From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4217 Path: news.gmane.org!not-for-mail From: Colin McLarty Newsgroups: gmane.science.mathematics.categories Subject: Re: A small cartesian closed concrete category Date: Fri, 15 Feb 2008 20:51:48 -0500 Message-ID: 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 1241019799 12256 80.91.229.2 (29 Apr 2009 15:43:19 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:43:19 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Sat Feb 16 10:19:51 2008 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 16 Feb 2008 10:19:51 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1JQNg9-0004Jn-W7 for categories-list@mta.ca; Sat, 16 Feb 2008 10:06:10 -0400 Content-Disposition: inline Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 39 Original-Lines: 10 Xref: news.gmane.org gmane.science.mathematics.categories:4217 Archived-At: Every finite category with binary products is a preorder: any two objects A,B have at most one arrow A-->B. Otherwise the successive powers of B would have unboundedly many arrows from A. This is Peter Freyd's proof that small complete categories are preorders. Andrei would have thought of it at a more reasonable hour. Colin