From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2434 Path: news.gmane.org!not-for-mail From: Jonas Eliasson Newsgroups: gmane.science.mathematics.categories Subject: Tree cover? Date: Mon, 1 Sep 2003 10:30:01 +0200 (CEST) Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: ger.gmane.org 1241018661 4154 80.91.229.2 (29 Apr 2009 15:24:21 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:24:21 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Mon Sep 1 15:18:23 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 01 Sep 2003 15:18:23 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 19ttCt-0006H4-00 for categories-list@mta.ca; Mon, 01 Sep 2003 15:15:15 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 2 Original-Lines: 32 Xref: news.gmane.org gmane.science.mathematics.categories:2434 Archived-At: It seems that you can modify the construction of the localic Diaconescu cover to get an open surjective _filtered_ cover of a Grothendieck topos Sh(C). Instead of using the category String(C) of strings in C, you could construct the category Tree(C) of finite, rooted, binary trees in C. If given c and d in C you can find e such that e --> c and e --> d then Tree(C) is a poset with binary upper bounds, i.e. a filtered category. Could anyone provide a reference for such a construction? Grateful for any help, Jonas Eliasson ------------------------------------------ | Jonas Eliasson | | Department of Mathematics | | Uppsala University | | Sweden | | E-mail: jonase@math.uu.se | | Homepage: http://www.math.uu.se/~jonase/ | ------------------------------------------