Definition is_causal : UU := ∏ (x y z w : C) (f : x --> y) (g : y --> z) (h1 h2 : z --> w), f · (g · ⟨h1, identity z⟩) = f · (g · ⟨h2, identity z⟩) -> f · ⟨g · ⟨h1, identity z⟩, identity y⟩ = f · ⟨g · ⟨h2, identity z⟩, identity y⟩.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Structure.Cartesian. Require Import UniMath.CategoryTheory.Monoidal.Structure.Symmetric. Require Import UniMath.CategoryTheory.MarkovCategories.MarkovCategory. Require Import UniMath.CategoryTheory.MarkovCategories.Determinism. Require Import UniMath.CategoryTheory.MarkovCategories.AlmostSurely. Require Import UniMath.CategoryTheory.MarkovCategories.Univalence. Import MonoidalNotations.