From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6613 Path: news.gmane.org!not-for-mail From: "F. William Lawvere" Newsgroups: gmane.science.mathematics.categories Subject: RE: Constitutive Structures Date: Wed, 13 Apr 2011 15:24:53 -0400 Message-ID: References: Reply-To: "F. William Lawvere" NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1302783084 23438 80.91.229.12 (14 Apr 2011 12:11:24 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Thu, 14 Apr 2011 12:11:24 +0000 (UTC) To: , categories Original-X-From: majordomo@mlist.mta.ca Thu Apr 14 14:11:19 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 1QALOH-00030z-DC for gsmc-categories@m.gmane.org; Thu, 14 Apr 2011 14:11:17 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:48581) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1QALNu-0000Ax-CZ; Thu, 14 Apr 2011 09:10:54 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1QALNr-0005ds-E4 for categories-list@mlist.mta.ca; Thu, 14 Apr 2011 09:10:51 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6613 Archived-At: It seems that what Ellis is asking for is not so much the interesting richn= ess per se of the real numbers but "the proper categorical framework"=2C that is a fra= gment of objective logicto explain how we relate partial structures of the= "same thing". Not necessarily an "intersection"but more precisely an inverse limit of a diagram of forgetful functors=20 may be the right sort of thing. Straining through many related layersvia na= turality is the standard way to extract the Structure of a given functor me= asuring given mathematical objects. Can it dually be a way to extract a ima= ge of the objects themselves?Bill > Date: Thu=2C 7 Apr 2011 08:50:11 -0400 > To: categories@mta.ca > From: xtalv1@netropolis.net > Subject: categories: Constitutive Structures >=20 > What might be the proper categorical framework to discuss=2C for > example=2C the fact that the Real Numbers have constitutive structures > such as additive abelian group=2C multiplicative abelian group=2C > topology generated by open intervals=2C totally ordered infinite set=2C a= nd so on? > At first one might think of forgetful functors=2C but then what would > be the category in which Real Numbers is one object among many? > Or=2C one might say take a category with exactly one object and a > functor to each of the categories of the constitutive structures. This ma= kes > 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? >=20 > Ellis D. Cooper >=20 [For admin and other information see: http://www.mta.ca/~cat-dist/ ]