 (26 Dec 2010 16:28:22 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Sun, 26 Dec 2010 16:28:22 +0000 (UTC) Cc: Categories list To: "Eduardo J. Dubuc" Original-X-From: majordomo@mlist.mta.ca Sun Dec 26 17:28:18 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 1PWtSD-0003lZ-Fa for gsmc-categories@m.gmane.org; Sun, 26 Dec 2010 17:28:17 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:40130) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1PWtRh-00060U-7L; Sun, 26 Dec 2010 12:27:45 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1PWtRe-0000r6-5r for categories-list@mlist.mta.ca; Sun, 26 Dec 2010 12:27:42 -0400 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6430 Archived-At: What might be relevant is the paper BROWN, R. and STREET, R. Covering morphisms of crossed complexes and of cubical omega-groupoids with connection are closed under tensor product arXiv:1009.5609 in math.AT since we have to move to cubical omega-groupoids and discuss covering morphisms (and so fibrations) there. It seems possible analogous ideas apply to globular and cubical omega-categories in view of 116. (with F.A. AL-AGL and R. STEINER), `Multiple categories: the equivalence between a globular and cubical approach', Advances in Mathematics, 170 (2002) 71-118. That is, it is easy to make a definition that a morphism of cubical omega-categories with connections is a fibration if and only if it is a Kan fibration of the underlying cubical sets. It is not so clear what is the implication for the equivalent globular omega-categories! Ronnie On 16/12/2010 01:19, Eduardo J. Dubuc wrote: > Hi, talking about fibrations, the usual ones live in the 2-category of > categories. My question is: > > Is there any work done on the concept of fibrations in the 2-category (or > 3-category) of 2-categories ?. > > eduardo dubuc > [For admin and other information see: http://www.mta.ca/~cat-dist/ ]