From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5042 Path: news.gmane.org!not-for-mail From: Andree Ehresmann Newsgroups: gmane.science.mathematics.categories Subject: Non-free cocompletions Date: Mon, 06 Jul 2009 10:08:59 +0200 Message-ID: Reply-To: Andree Ehresmann NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain;charset=ISO-8859-1;DelSp="Yes";format="flowed" Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1247189561 30262 80.91.229.12 (10 Jul 2009 01:32:41 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Fri, 10 Jul 2009 01:32:41 +0000 (UTC) To: Categories Original-X-From: categories@mta.ca Fri Jul 10 03:32:34 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 1MP4yW-0008Ss-Qj for gsmc-categories@m.gmane.org; Fri, 10 Jul 2009 03:32:32 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MP4Lj-0003NG-HA for categories-list@mta.ca; Thu, 09 Jul 2009 21:52:27 -0300 Content-Disposition: inline Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5042 Archived-At: Vaughan Pratt writes > Incidentally, of what use are non-free cocompletions? Is there any reason not to define "cocompletion" to make it free? I can indicate two important uses of non-free cocompletions, and more precisely cocompletions for particular classes of diagrams preserving some given colimits: 1. The construction of what, with Charles, we called the "prototype" and the "type" associated to a sketch (in "Categories of sketchd structures", Cahiers Top. et Geom. Diff. III-2, 1972) 2. The "complexification process" which, with Jean-Paul Vanbremeersch, we use extensively in our model for hierarchical evolutionary systems ("Memory Evolutive Systems: Hierarchy, Emergence, Cognition", Elsevier 2007) Kindly Andree [For admin and other information see: http://www.mta.ca/~cat-dist/ ]