From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6875 Path: news.gmane.org!not-for-mail From: "Prof. Peter Johnstone" Newsgroups: gmane.science.mathematics.categories Subject: Re: Grothendieck topology vs Lawvere-Tierney topology Date: Fri, 9 Sep 2011 12:11:31 +0100 (BST) Message-ID: References: Reply-To: "Prof. Peter Johnstone" NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed X-Trace: dough.gmane.org 1315582627 18717 80.91.229.12 (9 Sep 2011 15:37:07 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Fri, 9 Sep 2011 15:37:07 +0000 (UTC) Cc: Categories mailing list To: "Vasili I. Galchin" Original-X-From: majordomo@mlist.mta.ca Fri Sep 09 17:37:03 2011 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpy.mta.ca ([138.73.1.128]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1R238Y-0000hA-C5 for gsmc-categories@m.gmane.org; Fri, 09 Sep 2011 17:37:02 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:46358) by smtpy.mta.ca with esmtp (Exim 4.76) (envelope-from ) id 1R236w-0006gP-Rr; Fri, 09 Sep 2011 12:35:22 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1R236w-0007yq-7a for categories-list@mlist.mta.ca; Fri, 09 Sep 2011 12:35:22 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6875 Archived-At: On Wed, 7 Sep 2011, Vasili I. Galchin wrote: > In which paper did Lawvere and Tierney lay out the relationship > between these two topologies? > I don't know where the proof of the equivalence was first written down. But it was stated clearly by Lawvere in his Introduction to Springer LNM 274 (1972): "At the Rome and Overwolfach [sic] meetings I had pointed out that the usual notion of a Grothendieck topology is equivalent to a single such morphism j [that is, a Lawvere-Tierney topology]; Tierney showed that the appropriate axioms on j are simply that jj = j and j preserves finite conjunctions." Peter Johnstone [For admin and other information see: http://www.mta.ca/~cat-dist/ ]