From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/253 Path: news.gmane.org!not-for-mail From: John Bourke Newsgroups: gmane.science.mathematics.categories Subject: Category of categories with pullbacks is cartesian closed Date: Fri, 17 Apr 2009 11:22:32 +1000 Message-ID: Reply-To: John Bourke NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1239980000 31290 80.91.229.12 (17 Apr 2009 14:53:20 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Fri, 17 Apr 2009 14:53:20 +0000 (UTC) To: categories@mta.ca Original-X-From: categories@mta.ca Fri Apr 17 16:54:37 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 1LupSD-0006RL-4f for gsmc-categories@m.gmane.org; Fri, 17 Apr 2009 16:54:09 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LuodY-0003xI-EK for categories-list@mta.ca; Fri, 17 Apr 2009 11:01:48 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:253 Archived-At: Dear category theorists, I noticed recently that the category whose objects are categories with pullbacks and whose morphisms are pullback preserving functors is cartesian closed. Given a pair of categories with pullbacks A and B, the internal hom [A,B] has objects: pullback preserving functors from A to B, and morphisms: cartesian natural transformations. I have posted a short paper on the arxiv proving this fact: http://arxiv.org/abs/0904.2486 It seems like a fairly natural fact but is not to my knowledge in the literature. I am wondering whether anyone was previously aware of this result, and if so whether it might be mentioned somewhere in the literature? Thanks, John Bourke, University of Sydney.