From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6245 Path: news.gmane.org!not-for-mail From: Thomas Streicher Newsgroups: gmane.science.mathematics.categories Subject: Re: =?iso-8859-1?B?UkWg?= =?iso-8859-1?Q?=3A?= categories: Re: Not invariant but good Date: Tue, 28 Sep 2010 12:18:46 +0200 Message-ID: References: Reply-To: Thomas Streicher NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii X-Trace: dough.gmane.org 1285720325 15775 80.91.229.12 (29 Sep 2010 00:32:05 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Wed, 29 Sep 2010 00:32:05 +0000 (UTC) To: categories@mta.ca Original-X-From: majordomo@mlist.mta.ca Wed Sep 29 02:32:04 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 1P0kaZ-0003A1-26 for gsmc-categories@m.gmane.org; Wed, 29 Sep 2010 02:32:03 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:32954) by smtpy.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1P0kZl-0000Pm-PO; Tue, 28 Sep 2010 21:31:14 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1P0kZg-0003x8-UU for categories-list@mlist.mta.ca; Tue, 28 Sep 2010 21:31:09 -0300 Content-Disposition: inline In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6245 Archived-At: Thanks Andr'e for pointing out by various examples why it is not always wise to insist on invariance under equivalence or weak equivalence. This in my opinion is the real issue and not whether "evil" is a tasteless name or not. The problem rather is that people using "evil" really mean it so even if they deny it. An little comment on structure versus property which is an importnat distinction in my eyes. The notion of Grothendieck fibration is a property of functors and not an additional structure. However, the notion of fibration in a(n abstract) 2-category can be formulated only postulating a certain kind of structure which, however, is unique up to canonical isomorphism. But this amounts to defining Grothendieck fibrations in terms of cleavages (which certainly are all canonically isomorphic). But choosing cleavages amounts to accepting very strong choice principles which is maybe no real problem but at least aesthetically moderately pleasing. Thomas [For admin and other information see: http://www.mta.ca/~cat-dist/ ]