From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4568 Path: news.gmane.org!not-for-mail From: "zoran skoda" Newsgroups: gmane.science.mathematics.categories Subject: Re: Bourbaki and Categories Date: Fri, 12 Sep 2008 17:57:00 +0200 Message-ID: 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 1241020033 13888 80.91.229.2 (29 Apr 2009 15:47:13 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:47:13 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Fri Sep 12 15:02:21 2008 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 12 Sep 2008 15:02:21 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1KeCt5-00055p-3h for categories-list@mta.ca; Fri, 12 Sep 2008 14:56:55 -0300 Content-Disposition: inline Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 38 Original-Lines: 37 Xref: news.gmane.org gmane.science.mathematics.categories:4568 Archived-At: > > sustainable in commutative algebra anymore, and the discord between > Grothendieck and Bourbaki may well have been rooted in this rejection. I can not recall where, but I read more than once more detailed descriptions on what Bourbaki did not accept from Grothendieck. The conservativeness of Bourbaki who did not accept the usage of category theory (not only "neglect") and non-acceptance of a very general approach of Grothendieck to the notion of "manifold" he envisioned for the future Bourbaki works were some of the main points of departure. The remark that as a proponent of "structures" Bourbaki had to include categories is anyway a bit lacking an argument. First of all, because of the size problems one can not take big categories on equal footing with, say groups, and considering only small categories would be strange and lacking most interesting examples. On the other hand, Grothendieck judged the lack stemming in conservativeness rather than in consistency of the structure-oriented style. Indeed, according to Dieudonne, Bourbaki felt comfortable only in including to the books already (meta)stable, "dead" mathematics and not the structures in the unstable "living" phase of development. This was the intended scope and self-conscious (according to Dieudonne) limitation of the work. One can accept this and still cry for an exception for so economic tool as the category theory (if taken in conservative and very basic sense), especially in the vision of the wish for generality, Bourbaki followed otherwise. Zoran Skoda