From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2778 Path: news.gmane.org!not-for-mail From: "Townsend, Christopher" Newsgroups: gmane.science.mathematics.categories Subject: A representation theorem for Geometric Morphism Date: Tue, 9 Aug 2005 14:29:47 +0100 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1241018899 5766 80.91.229.2 (29 Apr 2009 15:28:19 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:28:19 +0000 (UTC) To: Original-X-From: rrosebru@mta.ca Wed Aug 10 10:05:31 2005 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 10 Aug 2005 10:05:31 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1E2q9Z-0005Jw-0D for categories-list@mta.ca; Wed, 10 Aug 2005 09:57:53 -0300 X-MimeOLE: Produced By Microsoft Exchange V6.0.6603.0 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 6 Original-Lines: 19 Xref: news.gmane.org gmane.science.mathematics.categories:2778 Archived-At: If f:F->E is a geometric morphism between elementary toposes then there is a, well known, adjunction Sigma_f -! f* between the category of locales internal to E and the category of locales internal to F. A property of this adjunction is that f* commutes with the upper (and lower) power locale functors. I think that this actually characterizes geometric morphisms: given an adjunction L-!R between locales internal in E and locales internal in F such that the right adjoint (R) commutes with the upper and lower power locales then there exists a geometric morphism, f:F->E such that L=3DSigma_f and R=3Df*. Has anyone looked at this type of result before?=20 =20 Thanks, Christopher (Townsend) =20 =20