From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/512 Path: news.gmane.org!not-for-mail From: categories Newsgroups: gmane.science.mathematics.categories Subject: Re: local maps of toposes are always UIAO Date: Tue, 4 Nov 1997 08:18:07 -0400 (AST) Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: ger.gmane.org 1241017009 26069 80.91.229.2 (29 Apr 2009 14:56:49 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 14:56:49 +0000 (UTC) To: categories Original-X-From: cat-dist Tue Nov 4 08:18:08 1997 Original-Received: by mailserv.mta.ca; id AA14936; Tue, 4 Nov 1997 08:18:07 -0400 Original-Lines: 15 Xref: news.gmane.org gmane.science.mathematics.categories:512 Archived-At: Date: Tue, 4 Nov 1997 10:31:16 +0000 (GMT) From: Dr. P.T. Johnstone Thomas Streicher asked > I'd like to know whether the following simple observation is well known. > If F -| U : E -> S is a local map of toposes i.e. Gamma : Gl(F) -> Gl(Id_S) > has a fibred right adjoint Nabla then U is full and faithful, i.e. one has > the situation of a Unity and Identity of Adjoint Opposites in Lawvere's > sense. Yes, there is a simple proof of this fact in Proposition 1.4 of "Local maps of toposes" by Johnstone & Moerdijk (Proc. London Math. Soc. (3) 58 (1989), 281--305).