Definition full_sub_category_equivalence : equivalence_of_cats (full_sub_category C₁ P) (full_sub_category C₂ Q). Proof. use make_equivalence_of_cats. - use make_adjunction_data. + exact L'. + exact R'. + exact full_sub_category_equivalence_unit. + exact full_sub_category_equivalence_counit. - split. + intro. apply is_iso_full_sub. apply unit_nat_z_iso_from_adj_equivalence_of_cats. + intro. apply is_iso_full_sub. apply counit_nat_z_iso_from_adj_equivalence_of_cats. 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. Require Import UniMath.CategoryTheory.Subcategory.Full. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Equivalences.Core.