(x : object ((C -> D) * (C -> D'))) : functor_morphism_of (identity x) = identity _. Proof. path_natural_transformation; reflexivity. Qed.
Require Import Category.Core Functor.Core Functor.Prod.Core FunctorCategory.Core Category.Prod NaturalTransformation.Prod NaturalTransformation.Composition.Core. Require Import NaturalTransformation.Paths.