proposition: 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: Proof. apply rad_equivalence_of_cats'. - exact HF. - apply ff_essentially_surjective_to_split; assumption. Defined.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.Tactics UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Adjunctions.Core