proposition: Lemma comonoid_disp_braiding (mx my : comonoid M) : comonoid_mor_struct M (tensor_of_comonoids mx my) (tensor_of_comonoids my mx) (sym_mon_braiding M mx my).
proof: Proof. apply make_is_comonoid_mor. - cbn. etrans. 2: { rewrite assoc. apply maponpaths_2. apply (tensor_sym_mon_braiding). } rewrite ! assoc'. apply comult_before_inner_swap_and_swap. - cbn. rewrite ! assoc. rewrite id_right. apply maponpaths_2. etrans. 2: { apply (tensor_sym_mon_braiding M). } cbn. refine (! id_right _ @ _). apply maponpaths. apply pathsinv0, sym_mon_braiding_id. 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