Definition cartesian_closed_struct_poset_data : hset_cartesian_closed_struct_data. Proof. refine (cartesian_struct_poset ,, _ ,, _). - abstract (intros X Y PX PY y x₁ x₂ p ; cbn ; apply refl_PartialOrder). - exact (λ X Y PX PY, poset_fun_space PX PY). Defined.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.OrderTheory.Posets. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Categories.HSET.All. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.Equalizers. Require Import UniMath.CategoryTheory.Limits.Products. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Structures.CartesianStructure. Require Import UniMath.CategoryTheory.DisplayedCats.Structures.StructureLimitsAndColimits.