Definition hor_id_data {C : category} (D : twosided_disp_cat C C) : UU := ∑ (Im : ∏ (x : C), D x x), ∏ (x y : C) (f : x --> y), Im x -->[ f ][ f ] Im y.
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.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos.