Why Functor class has no return function?

Question

From categorical point of view, functor is pair of two maps (one between objects and another between arrows of categories), following some axioms.

I have assumed, wh

Answer 1

If you have

instance Functor F where
    fmap = ...

Then the type constructor F is the action on objects (which are types) taking a type T to the type F T, and fmap is the action on morphisms (which are functions) taking a function f :: T -> U to fmap f :: F T -> F U.