From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/7284 Path: news.gmane.org!not-for-mail From: "Prof. Peter Johnstone" Newsgroups: gmane.science.mathematics.categories Subject: Re: Derived cotriples Date: Tue, 22 May 2012 17:34:25 +0100 (BST) Message-ID: References: Reply-To: "Prof. Peter Johnstone" NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed X-Trace: dough.gmane.org 1337707891 7250 80.91.229.3 (22 May 2012 17:31:31 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Tue, 22 May 2012 17:31:31 +0000 (UTC) Cc: Categories list To: Michael Barr Original-X-From: majordomo@mlist.mta.ca Tue May 22 19:31:30 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 1SWsvh-0006BQ-0R for gsmc-categories@m.gmane.org; Tue, 22 May 2012 19:31:29 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:43103) by smtpx.mta.ca with esmtp (Exim 4.77) (envelope-from ) id 1SWsuk-0000b9-PJ; Tue, 22 May 2012 14:30:30 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1SWsul-0006sV-EU for categories-list@mlist.mta.ca; Tue, 22 May 2012 14:30:31 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:7284 Archived-At: The dual construction was studied by Sabah Fakir in "Monade idempotente associee a une monade", C.R. Acad. Sci. Paris 270 (1970), A99-101. Peter Johnstone On Mon, 21 May 2012, Michael Barr wrote: > 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 > > [For admin and other information see: http://www.mta.ca/~cat-dist/ ]