From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6526 Path: news.gmane.org!not-for-mail From: Steve Lack Newsgroups: gmane.science.mathematics.categories Subject: Re: theorem about ends Date: Mon, 7 Feb 2011 14:00:16 +1100 Message-ID: References: Reply-To: Steve Lack NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 (Apple Message framework v1082) Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1297100472 658 80.91.229.12 (7 Feb 2011 17:41:12 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Mon, 7 Feb 2011 17:41:12 +0000 (UTC) Cc: categories list To: Paul Levy Original-X-From: majordomo@mlist.mta.ca Mon Feb 07 18:41:07 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 1PmV5F-0004IK-Te for gsmc-categories@m.gmane.org; Mon, 07 Feb 2011 18:41:06 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:32846) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1PmV4U-0001v2-58; Mon, 07 Feb 2011 13:40:18 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1PmV4N-0004Nd-07 for categories-list@mlist.mta.ca; Mon, 07 Feb 2011 13:40:11 -0400 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6526 Archived-At: Dear Paul, This is (a special case of) Lemma 2.1 in=20 G.M. Kelly & Stephen Lack, Finite-product-preserving functors, Kan = extensions, and strongly finitary 2-monads. Applied Categorical Structures 1:85-94, 1993. Steve. On 07/02/2011, at 11:25 AM, Paul Levy wrote: > Dear all, >=20 > Does the following result (which I learnt from Rasmus Mogelberg) > appear in the literature somewhere? >=20 >=20 > Given categories C and D, a functor P : C^op x D --> Set and an > adjunction F -| U : D --> C >=20 > the end over c in C of P(c,Fc) is (isomorphic to) the end over d in D > of P(Ud,d). >=20 >=20 > Paul >=20 >=20 > -- > Paul Blain Levy > School of Computer Science, University of Birmingham > +44 (0)121 414 4792 > http://www.cs.bham.ac.uk/~pbl >=20 >=20 >=20 >=20 >=20 >=20 >=20 >=20 >=20 >=20 >=20 > [For admin and other information see: http://www.mta.ca/~cat-dist/ ] [For admin and other information see: http://www.mta.ca/~cat-dist/ ]