Definition markov_category_laws (C : markov_category_data) : UU := (∏ (x : C), copy x · (identity _ #⊗ copy x) = copy x · (copy x #⊗ identity _) · mon_lassociator _ _ _) × (∏ (x : C), copy x · (identity _ #⊗ del x) · mon_runitor _ = identity _) × (∏ (x : C), copy x · (del x #⊗ identity _) · mon_lunitor _ = identity _) × (∏ (x : C), copy x · sym_mon_braiding _ _ _ = copy x) × (∏ (x y : C), (copy x #⊗ copy y) · inner_swap _ _ _ _ _ = copy (x ⊗ 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.Monoidal.Structure.SymmetricDiagonal. Import MonoidalNotations.