fact: Definition hset_struct_set_coprod_laws {P : hset_struct} {I : hSet} (HP : hset_struct_set_coprod_data P I) : UU := (∏ (D : I → hSet) (PD : ∏ (i : I), P (D i)) (i : I), mor_hset_struct P (PD i) (HP D PD) (λ d, i ,, d)) × (∏ (D : I → hSet) (PD : ∏ (i : I), P (D i)) (W : hSet) (PW : P W) (fs : ∏ (i : I), D i → W) (Pfs : ∏ (i : I), mor_hset_struct P (PD i) PW (fs i)), mor_hset_struct P (HP D PD) PW (λ id, fs (pr1 id) (pr2 id))).
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