Either a :: Type -> Type is a Haskell Functor (endofunctor), mapping (->) to (->). Either :: Type -> (Type -> Type) is not an endofunctor, it maps a type t

Either a :: Type -> Type is a Haskell Functor (endofunctor), mapping (->) to (->). Either :: Type -> (Type -> Type) is not an endofunctor, it maps a type to a type constructor and thus maps (->) to (~>) (natural transformations). If you uncurried Either, you would also get a non-endofunctor which maps from (-×>) (product category) to (->). Either' :: (Type, Type) -> Type Every function is a functor between equality, since equality satisfies congruence: isPrime :: Integer -> Bool is a functor between (:~:) @Integer an (:~:) @Bool. Boolean negation is a function between "less than or equal" to "greater than or equal" categories; mapping (<=) to (>=): not :: Bool -> Bool