Definition Copresheaf_RezkCompletion_monoidal_universalproperty : ∏ (E : monoidal_cat) (Euniv : is_univalent E), adj_equivalence_of_cats (total_functor (precompMonoidal (univalent_category_is_univalent (Rezk_completion M)) (Rezk_eta_essentially_surjective M) (Rezk_eta_fully_faithful M) _ _ (monoidal_cat_left_unitor M) (monoidal_cat_right_unitor M) (monoidal_cat_associator M) _ _ (monoidal_cat_left_unitor E) (monoidal_cat_right_unitor E) (monoidal_cat_associator E))) := λ E Euniv, RezkCompletion_monoidal_universalproperty M (Rezk_eta_essentially_surjective M) (Rezk_eta_fully_faithful M) E Euniv.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalCategoriesTensored. Require Import UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalFunctorCategory. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.Monoidal.RezkCompletion.LiftedMonoidal. Require Import UniMath.CategoryTheory.RezkCompletions.Construction.