fact: Definition hset_struct_laws (P : hset_struct_data) : UU := (∏ (X : hSet), isaset (P X)) × (∏ (X Y : hSet) (PX : P X) (PY : P Y) (f : X → Y), isaprop (mor_hset_struct P PX PY f)) × (∏ (X : hSet) (PX : P X), mor_hset_struct P PX PX (λ x, x)) × (∏ (X Y Z : hSet) (PX : P X) (PY : P Y) (PZ : P Z) (f : X → Y) (g : Y → Z) (Mf : mor_hset_struct P PX PY f) (Mg : mor_hset_struct P PY PZ g), mor_hset_struct P PX PZ (λ x, g(f x))) × (∏ (X : hSet) (PX PX' : P X), mor_hset_struct P PX PX' (λ x, x) → mor_hset_struct P PX' PX (λ x, x) → PX = PX').
imports: UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Categories.HSET.All UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.Univalence UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.CategoryTheory.DisplayedCats.SIP UniMath.CategoryTheory.DisplayedCats.Binproducts