From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4451 Path: news.gmane.org!not-for-mail From: Paul Taylor Newsgroups: gmane.science.mathematics.categories Subject: products preserve epis of locales Date: Tue, 22 Jul 2008 14:35:19 +0100 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 (Apple Message framework v624) Content-Type: text/plain; charset=US-ASCII; format=flowed Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241019954 13345 80.91.229.2 (29 Apr 2009 15:45:54 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:45:54 +0000 (UTC) To: Categories list Original-X-From: rrosebru@mta.ca Tue Jul 22 11:39:50 2008 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 22 Jul 2008 11:39:50 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1KLJ0c-0005ib-1W for categories-list@mta.ca; Tue, 22 Jul 2008 11:38:34 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 18 Original-Lines: 15 Xref: news.gmane.org gmane.science.mathematics.categories:4451 Archived-At: Where can I find a published proof that if X --->> Y is a (not necessarily regular) epi of locales then so is X x Z --->> Y x Z for any locale Z? NB (I know that) this is not true for general pullbacks of locales! Ideally, I'd like to cite a textbook-style account that begins by characterising epis and regular monos as idempotent adjunctions, saying that they form a factorisation system, and describes the product of locales fairly explicitly. Paul