From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/7313 Path: news.gmane.org!not-for-mail From: FEJ Linton Newsgroups: gmane.science.mathematics.categories Subject: Re: The Idea of Structure as Data and Conditions Date: Mon, 28 May 2012 02:00:12 -0400 Message-ID: References: Reply-To: FEJ Linton NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Content-Transfer-Encoding: 7bit X-Trace: dough.gmane.org 1338245731 24086 80.91.229.3 (28 May 2012 22:55:31 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Mon, 28 May 2012 22:55:31 +0000 (UTC) To: categories@mta.ca Original-X-From: majordomo@mlist.mta.ca Tue May 29 00:55:30 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 1SZ8qW-0006Tu-65 for gsmc-categories@m.gmane.org; Tue, 29 May 2012 00:55:28 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:45178) by smtpx.mta.ca with esmtp (Exim 4.77) (envelope-from ) id 1SZ8q4-00087e-1O; Mon, 28 May 2012 19:55:00 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1SZ8q4-0004H2-2Y for categories-list@mlist.mta.ca; Mon, 28 May 2012 19:55:00 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:7313 Archived-At: 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/ ]