x (F : Functor D' D) : diagonal_functor C D x o F = diagonal_functor _ _ x. Proof. path_functor. Qed.
Require Import Category.Core Functor.Core NaturalTransformation.Core. Require Import Functor.Composition.Core. Require Import ExponentialLaws.Law1.Functors FunctorCategory.Core. Require Import KanExtensions.Core InitialTerminalCategory.Core NatCategory. Require Import Functor.Paths. Import Comma.Core.