[Haskell-beginners] Is there a name for the following?

Hello -- I'm wondering if there is any "name" for a functor "F" that has a function with the following type: (a -> F b) -> F (a -> b) or (F a -> F b) -> F (a -> b) If there is, I would imagine it being related to Applicative in some way, though clearly there are many Applicatives that do not have an implementation of this. Thanks. -- gregory malecha