Definition twosided_opcartesian_factorisation {x₁ x₂ : C₁} {y₁ y₂ : C₂} {xy₁ : D x₁ y₁} {xy₂ : D x₂ y₂} {f : x₁ --> x₂} {g : y₁ --> y₂} {fg : xy₁ -->[ f ][ g ] xy₂} (H : twosided_opcartesian fg) {x₃ : C₁} {y₃ : C₂} {xy₃ : D x₃ y₃} {f' : x₂ --> x₃} {g' : y₂ --> y₃} (fg' : xy₁ -->[ f · f' ][ g · g' ] xy₃) : xy₂ -->[ f' ][ g' ] xy₃ := pr11 (H _ _ _ _ _ fg').
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Discrete.