proposition: Lemma diagonal_is_comonoid_mor_counit (m : comonoid V) : is_comonoid_mor_counit V m (tensor_of_comonoids V m m) δ_{m}.
proof: Proof. unfold is_comonoid_mor_counit. cbn. unfold monoidal_cat_tensor_mor. unfold functoronmorphisms1. rewrite ! assoc'. etrans. { apply maponpaths. apply maponpaths. exact (monoidal_leftunitornat V _ _ ε_{m}). } refine (_ @ id_left _). rewrite ! assoc. apply maponpaths_2. exact (comonoid_to_law_unit_left _ m). Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.Functors UniMath.CategoryTheory.Monoidal.Displayed.Monoidal UniMath.CategoryTheory.Monoidal.Displayed.TotalMonoidal UniMath.CategoryTheory.Monoidal.Structure.Cartesian UniMath.CategoryTheory.Monoidal.Structure.Symmetric UniMath.CategoryTheory.Monoidal.Structure.SymmetricDiagonal UniMath.CategoryTheory.Monoidal.Displayed.Symmetric UniMath.CategoryTheory.Categories.Dialgebras UniMath.CategoryTheory.Monoidal.Examples.MonoidalDialgebras UniMath.CategoryTheory.Monoidal.Comonoids.Category UniMath.CategoryTheory.Monoidal.Comonoids.Tensor UniMath.CategoryTheory.Monoidal.Comonoids.Monoidal UniMath.CategoryTheory.Monoidal.Comonoids.Symmetric UniMath.CategoryTheory.Monoidal.Comonoids.MonoidalCartesianBuilder