Definition twosided_disp_cat_comp {C₁ C₂ : precategory_data} (D : twosided_disp_cat_ob_mor C₁ C₂) : UU := ∏ (x₁ x₂ x₃ : C₁) (y₁ y₂ y₃ : C₂) (xy₁ : D x₁ y₁) (xy₂ : D x₂ y₂) (xy₃ : D x₃ y₃) (f₁ : x₁ --> x₂) (f₂ : x₂ --> x₃) (g₁ : y₁ --> y₂) (g₂ : y₂ --> y₃), xy₁ -->[ f₁ ][ g₁ ] xy₂ → xy₂ -->[ f₂ ][ g₂ ] xy₃ → xy₁ -->[ f₁ · f₂ ][ g₁ · g₂ ] xy₃.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.PrecategoryBinProduct.