=09charset=3D"iso-8859-1" Content-Transfer-Encoding: 8bit Sender: cat-dist@mta.ca Precedence: bulk I had sent a private e-mail to Bill Halchin explaining this, thinking there was no need to post it; now it appears that people will get the impression that 'Conceptual Mathematics' omits this topic. It doesn't; it's right after the definition of products, in the section entitled 'How to calculate products'. Incidentally, in case you have Spanish-speaking students who would like an introduction to categories, the translation (by Francisco Marmolejo, 'Matematicas Conceptuales', published by Siglo XXI) is now available, and i= s considerably cheaper than the English edition! Yours, Steve ----- Original Message ----- From: "Francois Magnan" <fmagnan@cogniscienceinc.com> To: <categories@mta.ca> Sent: Friday, February 21, 2003 9:35 AM Subject: categories: Re: Category of directed multigraphs with loops Hi, The product in the category of directed irreflexive multigraphs is simple to compute. In fact, if you learn further about topos theory you will learn that all finite limits in a presheaf topos are computed pointwise. The category that interests you is a presheaf category since it is the category of all functors from the category ------------> C^op =3D A V ------------> to the category of sets. In simpler words, it means that if you take two graphs: G_1 and G_2 with vertices sets V_1 and V_2 and arrows sets A_1 and A_2 respectively. The product graph P=3DG_1 x G_2 will have V_P=3DV_1xV_2 (normal catesian product in sets) as vertices and A_P=3DA_1xA_2 as arrows. The incidence relation are the expected ones. For the reflexive directed multigraphs as all presheafs the recipe is the same. I would suggest you to read the book: M.La Palme Reyes, G. Reyes, Generic Figures and their glueings: A constructive approach to functor categories. Which is still unpublished as of now but I can send you a PDF. Hope this helps, Francois Magnan On Monday, Feb 17, 2003, at 16:09 America/Montreal, Galchin Vasili wrote:

Hello,

Given two graphs, A and B, I am trying figure out how to construct the product AxB. I have been rereading "Conceptual Mathemtatics" by Lawvere. The category of irreflexive graphs is one of the running examples throughout the book. I have been concentrating on the chapters concerned with the product of objects, but I don't see any details of how to construct AxB. Have I skipped over something?

Regards, Bill Halchin

- -------------------------------------------- Francois Magnan Recherche & D=E9veloppement Cogniscience Editeurs Inc. fmagnan@cogniscienceinc.com