From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4592 Path: news.gmane.org!not-for-mail From: Andre.Rodin@ens.fr Newsgroups: gmane.science.mathematics.categories Subject: Re: Bourbaki and Categories Date: Tue, 16 Sep 2008 15:09:56 +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 1241020045 13969 80.91.229.2 (29 Apr 2009 15:47:25 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:47:25 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Tue Sep 16 21:22:38 2008 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 16 Sep 2008 21:22:38 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1Kfkir-0004Vb-Nh for categories-list@mta.ca; Tue, 16 Sep 2008 21:16:45 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 62 Original-Lines: 37 Xref: news.gmane.org gmane.science.mathematics.categories:4592 Archived-At: Of course, you are right about a point, I missed it! I must confess I did= n't think about this example in precise terms. My claim is that sketch theory doesn't fit the structuralist (Bourbaki-Hilbertian) pattern. It hardly precisely fits the ancient Euclidean pattern either but there is a sugges= tive analogy, which concerns the idea that certain basic objects like point, l= ine and circle *generate* the rest. A further claim is this: a specific reason *why* sketch theory doesn't fi= t the structuralist pattern is that in sketch theory (like in CT in general) isomorphisms don't have the same distinguished status. andrei >I don't know what to say about the suggestion that a circle and a line >make a sketch of which Euclidean plane geometry is a model. I would thi= nk >you would need a point too, since intersections are crucial. Maybe >complex projective geometry since then two lines intersect in one point >(unless they coincide), a line and a circle in two (unless they are >tangent or equal) and every pair of circles in four (ditto). Maybe the >exceptions could be handled in some sketch. At any rate, it wold e >interesting to try to sketch this in detail. At any rate, I never thoug= ht >about this before. >Michael