From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3688 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 15:33:12 +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 1241019456 9784 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: categories@mta.ca 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 1HPjoU-0005pl-GX for categories-list@mta.ca; Fri, 09 Mar 2007 14:27:35 -0400 Content-Disposition: inline Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 42 Original-Lines: 26 Xref: news.gmane.org gmane.science.mathematics.categories:3688 Archived-At: On 3/9/07, Jamie Vicary wrote: > > 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. Dear all, before the flood of complaints begins: I should make it clear that I am differentiating between the category of directed graphs, which is certainly a topos, and the category of graphs (i.e. edges have no orientation) which, as I have just managed to convince myself, is certainly _not_ a topos. The original poster was enquiring about the category of graphs, I believe, rather than the category of directed graphs. JAmie.