From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2950 Path: news.gmane.org!not-for-mail From: Eduardo Dubuc Newsgroups: gmane.science.mathematics.categories Subject: Re: Name for a concept Date: Wed, 7 Dec 2005 16:15:43 -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 1241019002 6500 80.91.229.2 (29 Apr 2009 15:30:02 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:30:02 +0000 (UTC) To: categories@mta.ca (Categories) Original-X-From: rrosebru@mta.ca Fri Dec 9 09:34:45 2005 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 09 Dec 2005 09:34:45 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1EkiEh-0003og-At for categories-list@mta.ca; Fri, 09 Dec 2005 09:24:31 -0400 In-Reply-To: from "jean benabou" at Dec 06, 2005 11:12:54 AM X-Mailer: ELM [version 2.5 PL2] Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 25 Original-Lines: 31 Xref: news.gmane.org gmane.science.mathematics.categories:2950 Archived-At: Jean Benabou wrote: > > (2)- In most cases the canonical map being epic is not what one really > wants. Of course Joyal assumes the category where the maps live to be a > pre-topos, then it's enough, otherwise one cannot "compose" such > squares. Do we have to rename the squares where the canonical map is a > universal epi, or those where its a universal regular epi? > very good point i suggest, since we can live with epics, strict(=regular) epis, universal such, etc etc, we should have: quasi-pullback strict(=regular) quasi pullback universal quasi-pullback of course, the useful concept being: "strict universal quasi-pullback" e.d.