Definition disp_functor_ess_split_surj {C' C} {F} {D' : disp_cat C'} {D : disp_cat C} (FF : disp_functor F D D') : UU := ∏ x (xx : D' (F x)), ∑ y : C, ∑ i : z_iso y x, ∑ yy : D y, z_iso_disp (functor_on_z_iso F i) (FF _ yy) xx.
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.