proposition: Proposition is_univalent_disp_disp_cat_of_strict_twosided_disp_cat : is_univalent_disp disp_cat_of_strict_twosided_disp_cat.
proof: Proof. use is_univalent_disp_from_fibers. intros C D₁ D₂. cbn in C, D₁, D₂. use weqhomot. - refine (_ ∘ path_sigma_hprop _ _ _ (isaprop_is_strict_twosided_disp_cat _))%weq. refine (_ ∘ make_weq _ (isweqmaponpaths (two_sided_disp_cat_weq_disp_cat C C) D₁ D₂))%weq. refine (_ ∘ disp_cat_eq _ _)%weq. use weqtotal2. + exact (invweq (two_sided_disp_functor_weq_disp_functor (functor_identity C) (functor_identity C) D₁ D₂) ∘ disp_functor_over_pair_weq _ _)%weq. + intro F. apply is_z_iso_disp_strict_twosided_disp_cat_weq. - intro p. induction p. use subtypePath. { intro. apply isaprop_is_z_iso_disp. } use subtypePath. { intro. apply isaprop_twosided_disp_functor_laws. } apply idpath. Qed.
imports: UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.Core.Setcategories UniMath.CategoryTheory.Categories.CategoryOfSetCategories UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Functors UniMath.CategoryTheory.DisplayedCats.NaturalTransformations UniMath.CategoryTheory.DisplayedCats.Isos UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.Univalence UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.CategoryTheory.DisplayedCats.DisplayedCatEq UniMath.CategoryTheory.DisplayedCats.Examples.DispFunctorPair UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat UniMath.CategoryTheory.TwoSidedDisplayedCats.DisplayedFunctor UniMath.CategoryTheory.TwoSidedDisplayedCats.DisplayedNatTrans UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence UniMath.CategoryTheory.TwoSidedDisplayedCats.Strictness UniMath.CategoryTheory.TwoSidedDisplayedCats.TransportLaws