Definition rezk_completion_functor_equivalence : adj_equivalence_of_cats (pre_composition_functor _ _ C (rezk_completion_functor D)). Proof. use (precomp_adjoint_equivalence (make_univalent_category _ _)). - apply HC. - apply rezk_completion_essentially_surjective. - apply rezk_completion_fully_faithful. 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.