From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/7304 Path: news.gmane.org!not-for-mail From: Charles Wells Newsgroups: gmane.science.mathematics.categories Subject: Re: The Idea of Structure as Data and Conditions Date: Sun, 27 May 2012 09:02:59 -0400 Message-ID: References: Reply-To: Charles Wells NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 X-Trace: dough.gmane.org 1338144924 28215 80.91.229.3 (27 May 2012 18:55:24 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Sun, 27 May 2012 18:55:24 +0000 (UTC) To: "Ellis D. Cooper" , catbb Original-X-From: majordomo@mlist.mta.ca Sun May 27 20:55:21 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 1SYica-00010M-Ij for gsmc-categories@m.gmane.org; Sun, 27 May 2012 20:55:20 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:44756) by smtpx.mta.ca with esmtp (Exim 4.77) (envelope-from ) id 1SYibY-0002Qt-Eu; Sun, 27 May 2012 15:54:16 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1SYibZ-0007mT-FR for categories-list@mlist.mta.ca; Sun, 27 May 2012 15:54:17 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:7304 Archived-At: Data and conditions constitute a presentation. The graph, diagrams, cones & cocones of a sketch are a presentation. This idea has not been superseded, not at all, but it has been completed (in two senses) by the concept of theory, which is the object generated by the presentation: The theory of a sketch, the classifiying topos, the algebraic theory in the sense of Lawvere, and so on. This object contains all the information about any model. That idea is in some way the other face of, or the complementary point of view about, data and conditions. Charles On Fri, May 25, 2012 at 6:09 PM, Ellis D. Cooper wrote: > In the 1952 document at > http://mathdoc.emath.fr/**archives-bourbaki/PDF/nbt_029.**pdfthe only > mathematician > "pr\'{e}sent" referenced by first name only is Sammy. > > I was permitted to audit a graduate course on category theory guided > by Sammy at Columbia University in the early 1960s. > I recall his insistence that mathematical structure is given by data > and conditions. Is that idea > implicit or explicit in Bourbaki? Has that idea been superceded? How > does it relate to the > development of algebraic theories as understood by Lawvere, Linton, > Barr-Wells, the Elephant, and so on? > > Ellis D. Cooper > > [For admin and other information see: http://www.mta.ca/~cat-dist/ ]