From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5335 Path: news.gmane.org!not-for-mail From: Tobias Heindel Newsgroups: gmane.science.mathematics.categories Subject: The converse of universality/pullback-stability Date: Tue, 08 Dec 2009 11:33:50 +0100 Message-ID: Reply-To: Tobias Heindel NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1260321935 17326 80.91.229.12 (9 Dec 2009 01:25:35 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 9 Dec 2009 01:25:35 +0000 (UTC) To: categories@mta.ca Original-X-From: categories@mta.ca Wed Dec 09 02:25:28 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 1NIBJ0-00039V-5d for gsmc-categories@m.gmane.org; Wed, 09 Dec 2009 02:25:26 +0100 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1NIAs0-0006XA-3Y for categories-list@mta.ca; Tue, 08 Dec 2009 20:57:32 -0400 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5335 Archived-At: I have a short question concerning terminology related to extensive categories. In the latter, coproducts enjoy the following property. U ----> Z <---- V | | | | | | v v v A ---> A+B <--- B /--------------------------------------------\ | In a double square diagram as illustrated, | | the top row is a coproduct diagram | | if and only if both squares are pullbacks. | \--------------------------------------------/ The "if"-part of this condition is known as universality or pullback-stability of co-products; it also can be formulated for arbitrary colimits. What about the "only if" direction? Is there a name for it in the case of arbitrary colimits? Tobias Heindel [For admin and other information see: http://www.mta.ca/~cat-dist/ ]