Definition strictlyunitpreserving_is_strong {upd : unit_preserving_data} (pfstrict : is_strictlyunitpreserving upd) : is_stronglyunitpreserving upd. Proof. use (iso_stable_under_equalitytransportation (pr2 pfstrict) (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.Isos. Require Import UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalCategoriesCurried.