Definition make_strong_monoidal_functor {V₁ V₂ : monoidal_cat} (F : lax_monoidal_functor V₁ V₂) (Hμ : ∏ (x y : V₁), is_z_isomorphism (mon_functor_tensor F x y)) (Hη : is_z_isomorphism (mon_functor_unit F)) : strong_monoidal_functor V₁ V₂ := pr1 F ,, pr2 F ,, Hμ ,, Hη.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Structure.Symmetric. Import BifunctorNotations. Import MonoidalNotations.