From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6265 Path: news.gmane.org!not-for-mail From: Thomas Streicher Newsgroups: gmane.science.mathematics.categories Subject: Re: Not invariant but good Date: Thu, 30 Sep 2010 13:34:21 +0200 Message-ID: <20100930113421.GA23528@mathematik.tu-darmstadt.de> 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 1285898847 8618 80.91.229.12 (1 Oct 2010 02:07:27 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Fri, 1 Oct 2010 02:07:27 +0000 (UTC) Cc: categories@mta.ca To: Michael Shulman Original-X-From: majordomo@mlist.mta.ca Fri Oct 01 04:07:25 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 1P1V1w-0008U2-2y for gsmc-categories@m.gmane.org; Fri, 01 Oct 2010 04:07:24 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:38580) by smtpy.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1P1V1A-00087x-K8; Thu, 30 Sep 2010 23:06:36 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1P1V16-0001o9-LQ for categories-list@mlist.mta.ca; Thu, 30 Sep 2010 23:06:32 -0300 Content-Disposition: inline In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6265 Archived-At: > However, in the absence of the axiom of choice, the naive definition > of "functor" is not very well-behaved; it's better to use "anafunctors," Nothing against anafunctors but it is an exaggeration to say that in absence of choice the usual notion of functor is not well-behaved. One just loses that full and faithful and essential surjective entails equivalence. That's like abandoning the notion of surjective map in case we can't split them all. Thomas [For admin and other information see: http://www.mta.ca/~cat-dist/ ]