From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2925 Path: news.gmane.org!not-for-mail From: Michael Barr Newsgroups: gmane.science.mathematics.categories Subject: Name for a concept Date: Wed, 30 Nov 2005 20:48:52 -0500 (EST) Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: ger.gmane.org 1241018987 6381 80.91.229.2 (29 Apr 2009 15:29:47 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:29:47 +0000 (UTC) To: Categories list Original-X-From: rrosebru@mta.ca Thu Dec 1 16:03:20 2005 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 01 Dec 2005 16:03:20 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1EhuZG-0006rY-0o for categories-list@mta.ca; Thu, 01 Dec 2005 15:58:10 -0400 X-Authentication-Warning: triples.math.mcgill.ca: barr owned process doing -bs Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 70 Original-Lines: 21 Xref: news.gmane.org gmane.science.mathematics.categories:2925 Archived-At: Is there a standard name for a square A ----> B | | | | | | v v C ----> D in which the canonical map A ---> B x_D C is epic? I had always called it a weak pullback, but Peter Freyd claims that that phrase is reserved for the case that it satisfies the existence, but not necessarily the uniqueness of the definition of pullback. In fact, he claims it means that Hom(E,-) converts it to the kind of square I am talking about. What is interesting is that in an abelian category, it satisfies this condition iff it satisfies the dual condition iff the evident sequence A ---> B x C ---> D is exact. Putting a zero at the left end characterizes a genuine pullback and at the other end a pushout. Michael