From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4580 Path: news.gmane.org!not-for-mail From: Michael Barr Newsgroups: gmane.science.mathematics.categories Subject: Re: Bourbaki and Categories Date: Mon, 15 Sep 2008 07:59:53 -0400 (EDT) Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed X-Trace: ger.gmane.org 1241020039 13922 80.91.229.2 (29 Apr 2009 15:47:19 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:47:19 +0000 (UTC) Cc: categories@mta.ca To: Andre.Rodin@ens.fr Original-X-From: rrosebru@mta.ca Mon Sep 15 19:20:38 2008 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 15 Sep 2008 19:20:38 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1KfMJQ-0003Qk-Ek for categories-list@mta.ca; Mon, 15 Sep 2008 19:12:52 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 50 Original-Lines: 45 Xref: news.gmane.org gmane.science.mathematics.categories:4580 Archived-At: I don't know about this. I took several courses in the late 1950s that seem to have been influenced by the structuralist ideas (certainly categories weren't mentioned; I never heard the word until Dave Harrison arrived in 1959) and each of them started by defining an appropriate notion of "admissible map". I do not recall any special point being made of isomorphism and I think in general it was used for what we now call a bimorphism (1-1 and onto) even in cases, such as topological groups, when they were not isomorphisms. To be sure Bourbaki was not mentioned either, but this structuralist influence seemed strong. Michael On Mon, 15 Sep 2008, Andre.Rodin@ens.fr wrote: > > 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 isomorphism; > in the structuralist mathematics the notion of isomorphism is basic and the > notion of general morphism is derived (as in Bourbaki). In CT this is the > other way round: the notion of general morphism is basic while isos are defined > 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 reasons > is closely related to structuralist mathematics it is not, in my understanding, > a part of structuralist mathematics - at least not if one takes CT *seriously*, > i.e. as foundations. > > best, > andrei > > >