What is the name of this type of function composition?

Question

If standard function composition is defined as:

 (define compose
   { (B → C) → (A → B) 
             → (A → C) }

   F G -> (λ X (F (G X))))

What type of composition does the below function describe? Is there a particular name for it in category theory?

 (define compose-2
   { (A → (X → C)) → (B → X)
                   → (A → B → C) }

   F G -> (λ Y (compose (F Y) G)))