From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6181 Path: news.gmane.org!not-for-mail From: Thomas Streicher Newsgroups: gmane.science.mathematics.categories Subject: Re: are fibrations evil? Date: Thu, 16 Sep 2010 12:46:54 +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 1284689262 17672 80.91.229.12 (17 Sep 2010 02:07:42 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Fri, 17 Sep 2010 02:07:42 +0000 (UTC) Cc: categories@mta.ca To: "Prof. Peter Johnstone" Original-X-From: majordomo@mlist.mta.ca Fri Sep 17 04:07:40 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 1OwQMU-0004uS-Uz for gsmc-categories@m.gmane.org; Fri, 17 Sep 2010 04:07:39 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:42675) by smtpy.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1OwQLN-0002yb-QM; Thu, 16 Sep 2010 23:06:29 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1OwQLJ-0002lj-14 for categories-list@mlist.mta.ca; Thu, 16 Sep 2010 23:06:25 -0300 Content-Disposition: inline Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6181 Archived-At: Sure, they are "evil" but it seems to be beneficial to be "evil" sometimes. If the equivalence closed version would have been the original one I doubt that it would have been recognized how useful they are for category theory over fairly general bases. Or, rather, people would have quickly shifted to the "evil" version. BTW under a regime which identifies equality with being isomorphic (or weakly equivalent) it looks tempting to use functors from B^\op to Cat. These should capture the pseudo-functors since equality and isomorphism are identified. But writing down functoriality in type theory using \Sigma for existence amounts to choosing a lot of not at all canonical "canonical isomorphisms". Actually, one would get something even more general than pseudo-functors because one wouldn't write down the coherence conditions (actually one couldn't even since there is no honest for good equality!). Thomas [For admin and other information see: http://www.mta.ca/~cat-dist/ ]