Definition hor_id_laws {C : category} {D : twosided_disp_cat C C} (I : hor_id_data D) : UU := (∏ (x : C), double_id_mor I (identity x) = id_two_disp _) × (∏ (x y z : C) (f : x --> y) (g : y --> z), double_id_mor I (f · g) = double_id_mor I f ;;2 double_id_mor I g).
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.