From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2363 Path: news.gmane.org!not-for-mail From: Michael Barr Newsgroups: gmane.science.mathematics.categories Subject: Re: first isomorphism theorem Date: Thu, 19 Jun 2003 08:52:03 -0400 (EDT) Message-ID: References: <20030619075917.GL13356@math-cl-n01.ucr.edu> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: ger.gmane.org 1241018604 3779 80.91.229.2 (29 Apr 2009 15:23:24 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:23:24 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Thu Jun 19 10:48:58 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 19 Jun 2003 10:48:58 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 19SzlA-0004gW-00 for categories-list@mta.ca; Thu, 19 Jun 2003 10:47:28 -0300 In-Reply-To: <20030619075917.GL13356@math-cl-n01.ucr.edu> Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 54 Original-Lines: 22 Xref: news.gmane.org gmane.science.mathematics.categories:2363 Archived-At: Let me just add to this reply (which is certainly one valid answer to the question) the comment that I sent privately to the questioner that exactness is sufficient for the FIT to be meaningful. On Thu, 19 Jun 2003, Toby Bartels wrote: > Andrei Prokopiw wrote: > > >Is there a suitable first isomorphism theorem in category theoretic language? > >One barrier for me seems to be the correct notion of an image. What seems best > >right now would be that given f:X->Y, ker(coker f) = coker ( ker f). Here the > >left hand side would represent im f, and the right hand side X/kerf. If this > >is the right notion, what are the necessary conditions on the category for it > >to hold? > > I'm not really answering your question, instead addressing the "if". > ...