Definition twosided_cleaving : UU := ∏ (x₁ x₂ : C₁) (y : C₂) (xy₂ : D x₂ y) (f : x₁ --> x₂), ∑ (xy₁ : D x₁ y) (ℓ : xy₁ -->[ f ][ identity _ ] xy₂), twosided_cartesian ℓ.
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.