(G : (C -> D)%category) : ((D -> E) -> (C -> E))%category := Build_Functor (D -> E) (C -> E) (fun F => F o G)%functor (fun _ _ T => T oR G) (fun _ _ _ _ _ => composition_of_whisker_r _ _ _) (fun _ => whisker_r_left_identity _ _).
Require Import Category.Core Functor.Core. Require Import FunctorCategory.Core Functor.Composition.Core NaturalTransformation.Composition.Core NaturalTransformation.Composition.Laws.