From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3687 Path: news.gmane.org!not-for-mail From: "Ronnie Brown" Newsgroups: gmane.science.mathematics.categories Subject: Re: relations on graphs Date: Fri, 9 Mar 2007 17:49:27 -0000 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain;format=flowed; charset="iso-8859-1";reply-type=response Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241019456 9780 80.91.229.2 (29 Apr 2009 15:37:36 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:37:36 +0000 (UTC) To: Original-X-From: rrosebru@mta.ca Fri Mar 9 14:32:45 2007 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 09 Mar 2007 14:32:45 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HPjr9-00067C-8y for categories-list@mta.ca; Fri, 09 Mar 2007 14:30:19 -0400 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 41 Original-Lines: 32 Xref: news.gmane.org gmane.science.mathematics.categories:3687 Archived-At: Jamie Vicary states `the category of graphs is not a topos'. The situation is not so simple, and is discussed for the combinatorially minded reader in 06.04 BROWN, R., MORRIS, I., SHRIMPTON, J. & WENSLEY, C.D. Graphs of morphisms of graphs http://www.informatics.bangor.ac.uk/public/mathematics/research/preprints/06/cathom06.html#06.04 There are categories of undirected graphs which are not toposes. But ... Ronnie Brown ----- Original Message ----- From: "Jamie Vicary" To: Sent: Friday, March 09, 2007 10:01 AM Subject: categories: Re: relations on graphs >> 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. >