From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3587 Path: news.gmane.org!not-for-mail From: Toby Bartels Newsgroups: gmane.science.mathematics.categories Subject: Re: Exactness without pullbacks Date: Fri, 19 Jan 2007 08:33:20 -0800 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii X-Trace: ger.gmane.org 1241019393 9365 80.91.229.2 (29 Apr 2009 15:36:33 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:36:33 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Fri Jan 19 19:42:59 2007 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 19 Jan 2007 19:42:59 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1H83FI-00026G-Dc for categories-list@mta.ca; Fri, 19 Jan 2007 19:34:08 -0400 Content-Disposition: inline Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 80 Original-Lines: 22 Xref: news.gmane.org gmane.science.mathematics.categories:3587 Archived-At: Michael Barr wrote: >Toby Bartels wrote: >>Has anybody considered (and are there any references with standard results) >>categories that do *not* have *all* pullbacks >>but nevertheless have some nice exactness properties? >My recollection is that in the original definition only pullbacks of >regular epis as well as kernel pairs were assumed to exist. By "the original definition", you mean the definitions here?: Michael Barr, Exact categories, in Exact Categories and Categories of Sheaves, Lecture Notes in Mathematics 236, Springer-Verlag, 1971. I've never read this, since you-exact categories are now standard, but I guess that one should always go back to the source! --Toby