Definition rezk_completion_2_1 (R : RezkCat) (B : bicat) : ∑ RB : bicat, ∑ HB : psfunctor B RB, is_univalent_2_1 RB × weak_biequivalence HB. Proof. exists (LRB R B). exists (psfunctor_B_to_LRB R B). exists (LRB_is_locally_univalent R B). exact (psfunctor_B_to_LRB_is_weak_biequivalence R B). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.YonedaLemma. Require Import UniMath.Bicategories.PseudoFunctors.PseudoFunctor. Require Import UniMath.Bicategories.PseudoFunctors.Examples.Composition. Require Import UniMath.Bicategories.PseudoFunctors.Properties. Require Import UniMath.Bicategories.RezkCompletions.BicatToLocalUnivalentBicat. Require Import UniMath.CategoryTheory.RezkCompletions.Construction. Require Import UniMath.CategoryTheory.RezkCompletions.RezkCompletions.