From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3689 Path: news.gmane.org!not-for-mail From: Thomas Streicher Newsgroups: gmane.science.mathematics.categories Subject: relations on graphs Date: Fri, 9 Mar 2007 20:10:58 +0100 (CET) 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 1241019457 9787 80.91.229.2 (29 Apr 2009 15:37:37 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:37:37 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Fri Mar 9 16:56:00 2007 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 09 Mar 2007 16:56:00 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HPm2k-0004lu-Va for categories-list@mta.ca; Fri, 09 Mar 2007 16:50:27 -0400 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 43 Original-Lines: 15 Xref: news.gmane.org gmane.science.mathematics.categories:3689 Archived-At: If one allows multiple edges with the same source and target then they certainly form a topos, namely that of presheaves over the category with 2 objects and 2 parallel nontrivial arrows. The \neg\neg-separated objects in this topos are precisely those graphs where there is at most one edge from one node to another one. The latter category is not a topos but a quasitopos. The non-full monos in this category are typical examples of epic monos which are not isos. All this can be found in Lawvere's "Qualitative distinctions between toposes of graphs". Thomas Streicher