[gclaramunt]

If you consider subtyping, Bottom is a type IIRC, In the category with types as objects and subtyping relationship (a->b if b is subtype of a) as morphisms, Any is the initial object and Bottom is the final object of the category

[catnaroek]

I think normally one considers the opposite category, where arrows go from subtypes to supertypes, because it can be embedded in the usual category of types and functions, by considering each arrow as the upcasting function.