From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/8382 Path: news.gmane.org!not-for-mail From: Paul B Levy Newsgroups: gmane.science.mathematics.categories Subject: Re: Request for a reference Date: Thu, 13 Nov 2014 21:07:05 +0000 Message-ID: References: Reply-To: Paul B Levy NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=windows-1252; format=flowed Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1415963148 2665 80.91.229.3 (14 Nov 2014 11:05:48 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Fri, 14 Nov 2014 11:05:48 +0000 (UTC) Cc: categories@mta.ca To: "Garraway, Dale" Original-X-From: majordomo@mlist.mta.ca Fri Nov 14 12:05:43 2014 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp3.mta.ca ([138.73.1.127]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1XpEhC-0006po-FJ for gsmc-categories@m.gmane.org; Fri, 14 Nov 2014 12:05:42 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:60684) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1XpEgl-0008SQ-Ei; Fri, 14 Nov 2014 07:05:15 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1XpEgl-0007J5-00 for categories-list@mlist.mta.ca; Fri, 14 Nov 2014 07:05:15 -0400 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:8382 Archived-At: Dear Dale, I don't know if it appeared anywhere earlier, but the result for an arbitrary poset is Proposition 8.4 in Birkedal, Mogelberg, Schwinghammer and Stovring's paper "First steps in synthetic domain theory: step-indexing in the topos of trees". http://www.cs.au.dk/~birke/papers/sgdt-journal.pdf Paul On 12/11/14 18:46, Garraway, Dale wrote: > > Hi All > > Could some one please send me a reference of the fact that the category of > presheaves on a Heyting algebra $H$ is equivalent to the category of > sheaves on the Heyting algebra of down closed subsets of $H$. I believe > this is true in general for any partial order so a reference to either > would be greatly appreciated. > > Dale Garraway > Dept. of Math, > Eastern Washington > dgarraway@ewu.edu -- Paul Blain Levy School of Computer Science, University of Birmingham http://www.cs.bham.ac.uk/~pbl [For admin and other information see: http://www.mta.ca/~cat-dist/ ]