Lemma rad_equivalence_of_cats (A B : category) (HA : is_univalent A) (F : functor A B) (HF : fully_faithful F) (HS : essentially_surjective F) : adj_equivalence_of_cats F. Proof. apply rad_equivalence_of_cats'. - exact HF. - apply ff_essentially_surjective_to_split; assumption. 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.