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.