proposition: Proposition monad_to_hset_struct_type_prod_laws (J : UU) : hset_struct_type_prod_laws (monad_to_hset_struct_type_prod_data J).
proof: Proof. split. - intros D PD i. apply idpath. - intros D PD W hW ps Mps. cbn -[Monad] in *. use funextsec ; intro x. use funextsec ; intro i. refine (eqtohomot (Mps i) x @ _). apply maponpaths. refine (!_). exact (!(eqtohomot (functor_comp M _ _) _)). Qed.
imports: UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Categories.HSET.All UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Equalizers UniMath.CategoryTheory.Limits.Coequalizers UniMath.CategoryTheory.Limits.Products UniMath.CategoryTheory.Limits.Preservation UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Structures.CartesianStructure UniMath.CategoryTheory.DisplayedCats.Structures.StructureLimitsAndColimits UniMath.CategoryTheory.Monads.Monads