Definition is_z_iso_disp {C : precategory} {D : disp_cat_data C} {x y : C} (f : z_iso x y) {xx : D x} {yy} (ff : xx -->[f] yy) : UU := ∑ (gg : yy -->[inv_from_z_iso f] xx), is_disp_inverse (z_iso_is_inverse_in_precat f) ff gg.
Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Core.