Definition braiding_law_naturality_left {C : category} {M : monoidal C} (B : braiding_data M) : UU := ∏ (x y1 y2 : C) (g : C⟦y1, y2⟧), (B x y1) · (g ⊗^{M}_{r} x) = (x ⊗^{M}_{l} g) · (B x y2).
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Import BifunctorNotations. Import MonoidalNotations.