From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/7305 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 09:06:14 -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 1338144969 28465 80.91.229.3 (27 May 2012 18:56:09 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Sun, 27 May 2012 18:56:09 +0000 (UTC) To: "Ellis D. Cooper" , catbb Original-X-From: majordomo@mlist.mta.ca Sun May 27 20:56:08 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 1SYidK-000245-0n for gsmc-categories@m.gmane.org; Sun, 27 May 2012 20:56:06 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:44762) by smtpx.mta.ca with esmtp (Exim 4.77) (envelope-from ) id 1SYico-0002VT-QK; Sun, 27 May 2012 15:55:34 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1SYicp-0007ng-VC for categories-list@mlist.mta.ca; Sun, 27 May 2012 15:55:35 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:7305 Archived-At: The sentence "contains all the info about any model" is ambiguous. I mean the theory contains everything you can say that is correct about every model. --C On Sun, May 27, 2012 at 9:02 AM, Charles Wells wrote: > 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 superseded, not at all, but it has been completed (in two senses) by the 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 > > [For admin and other information see: http://www.mta.ca/~cat-dist/ ]