fact: Definition hset_cartesian_struct_laws (P : hset_cartesian_struct_data) : UU := (∏ (X : hSet) (PX : P X), mor_hset_struct P PX (hset_struct_unit P) (λ _ : X, tt)) × (∏ (X Y : hSet) (PX : P X) (PY : P Y), mor_hset_struct P (hset_struct_prod P PX PY) PX dirprod_pr1) × (∏ (X Y : hSet) (PX : P X) (PY : P Y), mor_hset_struct P (hset_struct_prod P PX PY) PY dirprod_pr2) × (∏ (W X Y : hSet) (PW : P W) (PX : P X) (PY : P Y) (f : W → X) (g : W → Y) (Mf : mor_hset_struct P PW PX f) (Mg : mor_hset_struct P PW PY g), mor_hset_struct P PW (hset_struct_prod P PX PY) (prodtofuntoprod (f ,, g))).
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