Definition strong_monoidal_functor : UU := ∑ lmF : lax_monoidal_functor, (is_z_isomorphism (lax_monoidal_functor_ϵ lmF)) × (is_nat_z_iso (lax_monoidal_functor_μ lmF)).
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.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalCategoriesTensored. Require Import UniMath.CategoryTheory.whiskering.