x (F : Functor D' D) : NaturalTransformation (diagonal_functor C D x o F) (diagonal_functor _ _ x) := Build_NaturalTransformation (diagonal_functor C D x o F) (diagonal_functor _ _ x) (fun z => identity _) (fun _ _ _ => transitivity (left_identity _ _ _ _) (symmetry _ _ (right_identity _ _ _ _))).
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.