proposition: Proposition make_commutative_comonoid_laws : comonoid_laws V make_commutative_comonoid_data.
proof: Proof. repeat split. - refine (_ @ unit_left) ; cbn. apply maponpaths_2. apply maponpaths. rewrite tensor_mor_right. apply idpath. - refine (_ @ unit_left) ; cbn. refine (!_). etrans. { do 2 apply maponpaths_2. exact (!(comm)). } rewrite !assoc'. apply maponpaths. rewrite !assoc. rewrite <- tensor_sym_mon_braiding. rewrite !assoc'. rewrite sym_mon_braiding_lunitor. apply maponpaths_2. rewrite tensor_mor_left. apply idpath. - unfold comonoid_laws_assoc ; cbn. refine (_ @ assocδ @ _). + apply maponpaths_2. apply maponpaths. rewrite tensor_mor_right. apply idpath. + apply maponpaths. rewrite tensor_mor_left. apply idpath. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Isos UniMath.CategoryTheory.DisplayedCats.Univalence UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.Projection UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.CategoryTheory.DisplayedCats.Examples.Sigma UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.Functors UniMath.CategoryTheory.Monoidal.Structure.Symmetric UniMath.CategoryTheory.Monoidal.Structure.SymmetricDiagonal UniMath.CategoryTheory.Monoidal.Structure.Cartesian UniMath.CategoryTheory.Monoidal.Displayed.WhiskeredDisplayedBifunctors UniMath.CategoryTheory.Monoidal.Displayed.Monoidal UniMath.CategoryTheory.Monoidal.Displayed.TotalMonoidal UniMath.CategoryTheory.Monoidal.Displayed.Symmetric UniMath.CategoryTheory.Monoidal.Examples.Sigma UniMath.CategoryTheory.Monoidal.Examples.Fullsub UniMath.CategoryTheory.Monoidal.Examples.DiagonalFunctor UniMath.CategoryTheory.Monoidal.Examples.ConstantFunctor UniMath.CategoryTheory.Monoidal.CategoriesOfMonoids UniMath.CategoryTheory.Categories.Dialgebras