I've perhaps been trying everyones patiences with my noobish CT questions, but if you'll bear with me a little longer: I happened to notice that there is in fact a Category class in Haskell base, in Control.Category:
quote: -------- class Category cat where
A class for categories. id and (.) must form a monoid.
Methods
id :: cat a a
This says that 'cat' must be a type constructor with two type arguments. In an instance of this type, a and b will refer to objects of the category and cat a b to the morphisms. Integer is NOT a type constructor with two type arguments, so instance Category Integer makes no sense. [] is a type constructor with one type argument, not two, so instance Category [] makes no sense either. Can you make Either an instance of Category? Can you make (,) an instance of Category? Can you make (a copy of) -> an instance of Category a different way?