Haskell Functor vs \(\Hask\) Functor

A Haskell Functor is a type F :: * -> * which belong to the type class Functor ; thus instantiate fmap :: (a -> b) -> (F a -> F b).

& F: \(\ob{\Hask}→\ob{\Hask}\)
& fmap: \(\hom{\Hask}→\hom{\Hask}\)

The couple (F,fmap) is a \(\Hask\)'s functor if for any x :: F a:

• fmap id x = x
• fmap (f.g) x= (fmap f . fmap g) x