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