proposition: Proposition monad_to_hset_equalizer_struct_laws : hset_equalizer_struct_laws monad_to_hset_equalizer_struct_data.
proof: Proof. split. - intros X Y f g hX hY Mf Mg. apply idpath. - intros X Y f g hX hY Mf Mg W hW k Mk q. use funextsec. intro x. use subtypePath. { intro. apply setproperty. } cbn -[Monad] in *. refine (eqtohomot Mk 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