fact: Definition hset_coequalizer_struct_laws {P : hset_struct} (EP : hset_coequalizer_struct_data P) : UU := (∏ (X Y : hSet) (f g : X → Y) (PX : P X) (PY : P Y) (Pf : mor_hset_struct P PX PY f) (Pg : mor_hset_struct P PX PY g), mor_hset_struct P PY (hset_struct_coequalizer EP Pf Pg) (coequalizer_map_hSet f g)) × (∏ (X Y : hSet) (f g : X → Y) (PX : P X) (PY : P Y) (Pf : mor_hset_struct P PX PY f) (Pg : mor_hset_struct P PX PY g) (Z : hSet) (PZ : P Z) (h : Y → Z) (Ph : mor_hset_struct P PY PZ h) (q : (λ w, h(f w)) = (λ w, h(g w))), mor_hset_struct P (hset_struct_coequalizer EP Pf Pg) PZ (coequalizer_out_hSet f g h (eqtohomot q))).
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