From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3685 Path: news.gmane.org!not-for-mail From: "Jamie Vicary" Newsgroups: gmane.science.mathematics.categories Subject: Re: relations on graphs Date: Fri, 9 Mar 2007 10:01:41 +0000 Message-ID: NNTP-Posting-Host: main.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 1241019455 9772 80.91.229.2 (29 Apr 2009 15:37:35 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:37:35 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Fri Mar 9 09:17:46 2007 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 09 Mar 2007 09:17:46 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HPetI-0007Ii-0N for categories-list@mta.ca; Fri, 09 Mar 2007 09:12:12 -0400 Content-Disposition: inline Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 39 Original-Lines: 16 Xref: news.gmane.org gmane.science.mathematics.categories:3685 Archived-At: > Is there any literature which discusses different > possible notions for relations on graphs? In any regular category, and certainly any topos, there is a well defined notion of relation, where a relation between two objects is a subobject of their product. These admit a * operation and compose in a well-behaved way; look towards the end of McLarty's category theory textbook for info on this. The category of directed graphs is certainly such a category, being regular. The category of graphs is not a topos, I believe, but might still be regular. Jamie Vicary.