From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2976 Path: news.gmane.org!not-for-mail From: "Hans-E. Porst" Newsgroups: gmane.science.mathematics.categories Subject: Re: Terminology re fibrations and opfibrations of categories Date: Mon, 2 Jan 2006 17:20:57 +0100 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 (Apple Message framework v746.2) Content-Type: text/plain; charset=US-ASCII; delsp=yes; format=flowed Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241019017 6701 80.91.229.2 (29 Apr 2009 15:30:17 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:30:17 +0000 (UTC) To: categories@mta.ca, Original-X-From: rrosebru@mta.ca Tue Jan 3 09:39:36 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 03 Jan 2006 09:39:36 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1EtmHs-00059p-9K for categories-list@mta.ca; Tue, 03 Jan 2006 09:33:16 -0400 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 2 Original-Lines: 42 Xref: news.gmane.org gmane.science.mathematics.categories:2976 Archived-At: Note that the suggestion below is standard terminology since about 30 years. See also Adamek, Herrlich, Strecker: Abstract and concrete categories; Wiley 1990 (also available at http://katmat.math.uni-bremen.de) H.-E. Porst Am 26.12.2005 um 22:57 schrieb Eduardo Dubuc: > I am just writing a paper with Luis Espannol where we need to > develop (the > basic part of the theory of cartesian and cocartesian arrows) for > families > > we use the following terminology: > > consider a functor U: C ---> S, then: > > 1) a family in C Z _i ---> X > > over R_i ---> S is FINAL iff: > > given S ---> T = UY such that there exists Z_i --->Y over > R_i ---> S ---> T (that is, R_i ---> S ---> T lifts), then there > exists a > unique X ---> Y over S ---> T (that is, S ---> T lifts). > > For topological spaces this is the usual Bourbaki notion of final > topology. > > When U is not understood, we call this "U-FINAL" -- Hans-E. Porst porst@uni-bremen.de Bremen, Germany Fax: +49-421-75643