Lemma action_unitor_nat_z_iso {C : category} (Act : actegory C): nat_z_iso (leftwhiskering_functor Act I_{Mon_V}) (functor_identity C). Proof. use make_nat_z_iso. - use make_nat_trans. + exact (λ x, au_{Act} x). + exact (λ x y f, actegory_unitornat Act x y f). - intro x. exists (auinv_{Act} x). apply (actegory_unitorisolaw Act x). Defined.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.Foundations.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.Equivalences.Core. Require Import UniMath.CategoryTheory.Equivalences.FullyFaithful. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Import BifunctorNotations. Import MonoidalNotations. Section EquivalenceFromTensorWithUnit. Import MonoidalNotations. End EquivalenceFromTensorWithUnit. Import MonoidalNotations. Import ActegoryNotations.