From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4577 Path: news.gmane.org!not-for-mail From: Andre.Rodin@ens.fr Newsgroups: gmane.science.mathematics.categories Subject: Re: Bourbaki and Categories Date: Mon, 15 Sep 2008 06:55:55 +0200 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 1241020037 13914 80.91.229.2 (29 Apr 2009 15:47:17 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:47:17 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Mon Sep 15 08:34:23 2008 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 15 Sep 2008 08:34:23 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1KfCGg-0001Zw-9J for categories-list@mta.ca; Mon, 15 Sep 2008 08:29:22 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 47 Original-Lines: 35 Xref: news.gmane.org gmane.science.mathematics.categories:4577 Archived-At: zoran skoda wrote: >The remark that as a proponent of "structures" >Bourbaki had to include categories is anyway a bit lacking an argument. I think that as a 'proponent of "structures"' Bourbaki had NOT include categories - and not only because of the size problem. A more fundamental reason seems me to be this. Structures are things determined up to isomor= phism; in the structuralist mathematics the notion of isomorphism is basic and t= he notion of general morphism is derived (as in Bourbaki). In CT this is th= e other way round: the notion of general morphism is basic while isos are d= efined through a specific property (of reversibility). This is why the inclusion of CT would require a revision of fundamentals = of Bourbaki's structuralist thinking. Although CT for obvious historical rea= sons is closely related to structuralist mathematics it is not, in my understa= nding, a part of structuralist mathematics - at least not if one takes CT *serio= usly*, i.e. as foundations. best, andrei