proposition: Lemma comonoid_disp_lunitor (m : comonoid M) : comonoid_mor_struct M (tensor_of_comonoids comonoid_disp_unit m) m (mon_lunitor m).
proof: Proof. use make_is_comonoid_mor. - cbn. etrans. { apply maponpaths. apply pathsinv0. apply (precompose_inner_swap_with_lunitors_on_right (M)). } refine (_ @ monoidal_leftunitornat M _ _ δ_{m}). rewrite ! assoc. apply maponpaths_2. etrans. { apply maponpaths_2. rewrite assoc'. apply maponpaths. apply inner_swap_inv. } rewrite id_right. rewrite <- (when_bifunctor_becomes_rightwhiskering M). etrans. { apply pathsinv0, tensor_comp_mor. } rewrite id_right. rewrite <- (when_bifunctor_becomes_leftwhiskering M). apply maponpaths_2. apply (monoidal_leftunitorisolaw M I_{M}). - refine (_ @ monoidal_leftunitornat M _ _ ε_{m}). rewrite id_right. cbn. apply maponpaths_2. apply (when_bifunctor_becomes_leftwhiskering 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.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.Functors UniMath.CategoryTheory.Monoidal.Displayed.WhiskeredDisplayedBifunctors UniMath.CategoryTheory.Monoidal.Displayed.Monoidal UniMath.CategoryTheory.Monoidal.Displayed.TotalMonoidal UniMath.CategoryTheory.Monoidal.Examples.Fullsub UniMath.CategoryTheory.Monoidal.Examples.Sigma UniMath.CategoryTheory.Monoidal.Structure.Cartesian UniMath.CategoryTheory.Monoidal.Structure.Symmetric UniMath.CategoryTheory.Monoidal.Structure.SymmetricDiagonal UniMath.CategoryTheory.Monoidal.Displayed.Symmetric UniMath.CategoryTheory.Monoidal.Comonoids.Category