Definition rezk_completion_of_univalent {A : univalent_category} (D : rezk_completion A) : adj_equivalence_of_cats (rezk_completion_functor D). Proof. apply rad_equivalence_of_cats. - apply univalent_category_is_univalent. - apply rezk_completion_fully_faithful. - apply rezk_completion_essentially_surjective. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.Propositions. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.opp_precat. Require Import UniMath.CategoryTheory.PrecompEquivalence. Require Import UniMath.CategoryTheory.WeakEquivalences.Core. Require Import UniMath.CategoryTheory.whiskering.