From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/7315 Path: news.gmane.org!not-for-mail From: Staffan Angere Newsgroups: gmane.science.mathematics.categories Subject: Re: The Idea of Structure as Data and Conditions Date: Tue, 29 May 2012 13:28:25 +0000 Message-ID: References: Reply-To: Staffan Angere NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1338314159 1006 80.91.229.3 (29 May 2012 17:55:59 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Tue, 29 May 2012 17:55:59 +0000 (UTC) To: "categories@mta.ca" Original-X-From: majordomo@mlist.mta.ca Tue May 29 19:55:59 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 1SZQeE-00010H-6a for gsmc-categories@m.gmane.org; Tue, 29 May 2012 19:55:58 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:45382) by smtpx.mta.ca with esmtp (Exim 4.77) (envelope-from ) id 1SZQdI-0001yp-P4; Tue, 29 May 2012 14:55:00 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1SZQdI-0008P9-5K for categories-list@mlist.mta.ca; Tue, 29 May 2012 14:55:00 -0300 Thread-Topic: categories: Re: The Idea of Structure as Data and Conditions Thread-Index: AQHNPAZVW/HUDwHIaEu8wS7YUftvZJbf0e4WgADxcAU= In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:7315 Archived-At: I am not certain that is a good example, actually. The membership relation = is certainly what gives the structure of a model of ZFC, so it may be relev= ant to morphisms between such models. However, it does not have to have any= thing to do with the structure of individual sets. The structure of a single set is, I believe, most fruitfully thought of as = just consisting of the identity relation on its elements. That way, the mor= phisms come out as functions (i.e. identity-preserving total relations), ju= st as we expect them to. Best wishes, Staffan ________________________________________ Fr=E5n: FEJ Linton [FLinton@Wesleyan.edu] Skickat: den 28 maj 2012 08:00 Till: categories@mta.ca =C4mne: categories: Re: The Idea of Structure as Data and Conditions On Sat, 26 May 2012 19:48:26 -0400 (EDT), Michael Barr wrote: > Let me point out that not every structure comes with an obvious notion of > morphism. --- [examples snipped] --- The most common example: sets. The structure is based on membership. Virtually no one ever wants to restrict attention to functions that respect (preserve or reflect) membership (other than "preserve" between ordinals). Cheers, -- Fred [For admin and other information see: http://www.mta.ca/~cat-dist/ ] [For admin and other information see: http://www.mta.ca/~cat-dist/ ]