Theorem rezk_completion_opp_universal_property : isweq (pre_composition_functor A^op D^op C (functor_opp (rezk_completion_functor D))). Proof. apply adj_equiv_of_cats_is_weq_of_objects. - apply is_univalent_functor_category; exact HC. - apply is_univalent_functor_category; exact HC. - apply rezk_completion_opp_functor_equivalence. 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.