proposition: Lemma functor_unit_disp_cat_is_univalent : is_univalent_disp (functor_unit_disp_cat IC ID).
proof: Proof. apply is_univalent_disp_from_fibers. intros F pt1 pt2. use isweqimplimpl. - intro i. refine (_ @ pr1 i). apply (! id_right _). - apply D. - apply isaproptotal2. + intro ; apply Isos.isaprop_is_z_iso_disp. + do 4 intro ; apply D. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.CategoryTheory.DisplayedCats.Univalence UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalCategoriesTensored