From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6603 Path: news.gmane.org!not-for-mail From: "Olivia Caramello" Newsgroups: gmane.science.mathematics.categories Subject: Preprint: "A topos-theoretic approach to Stone-type dualities" Date: Tue, 5 Apr 2011 01:58:17 +0100 Message-ID: Reply-To: "Olivia Caramello" 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 1302011722 24492 80.91.229.12 (5 Apr 2011 13:55:22 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Tue, 5 Apr 2011 13:55:22 +0000 (UTC) To: Original-X-From: majordomo@mlist.mta.ca Tue Apr 05 15:55:16 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 1Q76ix-0003Vj-Tl for gsmc-categories@m.gmane.org; Tue, 05 Apr 2011 15:55:16 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:44354) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1Q76ij-00026u-HL; Tue, 05 Apr 2011 10:55:01 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1Q76ig-0002SB-96 for categories-list@mlist.mta.ca; Tue, 05 Apr 2011 10:54:58 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6603 Archived-At: Dear All, The following preprint is available from the Mathematics ArXiv at the address http://arxiv.org/abs/1103.3493: O. Caramello, "A topos-theoretic approach to Stone-type dualities" Abstract: We present an abstract unifying framework for interpreting Stone-type dualities; several known dualities are seen to be instances of just one topos-theoretic phenomenon, and new dualities are introduced. In fact, infinitely many new dualities between preordered structures and locales = or topological spaces can be generated through our topos-theoretic = machinery in a uniform way. We then apply our topos-theoretic interpretation to = obtain results connecting properties of preorders and properties of the corresponding locales or topological spaces, and we establish = adjunctions between various kinds of categories as natural applications of our = general methodology. In the last part of the paper, we exploit the theory = developed in the previous parts to obtain a topos-theoretic interpretation of the problem of finding explicit descriptions of models of 'ordered algebraic theories' presented by generators and relations, and give several = examples which illustrate the effectiveness of our methodology. In passing, we provide a number of other applications of our theory to Algebra, = Topology and Logic. This work represents a concrete implementation of the abstract = methodologies introduced in the paper "The unification of Mathematics via Topos = Theory", which I advertised on this list some months ago; incidentally, some subscribers to this list might be interested in the Russian translation = of the latter paper by Yury Bratkov, now available from the ArXiv at the address http://arxiv.org/abs/1104.0563. =A0=A0=A0 Comments are welcome. Best regards, Olivia Caramello [For admin and other information see: http://www.mta.ca/~cat-dist/ ]