From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3080 Path: news.gmane.org!not-for-mail From: Chris Wensley Newsgroups: gmane.science.mathematics.categories Subject: Re: Undirected graphs Date: Thu, 9 Mar 2006 17:38:04 +0000 (GMT) Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed X-Trace: ger.gmane.org 1241019083 7163 80.91.229.2 (29 Apr 2009 15:31:23 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:31:23 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Fri Mar 10 05:51:04 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 10 Mar 2006 05:51:04 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FHeCq-0001n2-TF for categories-list@mta.ca; Fri, 10 Mar 2006 05:46:44 -0400 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 26 Original-Lines: 28 Xref: news.gmane.org gmane.science.mathematics.categories:3080 Archived-At: Dear Bob > I've been following the recent posts on undirected graphs > with interest. But I have a question. I think it's being said > that undirected graphs are the same as directed graphs with > involution. (Presheaves on the full subcategory of SET determined > by 1 or 2, or just 2.) Which is nice but what about loops? > The involution might fix a loop or not. So wouldn't we be > getting undirected graphs with two kinds of loops, whole loops > and semiloops? What am I missing? There has been some 'work in progress' at Bangor on this very question for the past 8 years. This is intended to present a categorical approach to graph theory to workers in combinatorics, and is not intended for category theorists. The current draft, 06.04, is available at http://www.informatics.bangor.ac.uk/public/mathematics/research/preprints/06/ (follow the link 06.04 to 06_04.pdf). We do indeed discuss two types of loop, which we call 'loops' and 'bands'. Ronnie is away today, but may well add his own comment tomorrow. Best wishes, Chris Wensley