fact: Definition closed_under_fun_laws (P : hset_cartesian_closed_struct_data) : UU := (∏ (X Y : hSet) (PX : P X) (PY : P Y), mor_hset_struct P (hset_struct_prod P PX (hset_struct_fun P PX PY)) PY (λ xf, pr12 xf (pr1 xf))) × (∏ (X Y Z : hSet) (PX : P X) (PY : P Y) (PZ : P Z) (f : X × Z → Y) (Pf : mor_hset_struct P (hset_struct_prod P PX PZ) PY f), mor_hset_struct P PZ (hset_struct_fun P PX PY) (λ z, _ ,, hset_struct_pointwise P f Pf z)).
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