proposition: Proposition is_univalent_cat_of_setcategory : is_univalent cat_of_setcategory.
proof: Proof. intros C D. use weqhomot. - exact (weqfibtototal _ _ is_catiso_weq_is_z_isomorphism ∘ catiso_is_path_cat _ _ ∘ path_setcategory _ _)%weq. - intro p. induction p. use z_iso_eq. use subtypePath. { intro. apply isaprop_is_functor. apply homset_property. } apply idpath. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Setcategories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.catiso UniMath.CategoryTheory.CategoryEquality