From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6583 Path: news.gmane.org!not-for-mail From: zoran skoda Newsgroups: gmane.science.mathematics.categories Subject: Re: A conditon on maps between sheaves Date: Sun, 13 Mar 2011 17:25:00 +0100 Message-ID: References: Reply-To: zoran skoda NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 X-Trace: dough.gmane.org 1300057285 28691 80.91.229.12 (13 Mar 2011 23:01:25 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Sun, 13 Mar 2011 23:01:25 +0000 (UTC) Cc: categories list To: Andrej Bauer Original-X-From: majordomo@mlist.mta.ca Mon Mar 14 00:01:19 2011 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.114]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1PyuHn-0004ij-6e for gsmc-categories@m.gmane.org; Mon, 14 Mar 2011 00:01:19 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:35315) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1PyuHf-0006yi-GM; Sun, 13 Mar 2011 20:01:11 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1PyuHc-0001Ro-M7 for categories-list@mlist.mta.ca; Sun, 13 Mar 2011 20:01:08 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6583 Archived-At: Dear Andrej, I do not see that the condition as you stated it implies that the map is mono. For example, one can take an example such that for every x the U with above property is the whole base B, hence we have a mono on global sections over B, but this solely is very weak and does not imply we have mono locally, hence on stalks. Maybe you wanted that, in fact, for every nei W around x there is open U around x which is within U ? Zoran On Sat, Mar 12, 2011 at 2:33 AM, Andrej Bauer wrote: > Dear categorists, > > I have come across a condition on maps between sheaves which I am > unable to recognize as with my feeble knowledge of sheaf theory. I > would appreciate any hints as to what this condition is about. > > Succinctly but imprecisely my condition can be expressed as: the > inverse image of a sufficiently small section is again a section. > > More precisely, let p : E -> B be p' : E' -> B be two etale maps over > a base space B and let f : E -> E' be a continuous map such that p = f > p'. The mystery condition on f is as follows: for every x in B there > is a neighborhood U of x, such that for every section s : U -> E' of > p' there exists a unique section t : U -> E of p for which t(U) = > f^(-1)(s(U)). > > It follows from this condition that f is mono as a morphism in Sh(B) > because such an f is injective on each fiber. But I think the > condition says more than that. Am I looking at a standard notion? > > With kind regards, > > Andrej > [For admin and other information see: http://www.mta.ca/~cat-dist/ ]