From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5226 Path: news.gmane.org!not-for-mail From: Ross Street Newsgroups: gmane.science.mathematics.categories Subject: Re: Question on exact sequence Date: Wed, 11 Nov 2009 07:14:05 +1100 Message-ID: Reply-To: Ross Street NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 (Apple Message framework v936) Content-Type: text/plain; charset=US-ASCII; format=flowed; delsp=yes Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1257953371 28696 80.91.229.12 (11 Nov 2009 15:29:31 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 11 Nov 2009 15:29:31 +0000 (UTC) To: Michael Barr , Original-X-From: categories@mta.ca Wed Nov 11 16:29:24 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 1N8F8O-00074D-DG for gsmc-categories@m.gmane.org; Wed, 11 Nov 2009 16:29:24 +0100 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1N8EcR-00059c-Ht for categories-list@mta.ca; Wed, 11 Nov 2009 10:56:23 -0400 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5226 Archived-At: Dear Michael Murray Adelman used to use a generalized homology where the complex need not have consecutive composites zero. For any pair of maps u : A-->B and v:B-->C in an abelian category, there is a homology at B: take the image of the canonical map ker(v)-- >coker(u). Notice that the rows of the diagram in the snake lemma are exact and so have zero homology. The rows of your diagram (below) also have zero homology in the middle. Ross On 10/11/2009, at 9:57 AM, Michael Barr wrote: > > 1 f > A ----> A ----> B > | | | > | | | > |f |g |h > | | | > v v v > B ----> C ----> C > h 1 [For admin and other information see: http://www.mta.ca/~cat-dist/ ]