AZ
We can define the categorical version of the Haskell’s applicative functor as a lax closed functor going from a closed category C to Set. It’s a functor equipped with a natural transformation:
f (a => b) -> (f a -> f b)
where a=>b is the internal hom-object in C (the second arrow is a function type in Set), and a function:1 -> f i
where 1 is the singleton set and i is the unit object in C.