From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5078 Path: news.gmane.org!not-for-mail From: Dimitri Ara Newsgroups: gmane.science.mathematics.categories Subject: Re: making a cone universal in a faithful way Date: Tue, 4 Aug 2009 11:15:12 +0200 Message-ID: Reply-To: Dimitri Ara NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii X-Trace: ger.gmane.org 1249391445 22654 80.91.229.12 (4 Aug 2009 13:10:45 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Tue, 4 Aug 2009 13:10:45 +0000 (UTC) To: Lutz Schroeder , Original-X-From: categories@mta.ca Tue Aug 04 15:10:38 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 1MYJmn-00089e-Tm for gsmc-categories@m.gmane.org; Tue, 04 Aug 2009 15:10:38 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MYJ8l-0001FL-0J for categories-list@mta.ca; Tue, 04 Aug 2009 09:29:15 -0300 Content-Disposition: inline Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5078 Archived-At: Dear Lutz, > While I'm willing to believe the case of initial objects, the statement > is wrong already for the case of isomorphisms. You are right. I didn't checked very carefully the local confluence of my rewriting system. To get confluence, I need to add the fact that the bimorphism f satisfies "fu = vf implies u = 1 and v = 1". So this is enough for f to be a potential isomorphism. While the general statement I gave is wrong, I'm still interested in condition to make the conclusion true (for example, in the case of the sum or of the amalgated sum). Regards, -- Dimitri [For admin and other information see: http://www.mta.ca/~cat-dist/ ]