fact: Definition preserves_underlying_laws {V₁ V₂ : monoidal_cat} {F : lax_monoidal_functor V₁ V₂} (Fv : preserve_underlying_data F) : UU := (∏ (v : V₁) (f : I_{V₂} --> F v), mon_functor_unit F · #F (Fv v f) = f) × (∏ (v : V₁) (f : I_{V₁} --> v), Fv v (mon_functor_unit F · #F f) = f).
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.EnrichedCats.Enrichment UniMath.CategoryTheory.EnrichedCats.EnrichmentFunctor UniMath.CategoryTheory.EnrichedCats.EnrichmentTransformation UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.Functors