Functor B C. Proof. refine (Build_Functor B C (fun xym__Fx_to_Gy => fun x y z m1 m2 => p_morphism_of G m1 o xym__Fx_to_Gy x y m2)%functor (fun xym__s xym__d xym__m => fun x y z m1 m2 => p_morphism_of G m1 oL xym__m x y m2) _ _); simpl; repeat (intro || apply path_forall); [ apply composition_of_whisker_l | apply whisker_l_right_identity ]. Defined.
Require Import Category.Core Functor.Core NaturalTransformation.Core. Require Import Pseudofunctor.Core. Require Import Category.Morphisms FunctorCategory.Morphisms. Require Import Functor.Composition.Core. Require Import NaturalTransformation.Composition.Core NaturalTransformation.Composition.Laws. Require Import NaturalTransformation.Identity.