From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6199 Path: news.gmane.org!not-for-mail From: Michael Shulman Newsgroups: gmane.science.mathematics.categories Subject: Re: Re: are fibrations evil? Date: Mon, 20 Sep 2010 09:25:49 -0700 Message-ID: References: Reply-To: Michael Shulman NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 X-Trace: dough.gmane.org 1285118294 29472 80.91.229.12 (22 Sep 2010 01:18:14 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Wed, 22 Sep 2010 01:18:14 +0000 (UTC) Cc: categories@mta.ca To: Thomas Streicher Original-X-From: majordomo@mlist.mta.ca Wed Sep 22 03:18:12 2010 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpy.mta.ca ([138.73.1.139]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1OyDyK-000508-AF for gsmc-categories@m.gmane.org; Wed, 22 Sep 2010 03:18:08 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:52054) by smtpy.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1OyDxE-0006lX-30; Tue, 21 Sep 2010 22:17:00 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1OyDx9-00048K-7l for categories-list@mlist.mta.ca; Tue, 21 Sep 2010 22:16:55 -0300 In-Reply-To: <20100918134829.GB9467@mathematik.tu-darmstadt.de> Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6199 Archived-At: On Sat, Sep 18, 2010 at 6:48 AM, Thomas Streicher wrote: > But what I do not see is a correspondence between kosher and > non-kosher versions. If you start with a collection CC of 1-cells in a 2-cat > like Cat and close it under equivalences thus obtaining CC' I don't see any > way of reconstructing CC from CC' in a canonical way. I didn't mean to imply that there was. In general, a given kosher concept may correspond to more than one non-kosher concept. For instance, the notion of "weak n-category" is believed to be "semi-strictifiable" in multiple incompatible ways. It's known for n=3 that one can either make associativity and units strict but keep interchange weak, or make associativity and interchange strict but keep units weak, but one cannot make everything strict. However, if we choose a particular corresponding non-kosher concept, then we can talk about (semi)strictification of individual objects. Mike [For admin and other information see: http://www.mta.ca/~cat-dist/ ]