From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4600 Path: news.gmane.org!not-for-mail From: Andre Joyal Newsgroups: gmane.science.mathematics.categories Subject: Re: Bourbaki and Categories Date: Wed, 17 Sep 2008 13:13:21 -0400 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1241020050 13995 80.91.229.2 (29 Apr 2009 15:47:30 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:47:30 +0000 (UTC) To: "George Janelidze" , Original-X-From: rrosebru@mta.ca Thu Sep 18 10:41:52 2008 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 18 Sep 2008 10:41:52 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1KgJfh-0006Sb-Hi for categories-list@mta.ca; Thu, 18 Sep 2008 10:35:49 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 70 Original-Lines: 135 Xref: news.gmane.org gmane.science.mathematics.categories:4600 Archived-At: Dear George, I thank you for your message. You wrote: >I insist that Bourbaki group simply did >not see the importance of category theory. It is difficult to know. The Boubaki group had shielded itself in secrecy, like a free mason cell.=20 You are surely aware of the interview of Pierre Cartier=20 in the Mathematical Intelligencer No1 1998.=20 Everyone interested in the history of Bourbaki should read it. http://ega-math.narod.ru/Bbaki/Cartier.htm Let me stress a few passages:=20 >The fourth generation was more or less a group of students of = Grothendieck. But at that time Grothendieck had already left Bourbaki.=20 >He belonged to Bourbaki for about ten years but he left in anger. The = personalities were very strong at the time.=20 >I remember there were clashes very often. There was also, as usual, a = fight of generations, like in any family.=20 >I think a small group like that repeated more or less the psychological = features of a family.=20 >So we had clashes between generations, clashes between brothers, and so = on.=20 >But they did not distract Bourbaki from his main goal, even though they = were quite brutal occasionally.=20 >At least the goal was clear. There were a few people who could not take = the burden of this psychological style,=20 >for instance Grothendieck left and also Lang dropped out. > It is amazing that category theory was more or less the brainchild of = Bourbaki. The two founders were Eilenberg and MacLane.=20 > MacLane was never a member of Bourbaki, but Eilenberg was, and MacLane = was close in spirit. The first textbook on homo-logical=20 >algebra was Cartan-Eilenberg, which was published when both were very = active in Bourbaki. Let us also mention Grothendieck, who=20 >developed categories to a very large extent. I have been using = categories in a conscious or unconscious way in much of my work,=20 >and so had most of the Bourbaki members. But because the way of = thinking was too dogmatic, or at least the presentation in the=20 >books was too dogmatic, Bourbaki could not accommodate a change of = emphasis, once the publication process was started. >In accordance with Hilbert's views, set theory was thought by Bourbaki = to provide that badly needed general framework. If you need=20 > some logical foundations, categories are a more flexible tool than set = theory. The point is that categories offer both a general=20 > philosophical foundation=97that is the encyclopedic, or taxonomic = part=97and a very efficient mathematical tool, to be used in=20 >mathematical situations. That set theory and structures are, by = contrast, more rigid can be seen by reading the final chapter in=20 >Bourbaki set theory, with a monstrous endeavor to formulate categories = without categories. The interview ends with the following passage. The bold faces are from me. >When I began in mathematics the main task of a mathematician was to = bring order and make a synthesis of existing material, to create=20 >what Thomas Kuhn called normal science. Mathematics, in the forties and = fifties, was undergoing what Kuhn calls a solidification period.=20 >In a given science there are times when you have to take all the = existing material and create a unified terminology, unified standards,=20 >and train people in a unified style. The purpose of mathematics, in the = fifties and sixties, was that, to create a new era of normal science.=20 >Now we are again at the beginning of a new revolution. Mathematics is = undergoing major changes. We don't know exactly where it will go. > It is not yet time to make a synthesis of all these things=97MAYBE IN = TWENTY OR THIRTY CENTURY IT WILL BE TIME FOR A NEW BOURBAKI. >I consider myself very fortunate to have had two lives, a life of = normal science and a life of scientific revolution. Is it the time for a new Bourbaki? Best regards,=20 Andr=E9 -------- Message d'origine-------- De: cat-dist@mta.ca de la part de George Janelidze Date: lun. 15/09/2008 20:03 =C0: categories@mta.ca Objet : categories: Re: Bourbaki and Categories =20 Dear Andree, Could you please explain this better?: The only Bourbaki member I new personally was Sammy Eilenberg. As many = of us, I knew him very well and I would say that he was more skeptical = about the Bourbaki Tractate then one can conclude from Andre's message. Having = in mind not just this but the content of Bourbaki's "Homological algebra" = and what we see today from the followers of that Bourbaki group, I protest against Andre's "two options" and I insist that Bourbaki group simply = did not see the importance of category theory (in spite of being brilliant mathematicians, as I said in my previous message). I hope Andre will = forgive me and even agree with me. However, there were three great category-theorists in that group (plus = there is this mysterious story about Chevalley's book of category theory lost = in the train), and "did not see" cannot be said about them of course. On = the other hand I have never heard of any joint work of Charles Ehresmann = with any of the two others, Eilenberg and Grothendieck (and nothing jointly = from them). I think apart from the time issues you describe, the relationship between Bourbaki Tractate and category theory should have been = determined by their separate or joint influence and therefore also by their = communication with each other (if any). Is this true, and could you please give details? Respectfully, and with best regards- George