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 = 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=G_1 x G_2 will have V_P=V_1xV_2 (normal catesian product in sets) as vertices and A_P=A_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 Which is still unpublished as of now but I can send you a PDF.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 & Développement Cogniscience Editeurs Inc. fmagnan@cogniscienceinc.com