In a category,
what is the concept for "a generalized arrow from an object to an arrow"? For example, in programming language, such a generalized arrow is a curried function, i.e. a function which has a single parameter and returns a function.
what is the concept for a mapping that maps "a generaized arrow from an object to an arrow" to "another generalized arrow from an object to an arrow" (I think an applicative functor is such a mapping, but with more "generalization" on arrows.) We know that an endofunctor maps "an arrow" to "another arrow".
Thanks.