From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2937 Path: news.gmane.org!not-for-mail From: "Ronald Brown" Newsgroups: gmane.science.mathematics.categories Subject: Terminology question wrt fibrations of categories. Date: Tue, 6 Dec 2005 18:06:40 -0000 Message-ID: <006b01c5fa8f$e2502e20$61f94c51@brown1> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain;charset="iso-8859-1" Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241018993 6426 80.91.229.2 (29 Apr 2009 15:29:53 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:29:53 +0000 (UTC) To: Original-X-From: rrosebru@mta.ca Tue Dec 6 19:54:38 2005 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 06 Dec 2005 19:54:38 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1Ejmd7-0000oS-1S for categories-list@mta.ca; Tue, 06 Dec 2005 19:53:53 -0400 X-ME-UUID: 20051206181221664.A214D1C00142@mwinf3002.me.freeserve.com Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 12 Original-Lines: 45 Xref: news.gmane.org gmane.science.mathematics.categories:2937 Archived-At: I am writing about matters to do with computation of colimits of a category X in terms of colimits of a category B when there is a bifibration P: X --> B. Terminology already in use is P is cartesian P is cocartesian a lifting of u in B to \phi in X may be cartesian, cocartesian on the other hand Paul Taylor, following Peter Johnstone, I understand, uses \phi is prone, supine, instead of cartesian, cocartesian For the cofibration (?opfibration?) Ob: Groupoids --> Sets, Philip Higgins (1971) and I (1968) have previously used `universal' for cocartesian. In this situation, I would be happier with say 0-final instead of universal. But `supine' does not ring a bell with me, and carries a pejorative tone. Maybe for the general situation P: X --> B we could use P-initial, P-final morphism in X for cartesian, cocartesian morphism which would at least carry some intuition as to the meaning. Comments? I need to make a decision soon for the revision of my old topology book. Not much will be changed, and I might leave the old terminology and refer to more modern uses. However for the book on Nonabelian algebraic topology, I really do need to use modern terminologym, whatever that is, so it would be best to be consistent. I have been looking at Thomas Streicher's notes on fibrations, and at Paul Taylor's Practical Foundations. For my interest, see slides of a recent seminar at Oxford www.bangor.ac.uk/r.brown/oxford2811105.pdf called `Induced constructions and their computation'. Ronnie Brown www.bangor.ac.uk/r.brown