proposition: Lemma leftunitor_nat_z_iso {C : category} (M : monoidal C) : nat_z_iso (leftwhiskering_functor M I_{M}) (functor_identity C).
proof: Proof. use make_nat_z_iso. - use make_nat_trans. + exact (λ x, lu_{M} x). + exact (λ x y f, monoidal_leftunitornat M x y f). - intro x. exists (luinv_{M} x). apply (monoidal_leftunitorisolaw M x). Defined.
imports: UniMath.Foundations.All UniMath.MoreFoundations.Notations UniMath.MoreFoundations.PartA UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Equivalences.Core UniMath.CategoryTheory.Equivalences.FullyFaithful UniMath.CategoryTheory.opp_precat