From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6371 Path: news.gmane.org!not-for-mail From: "Fred E.J. Linton" Newsgroups: gmane.science.mathematics.categories Subject: Re: Communes paper, schismatic objects Date: Sun, 07 Nov 2010 15:05:23 -0500 Message-ID: Reply-To: "Fred E.J. Linton" 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 1289231878 20955 80.91.229.12 (8 Nov 2010 15:57:58 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Mon, 8 Nov 2010 15:57:58 +0000 (UTC) Cc: Categories list To: Todd Trimble , Vaughan Pratt Original-X-From: majordomo@mlist.mta.ca Mon Nov 08 16:57:54 2010 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.114]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1PFU6T-000339-4t for gsmc-categories@m.gmane.org; Mon, 08 Nov 2010 16:57:53 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:35811) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1PFU5L-00009t-QP; Mon, 08 Nov 2010 11:56:43 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1PFU5G-0004ny-0N for categories-list@mlist.mta.ca; Mon, 08 Nov 2010 11:56:38 -0400 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6371 Archived-At: Todd Trimble writes, inter alia, > ... The natural "home" of 2 from > this point of view is in Bool(CH) =3D CH(Bool). = I quite agree that Bool(CH) and CH(Bool) are quite equivalent. But they are far from *equal*. Each serves as a 'natural "home"' for 2, and the object 2 in its one home has a radically different personality -- and interacts with radically different colleagues -- than in its other. = Moreover, as shown in Stone Spaces, 2 has rather more natural homes -- and personalities -- than merely these two :-) , whence my inclination to speak of its *multiple* personalities (pace Tom L.). Cheers, -- Fred [For admin and other information see: http://www.mta.ca/~cat-dist/ ]