Lemma z_iso_disp_z_iso_fiber (a b : fiber_category) : z_iso a b ≃ z_iso_disp (identity_z_iso c) a b. Proof. exists (z_iso_disp_from_z_iso_fiber a b). use (isweq_iso _ (z_iso_fiber_from_z_iso_disp _ _ )). - intro. apply z_iso_eq. apply idpath. - intro. apply eq_z_iso_disp. apply idpath. Defined.
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.Core.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.NaturalTransformations. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Total.