proposition: Lemma bidisp_unit_disp_prebicat_is_globally_univalent : disp_univalent_2_0 bidisp_unit_disp_bicat.
proof: Proof. intros C D equalcats IC ID. induction equalcats. use weqhomot. - set (i1 := iso_dispadjequiv_equivalence C IC ID). set (i3 := (_ ,, (pr2 C) IC ID)). exact (i1 ∘ i3)%weq. - intro p. induction p; cbn. use subtypePath. + intro; simpl. apply (@isaprop_disp_left_adjoint_equivalence bicat_of_univ_cats bidisp_unit_disp_bicat). * exact univalent_cat_is_univalent_2_1. * exact bidisp_unit_disp_prebicat_is_locally_univalent. + apply idpath. Defined.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Functors UniMath.CategoryTheory.DisplayedCats.Total UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.Examples.BicatOfUnivCats UniMath.Bicategories.DisplayedBicats.DispBicat UniMath.Bicategories.DisplayedBicats.DispUnivalence UniMath.Bicategories.MonoidalCategories.UnivalenceMonCat.CurriedMonoidalCategories