Definition strictlyunitpreserving_is_strong {C D : category} {M : monoidal C} {N : monoidal D} {F : functor C D} {pu : preserves_unit M N F} (pus : preserves_unit_strictly pu) : preserves_unit_strongly pu. Proof. use (iso_stable_under_equalitytransportf (pr2 pus) (is_z_isomorphism_identity I_{N})). Defined.
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.