Lemma make_adj_equivalence_of_cats'_counit_is_nat_trans : is_nat_trans _ _ make_adj_equivalence_of_cats'_counit_nat_trans_data. Proof. intros a a' f. symmetry. apply z_iso_inv_on_right. rewrite assoc. apply z_iso_inv_on_left. symmetry. apply nat_trans_ax. Qed.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.Adjunctions.Core.