In category, a contravariant functor is not thing but a functor with reversed output. For example, given type a, b in category C and a morphism f :: a -> b, a functor CF is a contravariant functor if CF f has type as CF b -> CF a

Data.Functor.Contravariant

class Contravariant f where
  contramap :: (a -> b) -> f b -> f a
  (>$) :: b -> f b -> f a
  (>$) = contramap . const