Definition is_z_iso_disp {C : precategory} {D : disp_cat_data C} {x y : C} (f : z_iso x y) {xx : D x} {yy : D y} (ff : xx -->[f] yy) : UU := ∑ (gg : yy -->[inv_from_z_iso f] xx), (gg ;; ff = transportb _ (z_iso_after_z_iso_inv _) (id_disp _)) × (ff ;; gg = transportb _ (z_iso_inv_after_z_iso _) (id_disp _)).
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.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Core.Isos. Import BifunctorNotations. Import DisplayedBifunctorNotations.