From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5048 Path: news.gmane.org!not-for-mail From: "Szlachanyi Kornel" Newsgroups: gmane.science.mathematics.categories Subject: flat topologies Date: Fri, 10 Jul 2009 18:32:07 +0200 Message-ID: Reply-To: "Szlachanyi Kornel" NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain;charset=iso-8859-2 Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1247323344 26352 80.91.229.12 (11 Jul 2009 14:42:24 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Sat, 11 Jul 2009 14:42:24 +0000 (UTC) To: categories@mta.ca Original-X-From: categories@mta.ca Sat Jul 11 16:42:17 2009 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from mailserv.mta.ca ([138.73.1.1]) by lo.gmane.org with esmtp (Exim 4.50) id 1MPdmI-0006x3-3W for gsmc-categories@m.gmane.org; Sat, 11 Jul 2009 16:42:14 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MPdAf-0001Vs-FG for categories-list@mta.ca; Sat, 11 Jul 2009 11:03:21 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5048 Archived-At: Dear List, I have some questions on flat functors and Grothendieck topologies. It is probably well-known that if F: C--> Set is a flat functor on a small category then there is a Grothendieck topology on C in which the covering sieves S on the object c consist of sets of arrows to c such that {Fs|s in S} is jointly epimorphic on Fc. 1. Could you tell me a reference for this statement? 2. Is there a characterization of Grothendieck topologies that arise in this way from a flat functor? (`flat topologies'?) 3. For what categories C will there be a flat functor inducing the canonical topology on C? Thank you for any help. Kornel --------------------------------------------------- Kornel Szlachanyi Research Institute for Particle and Nuclear Physics of the Hungarian Academy of Science Budapest --------------------------------------------------- [For admin and other information see: http://www.mta.ca/~cat-dist/ ]