From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/778 Path: news.gmane.org!not-for-mail From: John R Isbell Newsgroups: gmane.science.mathematics.categories Subject: Re: co- Date: Fri, 3 Jul 1998 15:37:48 -0400 (EDT) Message-ID: References: <199807031139.MAA09161@ruby.dcs.qmw.ac.uk> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: ger.gmane.org 1241017175 27337 80.91.229.2 (29 Apr 2009 14:59:35 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 14:59:35 +0000 (UTC) Cc: categories@mta.ca To: Paul Taylor Original-X-From: cat-dist Sat Jul 4 10:35:48 1998 Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id JAA16463 for categories-list; Sat, 4 Jul 1998 09:48:32 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f In-Reply-To: <199807031139.MAA09161@ruby.dcs.qmw.ac.uk> Original-Sender: cat-dist@mta.ca Precedence: bulk Original-Lines: 34 Xref: news.gmane.org gmane.science.mathematics.categories:778 Archived-At: On Fri, 3 Jul 1998, Paul Taylor wrote: > What are the origins of the co- prefix, as in coproduct, coequaliser ..., > and who established their use? > > Has anybody ever thought through and written down any guidelines on > which of a pair of dual concepts is co-? > > Who is reponsible for dropping this prefix from cofinal? > (A mistake, IMHO). > > Paul > Fragments: (1) Origin, I don't know, but surely cohomology is where it started. The term was used very early, 1937 I think, by Norman Steenrod in a paper mainly on universal coefficient theorems. (2) The idea of putting forward some such guidelines was seriously discussed at La Jolla 1965, and I should say that Sammy Eilenberg killed it single-handed. His main point was that anything we Americans might propose would be absolutely unacceptable in Paris. Verdier was the only Frenchman present; he was well thought of but very young. (1 bis) Of course not covariant-contravariant. (3) I'm not sure what "A mistake IMHO" means. Of course, the "co" in cofinal is genetically "con" of congress, concatenation. I don't have nice illustrations of antecedents of co-homology but it is not 'together' like in congress & concatenation. But it is dropped in categorical contexts because it is a distracting "co". John Isbell