From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/1746 Path: news.gmane.org!not-for-mail From: "Dr. P.T. Johnstone" Newsgroups: gmane.science.mathematics.categories Subject: Re: Terminology Date: Wed, 13 Dec 2000 11:10:32 +0000 (GMT) Message-ID: References: <3a35cdd73a39f901@amyris.wanadoo.fr> 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 1241018065 32720 80.91.229.2 (29 Apr 2009 15:14:25 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:14:25 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Wed Dec 13 09:21:14 2000 -0400 Return-Path: Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id eBDCg4q27816 for categories-list; Wed, 13 Dec 2000 08:42:04 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f In-Reply-To: <3a35cdd73a39f901@amyris.wanadoo.fr> (added by amyris.wanadoo.fr) from "Jean Benabou" at Dec 12, 2000 08:19:37 AM X-Mailer: ELM [version 2.5 PL2] Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 19 Original-Lines: 22 Xref: news.gmane.org gmane.science.mathematics.categories:1746 Archived-At: > I am confronted with problems of "contradictory terminology" which I would > like to solve and, since english is not my language, I need some > suggestions. > Let F: Y-----> X be a functor such that for every object x of X the comma > category (x,F) is connected.Such functors, although they are not defined in > all generality, are called "cofinal" in SGA 4 , and "initial" in Borceux's > handbook (Vol.1-'2.11-p.69) but none of these terms is satisfactory. > The "cofinal" name comes obviously from the vocabulary of ordered sets > which are special cases, but in category theory "co" is now associated with > dual notions. There was some discussion of this point on the categories mailing list a year or two back. I think there was general consensus that the "co" in "cofinal" was redundant, and that such functors should simply be called "final". This is the term used in Mac Lane's book (section IX 3, p.217) -- I believe Mac Lane was the first to shorten "cofinal" to "final". For some reason, Borceux chose to use the opposite convention regarding "initial" and "final" in his book (although, in Exercise 2.17.8 on page 94, he seems to have reverted to the same convention as Mac Lane). Peter Johnstone