Re: [Axiom-developer] Graph theory

[Ralf Hemmecke]

> For example, is an Axiom set, i.e. a member of the domain Set, a
> data structure or a mathematical structure? Should we call the
> domain Set a mathematical structure or only the category SetCategory
> to which it belongs? And of course not everything that we would
> like to call a set in Axiom is finite.

Actually, "Set" is a bad choice for the domain of finite sets that all
have the same type of elements. It should at least be called
"FiniteSet". But then, would make "Set" as a _domain_ in the sense of
mathematics be an interesting domain at all?

> Essentially the only requirement of SetCategory is that the domain
> has equality and inequality.

That is OK, I think.

> I think a Graph in Axiom has to be something nearly as fundamental
> as a Set.

As a category, I agree, but there is not *the* graph domain.

Ralf