Definition disp_functor_on_is_z_iso_disp {C C'} {F} {D : disp_cat C} {D' : disp_cat C'} (FF : disp_functor F D D') {x y} {xx : D x} {yy} {f : z_iso x y} {ff : xx -->[f] yy} (Hff : is_z_iso_disp f ff) : is_z_iso_disp (functor_on_z_iso F f) (♯ FF ff). Proof. exists (transportf _ (functor_on_inv_from_z_iso F f) (♯ FF (inv_mor_disp_from_z_iso Hff))); split. - apply disp_functor_on_z_iso_disp_aux1. - apply disp_functor_on_z_iso_disp_aux2. Defined.
Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Isos.