From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/1074 Path: news.gmane.org!not-for-mail From: Francois Lamarche Newsgroups: gmane.science.mathematics.categories Subject: Monoidal structure on graphs Date: Wed, 17 Mar 1999 16:24:26 +0100 Organization: LORIA Message-ID: <36EFC92A.6C34DC4B@loria.fr> 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 1241017549 29387 80.91.229.2 (29 Apr 2009 15:05:49 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:05:49 +0000 (UTC) To: categories@mta.ca Original-X-From: cat-dist Wed Mar 17 14:35:08 1999 Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id LAA06946 for categories-list; Wed, 17 Mar 1999 11:48:30 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Mailer: Mozilla 4.5 [en] (X11; I; SunOS 5.5 sun4m) X-Accept-Language: fr, en Original-Sender: cat-dist@mta.ca Precedence: bulk Original-Lines: 29 Xref: news.gmane.org gmane.science.mathematics.categories:1074 Archived-At: Greetings, fellow categorists. I'm wondering, if anybody has ever described the following monoidal structure on the category of oriented multigraphs, what MacLane calls graphs, the most common kind of graph in category theory (but not everywhere) : Given mgs X, Y, the set |X-oY| of vertices on X-oY is the set of mg morphisms X --> Y. Given f,g : X --> Y the set of arrows f-->g is the set of pairs (p_0,p_1) of functions such that forall x in |X|, p_0(x) : f-->g forall k: x-->y in X, p_1(k) : f(x)-->g(y) This co-contra bifunctor has a tensor left adjoint, which is symmetric and monoidal. I would be quite surprised if this structure had never been seen before. Enriched universal algebra in there has applications in computer science. Thanks, Francois Lamarche