Definition hor_comp_data {C : category} (D : twosided_disp_cat C C) : UU := ∑ (Cm : ∏ (x y z : C), D x y → D y z → D x z), ∏ (x₁ x₂ y₁ y₂ z₁ z₂ : C) (v₁ : x₁ --> x₂) (v₂ : y₁ --> y₂) (v₃ : z₁ --> z₂) (h₁ : D x₁ y₁) (h₂ : D y₁ z₁) (k₁ : D x₂ y₂) (k₂ : D y₂ z₂) (s₁ : h₁ -->[ v₁ ][ v₂ ] k₁) (s₂ : h₂ -->[ v₂ ][ v₃ ] k₂), Cm _ _ _ h₁ h₂ -->[ v₁ ][ v₃ ] Cm _ _ _ k₁ k₂.
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.