Definition preserves_leftunitality {C D : category} {M : monoidal C} {N : monoidal D} {F : functor C D} (pt : preserves_tensordata M N F) (pu : preserves_unit M N F) : UU := ∏ (x : C), (pu ⊗^{ N}_{r} F x) · (pt I_{M} x) · (# F lu^{ M }_{ x}) = lu^{ N }_{ F x}.
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.