From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6527 Path: news.gmane.org!not-for-mail From: "Fred E.J. Linton" Newsgroups: gmane.science.mathematics.categories Subject: Re: theorem about ends Date: Sun, 06 Feb 2011 22:06:32 -0500 Message-ID: Reply-To: "Fred E.J. Linton" NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1297100493 803 80.91.229.12 (7 Feb 2011 17:41:33 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Mon, 7 Feb 2011 17:41:33 +0000 (UTC) To: "categories" Original-X-From: majordomo@mlist.mta.ca Mon Feb 07 18:41:29 2011 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.114]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1PmV5Y-0004Yw-Kv for gsmc-categories@m.gmane.org; Mon, 07 Feb 2011 18:41:24 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:32852) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1PmV4t-0001we-Tk; Mon, 07 Feb 2011 13:40:43 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1PmV4p-0004OE-Tf for categories-list@mlist.mta.ca; Mon, 07 Feb 2011 13:40:40 -0400 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6527 Archived-At: Paul Blain Levy asks: > Does the following result (which I learnt from Rasmus Mogelberg) > appear in the literature somewhere? > = > Given categories C and D, a functor P : C^op x D --> Set and an > adjunction F -| U : D --> C > = > the end over c in C of P(c,Fc) is (isomorphic to) the end over d in D > of P(Ud,d). For well over 40 years I've always thought of that as = the Beck/Lawvere vision of what an adjunction *is* :-) . Cheers, -- Fred [For admin and other information see: http://www.mta.ca/~cat-dist/ ]