From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2189 Path: news.gmane.org!not-for-mail From: Thomas Streicher Newsgroups: gmane.science.mathematics.categories Subject: preservation of exponentials Date: Tue, 18 Feb 2003 14:32:50 +0100 (CET) Message-ID: <200302181332.OAA06673@fb04209.mathematik.tu-darmstadt.de> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241018477 2934 80.91.229.2 (29 Apr 2009 15:21:17 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:21:17 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Thu Feb 20 12:23:40 2003 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 20 Feb 2003 12:23:40 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 18ltT8-0006Ow-00 for categories-list@mta.ca; Thu, 20 Feb 2003 12:22:42 -0400 X-Mailer: ELM [version 2.4ME+ PL66 (25)] X-MailScanner: Found to be clean Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 45 Original-Lines: 16 Xref: news.gmane.org gmane.science.mathematics.categories:2189 Archived-At: Recently when rereading an old paper I came across a passage insinuating that every finite limit preserving full and faithful functor between toposes does also preserve exponentials. I am sceptical because I don't see any obvious reason for it. It is certainly wrong for ccc's (a counterexample is the inclusion of open sets of reals into powersets of reals). On the other hand Yoneda functors and direct image parts of injective geom morphs do preserve exponentials. So I was thinking of inverse image parts of connected geom.morph.'s. Of course, \Delta : Set -> Psh(C) for a connected C does preserve exponentials. What about Delta : Set -> Sh(X) for X connected but not locally connected, e.g. take for X Cantor space with a focal point added? Thomas Streicher