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.

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gregory malecha