Definition is_strictlytensorpreserving (tpd : tensor_preserving_data) : UU := ∏ (x y : C), ∑ (pf : (F x) ⊗_{N} (F y) = F (x ⊗_{M} y)), (tpd x y ) = transportf _ pf (identity ((F x) ⊗_{N} (F y))).
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.