Definition swapping_of_monoidal_cat: monoidal_cat. Proof. use (make_monoidal_cat M swapping_of_tensor). - exact (monoidal_cat_unit M). - apply monoidal_cat_right_unitor. - apply monoidal_cat_left_unitor. - exact associator_swapping_of_tensor. - exact triangle_eq_swapping_of_tensor. - exact pentagon_eq_swapping_of_tensor. Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.ProductCategory. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.whiskering.