From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6596 Path: news.gmane.org!not-for-mail From: "Prof. Peter Johnstone" Newsgroups: gmane.science.mathematics.categories Subject: Re: A conditon on maps between sheaves Date: Mon, 28 Mar 2011 10:40:20 +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 1301403722 6579 80.91.229.12 (29 Mar 2011 13:02:02 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Tue, 29 Mar 2011 13:02:02 +0000 (UTC) Cc: Steve Vickers , zoran skoda , categories list To: Andrej Bauer Original-X-From: majordomo@mlist.mta.ca Tue Mar 29 15:01:57 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 1Q4YYX-0007jL-7Z for gsmc-categories@m.gmane.org; Tue, 29 Mar 2011 15:01:57 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:60137) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1Q4YYN-0007oF-L5; Tue, 29 Mar 2011 10:01:47 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1Q4YYJ-0001S8-UC for categories-list@mlist.mta.ca; Tue, 29 Mar 2011 10:01:44 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6596 Archived-At: On Sun, 27 Mar 2011, Andrej Bauer wrote: > Steve Vickers wrote: >> For example: take B to be the circle and E' its Moebius double cover, >> which has no global sections. Then for every x in B you can take U = B >> and your condition holds vacuously for any f whatsoever. >> >> If E = E'+E' then the codiagonal f has your property but is not mono. > > I apologize for the noise, I got my conditions all wrong when I tried > to "optimize" them for the categories list. As it turns out my > condition means that I have a map of etale spaces which is bijective > on fibers (and the spaces in question are Hausdorff locally compact). > So is there a name for that other than "bijective on fibers"? Yes -- it's called an isomorphism. The fibre functors are jointly conservative. Peter Johnstone [For admin and other information see: http://www.mta.ca/~cat-dist/ ]