From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6183 Path: news.gmane.org!not-for-mail From: David Roberts Newsgroups: gmane.science.mathematics.categories Subject: Re: are fibrations evil? Date: Fri, 17 Sep 2010 11:47:06 +0930 Message-ID: Reply-To: David Roberts NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 X-Trace: dough.gmane.org 1284773214 26310 80.91.229.12 (18 Sep 2010 01:26:54 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Sat, 18 Sep 2010 01:26:54 +0000 (UTC) To: "categories@mta.ca" Original-X-From: majordomo@mlist.mta.ca Sat Sep 18 03:26:53 2010 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.138]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1OwmCa-0008Fg-Dd for gsmc-categories@m.gmane.org; Sat, 18 Sep 2010 03:26:53 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:51078) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1OwmB8-0007Ei-8i; Fri, 17 Sep 2010 22:25:22 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1OwmB5-0000wX-LK for categories-list@mlist.mta.ca; Fri, 17 Sep 2010 22:25:19 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6183 Archived-At: Mike wrote: >If one defined the identity types and pullbacks using limits in Gpd in the >kosher 2-categorical sense, then it seems to me that one should be >able to define an equivalent model using arbitrary functors between >groupoids to represent the dependent types, rather than merely the >fibrations. This seems (to me) to be analogous to extending one's notion of covering space to allow for empty fibres - indeed, the characterisation of covering spaces as representations of Pi_1 needs this. David PS +1 for using 'kosher' :) [For admin and other information see: http://www.mta.ca/~cat-dist/ ]