proposition: Lemma functor_total_cat_univalent : is_univalent D → is_univalent functor_total_cat.
proof: Proof. intros HD. apply is_univalent_total_category. - apply is_univalent_total_category. + apply base_category_univalent, HD. + apply step1_disp_univalent. - apply functor_disp_cat_univalent. Defined.
imports: UniMath.Foundations.PartD UniMath.Foundations.UnivalenceAxiom UniMath.MoreFoundations.Propositions UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.Monads.Monads UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.Isos UniMath.CategoryTheory.DisplayedCats.Univalence UniMath.CategoryTheory.DisplayedCats.Constructions