Definition disp_alg_bicat_univalent_2_0 (HC : is_univalent_2_1 C) : disp_univalent_2_0 disp_alg_bicat. Proof. intros a b p aa bb. induction p. use weqhomot. - exact (disp_alg_bicat_adjoint_equivalence_weq HC aa bb ∘ (_ ,, HC _ _ aa bb))%weq. - intros p. induction p ; cbn. use subtypePath. + intro ; simpl. apply (@isaprop_disp_left_adjoint_equivalence C disp_alg_bicat). * exact HC. * exact disp_alg_bicat_univalent_2_1. + cbn ; unfold left_adjoint_2cell ; cbn. use subtypePath. { intro ; apply isaprop_is_invertible_2cell. } cbn. rewrite id2_right. reflexivity. Defined.
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.PrecategoryBinProduct. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat. Require Import UniMath.Bicategories.PseudoFunctors.PseudoFunctor. Import PseudoFunctor.Notations. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.DisplayedBicats.DispAdjunctions. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence.