From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/7067 Path: news.gmane.org!not-for-mail From: Ross Street Newsgroups: gmane.science.mathematics.categories Subject: Re: Dualities arising via pairs of schizophrenic objects Date: Fri, 25 Nov 2011 15:10:08 +1100 Message-ID: References: Reply-To: Ross Street NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 (Apple Message framework v936) Content-Type: text/plain;charset=WINDOWS-1252;format=flowed; delsp=yes Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1322227493 27622 80.91.229.12 (25 Nov 2011 13:24:53 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Fri, 25 Nov 2011 13:24:53 +0000 (UTC) Cc: categories list To: Sebastian Kerkhoff Original-X-From: majordomo@mlist.mta.ca Fri Nov 25 14:24:49 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 1RTvlo-0003xY-Qv for gsmc-categories@m.gmane.org; Fri, 25 Nov 2011 14:24:49 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:49901) by smtpx.mta.ca with esmtp (Exim 4.76) (envelope-from ) id 1RTvkT-0005zD-CQ; Fri, 25 Nov 2011 09:23:25 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1RTvkQ-00037I-Pz for categories-list@mlist.mta.ca; Fri, 25 Nov 2011 09:23:22 -0400 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:7067 Archived-At: On 25/11/2011, at 3:06 AM, Sebastian Kerkhoff wrote: > > I believe it is a well-known fact that a potential duality arises =20 > when a > single object essentially lives in two different categories. Dear Sebastian This topic has been discussed in this forum before (e.g. Oct 2010) and I recommend looking at the past emails. I don't think anyone mentioned the following paper which uses the idea of an A-object in B (which is =20 equally a B-object in A) to provide examples as stated in the title. F. Foltz, G.M. Kelly and C. Lair, Algebraic categories with few monoidal biclosed structures or none, J. Pure and Applied Algebra 17 (1980) 171=96177. The work of Lambek and Rattray, such as Lambek, J.; Rattray, B. A. A general Stone-Gelfand duality. Trans. Amer. Math. Soc. 248 (1979), no. 1, 1=9635, should also be emphasized. Best wishes, Ross= [For admin and other information see: http://www.mta.ca/~cat-dist/ ]