Definition to_z_iso_disp_op_disp_cat {C : category} {D : disp_cat C} {x y : C} {f : z_iso y x} {xx : D x} {yy : D y} (ff : yy -->[ f ] xx) (Hff : is_z_iso_disp f ff) : @is_z_iso_disp _ (op_disp_cat D) x y (opp_z_iso f) _ _ ff. Proof. simple refine (_ ,, _ ,, _). - simple refine (transportb (λ z, _ -->[ z ] _) _ (inv_mor_disp_from_z_iso Hff)). apply idpath. - cbn. apply inv_mor_after_z_iso_disp. - cbn. apply z_iso_disp_after_inv_mor. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.opp_precat. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence.