From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5108 Path: news.gmane.org!not-for-mail From: Chris Heunen Newsgroups: gmane.science.mathematics.categories Subject: Re: pushouts in REL Date: Sat, 22 Aug 2009 11:00:54 +0200 Message-ID: Reply-To: Chris Heunen NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1250947145 8681 80.91.229.12 (22 Aug 2009 13:19:05 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Sat, 22 Aug 2009 13:19:05 +0000 (UTC) To: categories@mta.ca Original-X-From: categories@mta.ca Sat Aug 22 15:18:59 2009 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from mailserv.mta.ca ([138.73.1.1]) by lo.gmane.org with esmtp (Exim 4.50) id 1MeqUk-00073i-Rn for gsmc-categories@m.gmane.org; Sat, 22 Aug 2009 15:18:59 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1Meq25-0007HW-IY for categories-list@mta.ca; Sat, 22 Aug 2009 09:49:21 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5108 Archived-At: Dear all, > let A and B be sets and R,S \inc A x B. Let A_0 be the subset of A consisting > of all a such that (a,b) \in R iff (a,b) \in S. Then it seems to me that > the inclusion function of A_0 into A is the equalizer of R and S. I already answered Sergei privately, but this should be corrected publicly: Rel does not have equalisers. In fact, it has almost no equalisers. For a counterexample, consider the sets A = {0,1} and B = {0}, and the parallel relations R = A x B and S = {(0,0)}. Their equaliser, if it existed, must be contained in T = {(0,0)}. But T' = {0} x A also satisfies RT'=ST', but does not factor through any subrelation of T. Best wishes, Chris Heunen [For admin and other information see: http://www.mta.ca/~cat-dist/ ]