fact: Definition preserves_unit {C D : category} (M : monoidal C) (N : monoidal D) (F : functor C D) : UU := D ⟦ I_{N} , F I_{M} ⟧.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.Structure.Symmetric