A Functor is a fundamental category-theoretical term with a specific definition that simply isn't captured by something vague like "Mappable". Precision is impo

A Functor is a fundamental category-theoretical term with a specific definition that simply isn't captured by something vague like "Mappable". Precision is important when talking about such terms. It is not at all clear that (-> a) is "Mappable". Lots of terms like Profunctor, Contravariant Functor, Bifunctor etc. (which are also the names of typecasses in Haskell) rely on the precise, category-theoretical definition of Functor.