From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6581 Path: news.gmane.org!not-for-mail From: Andrej Bauer Newsgroups: gmane.science.mathematics.categories Subject: A conditon on maps between sheaves Date: Sat, 12 Mar 2011 02:33:31 +0100 Message-ID: Reply-To: Andrej Bauer NNTP-Posting-Host: lo.gmane.org Content-Type: text/plain; charset=UTF-8 X-Trace: dough.gmane.org 1299941278 11073 80.91.229.12 (12 Mar 2011 14:47:58 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Sat, 12 Mar 2011 14:47:58 +0000 (UTC) To: categories list Original-X-From: majordomo@mlist.mta.ca Sat Mar 12 15:47:54 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 1PyQ6i-0007fp-V7 for gsmc-categories@m.gmane.org; Sat, 12 Mar 2011 15:47:53 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:35032) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1PyQ65-0007LG-Td; Sat, 12 Mar 2011 10:47:13 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1PyQ63-00058P-Gi for categories-list@mlist.mta.ca; Sat, 12 Mar 2011 10:47:11 -0400 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6581 Archived-At: 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/ ]