From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/7282 Path: news.gmane.org!not-for-mail From: Michael Barr Newsgroups: gmane.science.mathematics.categories Subject: Derived cotriples Date: Mon, 21 May 2012 17:23:29 -0400 (EDT) Message-ID: Reply-To: Michael Barr NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; format=flowed; charset=US-ASCII X-Trace: dough.gmane.org 1337703096 30979 80.91.229.3 (22 May 2012 16:11:36 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Tue, 22 May 2012 16:11:36 +0000 (UTC) To: Categories list Original-X-From: majordomo@mlist.mta.ca Tue May 22 18:11:35 2012 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.80]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1SWrgJ-0001WH-EU for gsmc-categories@m.gmane.org; Tue, 22 May 2012 18:11:31 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:43056) by smtpx.mta.ca with esmtp (Exim 4.77) (envelope-from ) id 1SWrfE-0007gH-EV; Tue, 22 May 2012 13:10:24 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1SWrfE-0006bv-Tb for categories-list@mlist.mta.ca; Tue, 22 May 2012 13:10:24 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:7282 Archived-At: Suppose (G,\epsilon,\delta) is a cotriple on a complete category. Let G^2 ===> G ---> G' be a coequalizer. Then we can find canonical (perhaps unique) \epsilon': G' ---> Id and \delta': G' ---> G'^2 such that (G',\epsilon',\delta') is a new cotriple on the category and such that G ---> G' is a map of cotriples. It seems reasonable to call this the derived cotriple. This process can be repeated, apparently forever, using colimits at limit ordinals. If it ever stablizes, the resultant cotriple will be idempotent and vice versa. Does any know whether this construction has been studied before? Michael -- The United States has the best congress money can buy. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]