Definition double_associator_data {C : category} {D : twosided_disp_cat C C} (Cm : hor_comp D) : UU := ∏ (w x y z : C) (h₁ : D w x) (h₂ : D x y) (h₃ : D y z), iso_twosided_disp (identity_z_iso w) (identity_z_iso z) (double_hor_comp Cm h₁ (double_hor_comp Cm h₂ h₃)) (double_hor_comp Cm (double_hor_comp Cm h₁ h₂) h₃).
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.