s d (m : morphism ((C -> D) * (C -> D')) s d) : morphism (_ -> _) (fst s * snd s)%functor (fst d * snd d)%functor := fst_type m * snd_type m.
Require Import Category.Core Functor.Core Functor.Prod.Core FunctorCategory.Core Category.Prod NaturalTransformation.Prod NaturalTransformation.Composition.Core. Require Import NaturalTransformation.Paths.