From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/7299 Path: news.gmane.org!not-for-mail From: "Eduardo J. Dubuc" Newsgroups: gmane.science.mathematics.categories Subject: Re: Bourbaki & category theory Date: Wed, 23 May 2012 21:03:55 -0300 Message-ID: References: Reply-To: "Eduardo J. Dubuc" NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1337908569 27758 80.91.229.3 (25 May 2012 01:16:09 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Fri, 25 May 2012 01:16:09 +0000 (UTC) To: "Eduardo J. Dubuc" , "categories@mta.ca" Original-X-From: majordomo@mlist.mta.ca Fri May 25 03:16:06 2012 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.80]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1SXj8P-00006V-GN for gsmc-categories@m.gmane.org; Fri, 25 May 2012 03:16:05 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:44090) by smtpx.mta.ca with esmtp (Exim 4.77) (envelope-from ) id 1SXj7d-0006Kd-L7; Thu, 24 May 2012 22:15:17 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1SXj7f-0000Xv-QI for categories-list@mlist.mta.ca; Thu, 24 May 2012 22:15:19 -0300 User-Agent: Mozilla/5.0 (Macintosh; Intel Mac OS X 10.7; rv:12.0) Gecko/20120428 Thunderbird/12.0.1 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:7299 Archived-At: On 22/05/12 14:49, Eduardo J. Dubuc wrote: > The reason why category theory "is what it is" is that > > it is the language that allows to define the notion of universal > property in its right generality. > > The notion of universal property first appears in Bourbaki, which > decided not to use the language of categories to formulate it, on spite > of the advice of Grothendieck. > Concerning the remark "on spite of the advice of Grothendieck" (that I concluded following some readings I do not remember where, and=20 that if I remember correctly, Grothendieck wanted to rewrite the whole=20 project (before it was published) using Category Theory, and presented a=20 proposal that after some consideration was turned off by Bourbaki) I received a private mail that can be of interest to many and that I=20 copy and paste below: =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D Pierre Cartier, Chritian Houzel, Andrej Rodin and Ralf Kr=F6mer wrote=20 about that issue. You will find the source material, i.e. the early Bourbaki archives=20 (1934-1954), which show various early attempts at defining "structure",=20 online at http://mathdoc.emath.fr/archives-bourbaki/ A bibliography of sources on Bourbaki is at=20 http://poincare.univ-nancy2.fr/Actu/?contentId=3D9473 One may not confuse any edition of the first volume of the Elements with=20 Bourbaki relatively evolving thoughts on this matter. There is a lot to be learnt from reading the sources. Please notice that=20 I replied to you personally and not to the whole list. Be kind to a shy=20 person. Best regards, LB =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D e.d. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]