Lemma symmetric_whiskers_swap_is_nat_iso {C : category} {M : monoidal C} (B : symmetric M) (x : C) : is_nat_z_iso (symmetric_whiskers_swap_nat_trans B x). Proof. intro y. exists ((monoidal_braiding_data B) y x). split ; apply monoidal_braiding_inverses. Defined.
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.