Re: relations on graphs

["Jamie Vicary" <jamie.vicary@imperial.ac.uk>]

On 3/9/07, Jamie Vicary <jamie.vicary@imperial.ac.uk> wrote:
> > Is there any literature which discusses different
> > possible notions for relations on graphs?
>
> In any regular category, and certainly any topos, there is a well
> defined notion of relation, where a relation between two objects is a
> subobject of their product. These admit a * operation and compose in a
> well-behaved way; look towards the end of McLarty's category theory
> textbook for info on this.
>
> The category of directed graphs is certainly such a category, being
> regular. The category of graphs is not a topos, I believe, but might
> still be regular.

Dear all, before the flood of complaints begins: I should make it
clear that I am differentiating between the category of directed
graphs, which is certainly a topos, and the category of graphs (i.e.
edges have no orientation) which, as I have just managed to convince
myself, is certainly _not_ a topos.

The original poster was enquiring about the category of graphs, I
believe, rather than the category of directed graphs.

            JAmie.