From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4579 Path: news.gmane.org!not-for-mail From: Andree Ehresmann Newsgroups: gmane.science.mathematics.categories Subject: Re: Bourbaki and Categories Date: Mon, 15 Sep 2008 09:58:33 +0200 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain;charset=ISO-8859-1;DelSp="Yes";format="flowed" Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1241020038 13919 80.91.229.2 (29 Apr 2009 15:47:18 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:47:18 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Mon Sep 15 08:37:29 2008 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 15 Sep 2008 08:37:29 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1KfCJP-0001pm-V4 for categories-list@mta.ca; Mon, 15 Sep 2008 08:32:12 -0300 Content-Disposition: inline Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 49 Original-Lines: 52 Xref: news.gmane.org gmane.science.mathematics.categories:4579 Archived-At: Dear all, I would add some information on Bourbaki/categories/France. Charles Ehresmann has been an active member of Bourbaki from 1936 up =20 to the end of the war, when he began to no more regularly participate =20 and wanted to resign (it was not accepted but replaced by an age limit =20 for active participation). What Andre says: >Bourbaki had essentially two options: rewrite the whole treaty using > categories, or just introduce them in the book on homological algebra, >The second option won, essentially because of the enormity of the task > of rewriting everything. is more easily understood if we take into account that communication =20 between France and the USA were entirely broken during the war, so =20 that mathematical ideas could not circulate and categories were only =20 heard of after the war, at a time where the more general parts of the =20 treatise were written or at least prepared (the successive versions =20 process was very slow). Charles said to me that he did not recall to have read Eilenberg =20 & Mac Lane's paper before the fifties, or at least not seen its =20 interest. Naturally he had sooner made a large use of groupoids in is =20 foundation of differential geometry, and he had even defined the =20 general "composition of jets" and given its properties, but without =20 linking it to the notion of a category. He exposed it in a course in =20 Rio de Janeiro in the early fifties, and one of his students =20 (Constantino de Barros who later came to Paris to prepare a thesis =20 with him) suggested that there was a connection with categories. =20 Charles' first large use of categories is in his seminal paper =20 "Gattungen von lokalen Strukturen" (1957, reprinted in "Charles =20 Ehresmann: Oeuvres completes et commentees" Part I). It is around this date that the word "category" began to circulate =20 in France. In 1957, Choquet (with whom I prepared my thesis) =20 suggested that I learnt more on the notion of category which he did =20 not know but seemed to have many applications (it was the reason for =20 which I first went to see Charles!). It should be noted that Choquet =20 was less conservative than many French mathematicians. In 1959, he =20 defended the development of probabilities by inviting Loomis to give a =20 course (I remember Henri Cartan saying then to Paul-Andre Meyer that =20 he should not study this domain for it would be bad for his career!). =20 And later on, he defended Logic which was very badly considered. A final remark: the "disdain" for categories (not to be confused =20 with 'ignorance') came only later on, since Charles was given the =20 "Prix Petit d'Ormoy" by the French Academy in 1965, essentially for =20 his recent work on categories... Andree C. Ehresmann