From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2935 Path: news.gmane.org!not-for-mail From: jean benabou Newsgroups: gmane.science.mathematics.categories Subject: Re: Name for a concept Date: Tue, 6 Dec 2005 11:12:54 +0100 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 (Apple Message framework v543) Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1241018992 6419 80.91.229.2 (29 Apr 2009 15:29:52 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:29:52 +0000 (UTC) To: Categories Original-X-From: rrosebru@mta.ca Tue Dec 6 19:53:52 2005 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 06 Dec 2005 19:53:52 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1EjmZR-0000Zp-9K for categories-list@mta.ca; Tue, 06 Dec 2005 19:50:05 -0400 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 10 Original-Lines: 55 Xref: news.gmane.org gmane.science.mathematics.categories:2935 Archived-At: Continuation of namings (1) - Is there a standard name for the squares where the canonical map=20= is monic , i.e. the pair of maps A --->B and A --->C is jointly =20 monic. I propose semi-pullback (2)- In most cases the canonical map being epic is not what one really=20= wants. Of course Joyal assumes the category where the maps live to be a=20= pre-topos, then it's enough, otherwise one cannot "compose" such=20 squares. Do we have to rename the squares where the canonical map is a=20= universal epi, or those where its a universal regular epi? In view of (1), one would like to say that a square is a pullback iff=20 it is both a quasi and semi pullback D=E9but du message r=E9exp=E9di=E9 : > De: Eduardo Dubuc > Date: Lun 5 d=E9c 2005 17:16:13 Europe/Paris > =C0: categories@mta.ca (Categories list) > Objet: categories: Re: Name for a concept > >> >> 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=20= > 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. > > > > >