Definition monoidal_to_monoidal_struct {C : category} (M : monoidal C) : monoidal_struct C. Proof. exists (monoidal_to_tensor_unit_unitors_associator M). repeat split. - exact (monoidal_triangleidentity M). - exact (monoidal_pentagonidentity M). - exists (monoidal_leftunitorinvdata M). exact (monoidal_leftunitorisolaw M). - exists (monoidal_rightunitorinvdata M). exact (monoidal_rightunitorisolaw M). - exists (monoidal_associatorinvdata M). exact (monoidal_associatorisolaw M). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories.