fact: Definition hset_binary_coprod_struct_laws {P : hset_struct} (EP : hset_binary_coprod_struct_data P) : UU := (∏ (X Y : hSet) (PX : P X) (PY : P Y), mor_hset_struct P PX (hset_struct_binary_coprod EP PX PY) inl) × (∏ (X Y : hSet) (PX : P X) (PY : P Y), mor_hset_struct P PY (hset_struct_binary_coprod EP PX PY) inr) × (∏ (X Y Z : hSet) (PX : P X) (PY : P Y) (PZ : P Z) (f : X → Z) (g : Y → Z) (Pf : mor_hset_struct P PX PZ f) (Pg : mor_hset_struct P PY PZ g), mor_hset_struct P (hset_struct_binary_coprod EP PX PY) PZ (sumofmaps f g)).
imports: UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Categories.HSET.All UniMath.CategoryTheory.Limits.Equalizers UniMath.CategoryTheory.Limits.Coequalizers UniMath.CategoryTheory.Limits.Products UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Coproducts UniMath.CategoryTheory.exponentials UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Binproducts UniMath.CategoryTheory.Monads.Monads UniMath.CategoryTheory.Monads.MonadAlgebras UniMath.CategoryTheory.DisplayedCats.Structures.CartesianStructure