Definition double_associator {C : category} {D : twosided_disp_cat C C} {Cm : hor_comp D} (a : double_cat_associator Cm) {w x y z : C} (h₁ : D w x) (h₂ : D x y) (h₃ : D y z) : double_hor_comp Cm h₁ (double_hor_comp Cm h₂ h₃) -->[ identity w ][ identity z ] double_hor_comp Cm (double_hor_comp Cm h₁ h₂) h₃ := pr1 a w x y z 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.