Lemma make_adj_equivalence_of_cats'_form_adjunction : form_adjunction F G make_adj_equivalence_of_cats'_unit make_adj_equivalence_of_cats'_counit. Proof. use make_form_adjunction. - intro a. refine (maponpaths (λ x, x · _) (functor_on_inv_from_z_iso _ _) @ _). apply z_iso_inv_on_right. symmetry. refine (id_right _ @ _). refine (_ @ id_right _). symmetry. apply z_iso_inv_on_right. symmetry. apply (pr2 H1). - intro a. refine (maponpaths _ (functor_on_inv_from_z_iso _ _) @ _). apply z_iso_inv_on_right. symmetry. refine (id_right _ @ _). refine (_ @ id_right _). symmetry. apply z_iso_inv_on_right. symmetry. apply (pr1 H1). 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.