Definition full_image_inclusion_commute_nat_iso {C₁ C₂ : category} (F : C₁ ⟶ C₂) : nat_z_iso (functor_full_img F ∙ sub_precategory_inclusion C₂ (full_img_sub_precategory F)) F. Proof. use make_nat_z_iso. - exact (full_image_inclusion_commute F). - intro. apply identity_is_z_iso. Defined.
Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Subcategory.Core.