From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2933 Path: news.gmane.org!not-for-mail From: Eduardo Dubuc Newsgroups: gmane.science.mathematics.categories Subject: Re: Name for a concept Date: Mon, 5 Dec 2005 13:16:13 -0300 (ART) Message-ID: References: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241018991 6412 80.91.229.2 (29 Apr 2009 15:29:51 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:29:51 +0000 (UTC) To: categories@mta.ca (Categories list) Original-X-From: rrosebru@mta.ca Mon Dec 5 16:07:06 2005 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 05 Dec 2005 16:07:06 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1EjMUc-0000cY-8W for categories-list@mta.ca; Mon, 05 Dec 2005 15:59:22 -0400 In-Reply-To: from "Michael Barr" at Nov 30, 2005 08:48:52 PM X-Mailer: ELM [version 2.5 PL2] X-Spam-Checker-Version: SpamAssassin 3.0.4 (2005-06-05) on mx1.mta.ca X-Spam-Level: X-Spam-Status: No, score=0.0 required=5.0 tests=none autolearn=disabled version=3.0.4 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 8 Original-Lines: 21 Xref: news.gmane.org gmane.science.mathematics.categories:2933 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? These are called "quasi-pullbacks" by Joyal, and they form a class of "open maps" in the category of squares. The pullbacks form the corresponding class of etal maps. These two classes are essential for the development of the theory (etal class and open class in the sense of Joyal). There are published articles by Joyal and Moerdijk on the subject.