Definition make_adj_equivalence_of_cats {A B : category} (F : functor A B) (G : functor B A) η ε (H1 : form_adjunction F G η ε) (H2 : forms_equivalence ((F,,G,,η,,ε))) : adj_equivalence_of_cats F. Proof. use tpair. - exists G. exists (η,,ε). apply H1. - apply H2. Defined.
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.