Lemma functor_unit_disp_cat_is_univalent : is_univalent_disp (functor_unit_disp_cat IC ID). 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.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalCategoriesTensored.