From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/1752 Path: news.gmane.org!not-for-mail From: Michael Barr Newsgroups: gmane.science.mathematics.categories Subject: Re: Query about Ab[C] Date: Thu, 14 Dec 2000 12:39:57 -0500 (EST) Message-ID: References: <200012140419.eBE4JSF19580@transbay.net> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: ger.gmane.org 1241018069 32742 80.91.229.2 (29 Apr 2009 15:14:29 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:14:29 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Thu Dec 14 16:19:01 2000 -0400 Return-Path: Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id eBEJRRa11515 for categories-list; Thu, 14 Dec 2000 15:27:27 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Authentication-Warning: triples.math.mcgill.ca: barr owned process doing -bs X-Sender: barr@triples.math.mcgill.ca In-Reply-To: <200012140419.eBE4JSF19580@transbay.net> Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 25 Original-Lines: 19 Xref: news.gmane.org gmane.science.mathematics.categories:1752 Archived-At: I suspect that it is too much to hope for a characterization. But it is sufficient that either C or C^op be exact. For C to be exact, it is required that it have finite limits, coequalizers of equivalence relations, that regular epis be stable under pullback and that every equivalence relation is the kernel pair of its coequalizer. On Wed, 13 Dec 2000, Bill Rowan wrote: > > Hi all, > > Ab[C] is just my notation for the category of abelian group objects in > the category C. I was wondering if there is a simple characterization of > those categories C for which Ab[C] is abelian. > > Bill Rowan >