Definition twosided_cartesian_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_cartesian fg) {x₀ : C₁} {y₀ : C₂} {xy₀ : D x₀ y₀} {f' : x₀ --> x₁} {g' : y₀ --> y₁} (fg' : xy₀ -->[ f' · f ][ g' · g ] xy₂) : xy₀ -->[ f' ][ g' ] xy₁ := 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.