From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6604 Path: news.gmane.org!not-for-mail From: "Ellis D. Cooper" Newsgroups: gmane.science.mathematics.categories Subject: Constitutive Structures Date: Thu, 07 Apr 2011 08:50:11 -0400 Message-ID: Reply-To: "Ellis D. Cooper" NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii"; format=flowed X-Trace: dough.gmane.org 1302197563 15646 80.91.229.12 (7 Apr 2011 17:32:43 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Thu, 7 Apr 2011 17:32:43 +0000 (UTC) To: categories Original-X-From: majordomo@mlist.mta.ca Thu Apr 07 19:32:38 2011 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.4]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1Q7t4P-0001wK-32 for gsmc-categories@m.gmane.org; Thu, 07 Apr 2011 19:32:37 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:37779) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1Q7t43-0003Ce-RP; Thu, 07 Apr 2011 14:32:15 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1Q7t3w-0005lH-Gb for categories-list@mlist.mta.ca; Thu, 07 Apr 2011 14:32:08 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6604 Archived-At: What might be the proper categorical framework to discuss, for example, the fact that the Real Numbers have constitutive structures such as additive abelian group, multiplicative abelian group, topology generated by open intervals, totally ordered infinite set, and so on? At first one might think of forgetful functors, but then what would be the category in which Real Numbers is one object among many? Or, one might say take a category with exactly one object and a functor to each of the categories of the constitutive structures. This makes the Real Numbers look like an "element" of the "intersection" of diverse categories. Then the Complex Numbers or the Hyperreal Numbers which contain the Real Numbers as sub-objects in certain ways are "elements" of other "intersections" of categories. What am I talking about? Ellis D. Cooper [For admin and other information see: http://www.mta.ca/~cat-dist/ ]