Definition iso_to_nat_iso {C D : category} (F G : C ⟶ D) : @iso (functor_category C D) F G → nat_iso F G. Proof. intros α. use make_nat_iso. - exact (pr1 α). - use is_functor_iso_pointwise_if_iso. apply α. Defined.
Require Import UniMath.Foundations.Propositions. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.MoreFoundations.Univalence. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.TransportMorphisms. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence.