From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4607 Path: news.gmane.org!not-for-mail From: Andree Ehresmann Newsgroups: gmane.science.mathematics.categories Subject: Re: Bourbaki and Categories Date: Thu, 18 Sep 2008 23:52:47 +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 1241020054 14027 80.91.229.2 (29 Apr 2009 15:47:34 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:47:34 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Fri Sep 19 13:28:10 2008 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 19 Sep 2008 13:28:10 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1Kgij4-0003pt-9X for categories-list@mta.ca; Fri, 19 Sep 2008 13:20:58 -0300 Content-Disposition: inline Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 77 Original-Lines: 49 Xref: news.gmane.org gmane.science.mathematics.categories:4607 Archived-At: George Janedlize writes > Could you please explain this better... > the Bourbaki group simply did not see the importance of category theory... > However, there were three great category-theorists in that group... > I have never heard of any joint work of Charles Ehresmann with any =20 > of the two others, Eilenberg and Grothendieck... ...the relation =20 > between Bourbaki Tractate and category theory should have been =20 > determined by their separate or joint influence and therefore also =20 > by their communication with each other (if any). I'll try to explain why there is no contradiction. 1. Charles only participated actively to the Bourbaki group from 1935 =20 to the mid forties, at a time he did not know category theory. In 1935 =20 he had written a first version for the volume "Theorie des ensembles" =20 where he introduced the notions of local structures and associated =20 pseudogroups of transformations (not so far from groupoids!), but this =20 version was not accepted and he did not like the final version =20 published much later. After the war, he only participated irregularly =20 because he felt that he was no more able to make himself heard, the =20 decisions being taken by "those who spoke the more loudly" (as he said =20 to me). 2. Around 1950 it was decided that active participation ended at 45 =20 (the age Charles had then), lessening the influence of those =20 (Eilenberg, Cartan, Chevalley and Dieudonne) who could have stressed =20 the importance of categories. I don't know exactly when Grothendieck =20 became a member, but it was much later, and I think he did not remain =20 for long. Later on, disdain for category theory had developed in =20 France... 3. As for the communication between Charles and the other =20 category-theorists, he had no contact with Grothendieck who was much =20 younger. He was friendly with Eilenberg but did not see him often. =20 Before the war he lived in Paris and regularly met Henri Cartan, =20 Dieudonne, and more specially, Chevalley (both had regular exchanges =20 with the philosophers Cavailles and Lautman). But their communication =20 almost ceased after the war when he developed all his activity in =20 Strasbourg (up to 1955) and was out of France for a long part of the =20 year. Anyway, before our joint work (from the mid sixties up to his =20 death), Charles worked essentially alone and published no joint work =20 at all, except 6 Notes on Topology or Geometry with some of his =20 students. When he began to specialize in category theory in the =20 sixties, it was not well understood by other French mathematicians, =20 and his influence dwindled up to a real opposition in the seventies. Andree