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From: Francois Magnan <fmagnan@cogniscienceinc.com>
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Subject: Re: Category of directed multigraphs with loops
Date: Fri, 21 Feb 2003 09:35:39 -0500
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Hi,=0D
=0D
	The product in the category of directed irreflexive multigraphs =
is =0D
simple to compute. In fact, if you learn further about topos theory you =0D=

will learn that all finite limits in a presheaf topos are computed =0D
pointwise. The category that interests you is a presheaf category since =0D=

it is the category of all functors from the category=0D
=0D
                      ------------>=0D
C^op  =3D  A                     V=0D
                      ------------>=0D
=0D
to the category of sets.=0D
=0D
=0D
In simpler words, it means that if you take two graphs: G_1 and G_2 =0D
with vertices sets V_1 and  V_2 and arrows sets A_1 and A_2 =0D
respectively. The product graph P=3DG_1 x G_2 will have V_P=3DV_1xV_2 =0D=

(normal catesian product in sets) as vertices and A_P=3DA_1xA_2 as =0D
arrows. The incidence relation are the expected ones.=0D
=0D
For the reflexive directed multigraphs as all presheafs the recipe is =0D=

the same. I would suggest you to read the book:=0D
=0D
M.La Palme Reyes, G. Reyes, Generic Figures and their glueings: A =0D
constructive approach to functor categories.=0D
=0D
Which is still unpublished as of now but I can send you a PDF.=0D
=0D
Hope this helps,=0D
Francois Magnan=0D
=0D
=0D
On Monday, Feb 17, 2003, at 16:09 America/Montreal, Galchin Vasili =0D
wrote:=0D
=0D
>=0D
> Hello,=0D
>=0D
>       Given two graphs, A and B, I am trying figure out how to =0D
> construct=0D
> the product AxB. I have been rereading "Conceptual Mathemtatics" by=0D
> Lawvere. The category of irreflexive graphs is one of the running =0D
> examples=0D
> throughout the book. I have been concentrating on the chapters =0D
> concerned=0D
> with the product of objects, but I don't see any details of how to=0D
> construct AxB. Have I skipped over something?=0D
>=0D
> Regards, Bill Halchin=0D
>=0D
>=0D
>=0D
>=0D
- --------------------------------------------=0D
Francois Magnan=0D
Recherche & D=E9veloppement=0D
Cogniscience Editeurs Inc.=0D
fmagnan@cogniscienceinc.com=0D
=0D