From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5304 Path: news.gmane.org!not-for-mail From: Thomas Streicher Newsgroups: gmane.science.mathematics.categories Subject: Re: Question on adjoints Date: Mon, 30 Nov 2009 12:34:46 +0100 Message-ID: References: Reply-To: Thomas Streicher NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii X-Trace: ger.gmane.org 1259589012 27688 80.91.229.12 (30 Nov 2009 13:50:12 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Mon, 30 Nov 2009 13:50:12 +0000 (UTC) To: claudio pisani , categories@mta.ca Original-X-From: categories@mta.ca Mon Nov 30 14:50:05 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 1NF6df-0002Cz-JZ for gsmc-categories@m.gmane.org; Mon, 30 Nov 2009 14:50:03 +0100 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1NF61q-0006IY-7b for categories-list@mta.ca; Mon, 30 Nov 2009 09:10:58 -0400 Content-Disposition: inline Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5304 Archived-At: Dear Claudio, > If F is left adjoint to G : D --> C and there is a natural isomorphism > FG --> 1_D (not necessarily the counit), then G is full and faithful. A proof of the (dual) claim you find as the proof of Lemma 8.1 of my course on basic category theory www.mathematik.tu-darmstadt.de/~streicher/CTCL.pdf.gz on p.45. Thomas [For admin and other information see: http://www.mta.ca/~cat-dist/ ]