From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/7690 Path: news.gmane.org!not-for-mail From: Toby Bartels Newsgroups: gmane.science.mathematics.categories Subject: Re: Terminology: Remarks Date: Wed, 1 May 2013 23:46:54 -0700 Message-ID: References: Reply-To: Toby Bartels NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit X-Trace: ger.gmane.org 1367536821 15168 80.91.229.3 (2 May 2013 23:20:21 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Thu, 2 May 2013 23:20:21 +0000 (UTC) To: Categories Original-X-From: majordomo@mlist.mta.ca Fri May 03 01:20:21 2013 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp3.mta.ca ([138.73.1.186]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1UY2nV-0006XY-2P for gsmc-categories@m.gmane.org; Fri, 03 May 2013 01:20:21 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:44675) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1UY2m3-0008W1-Jg; Thu, 02 May 2013 20:18:51 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1UY2m4-0008Ed-Pm for categories-list@mlist.mta.ca; Thu, 02 May 2013 20:18:52 -0300 Content-Disposition: inline In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:7690 Archived-At: Jean B?nabou wrote in small part: >The one [notion of equivalence of categories] which might serve here is f >full and faithful and essentially surjective. But unless we have AC it is >not symmetric, even for A and B small. Then the obvious thing to try is to symmetrise it: An equivalence between A and B is a span A <- X -> B of fully faithful and essentially surjective functors. --Toby [For admin and other information see: http://www.mta.ca/~cat-dist/ ]