Definition hset_struct_with_smash_closed_data {P : hset_cartesian_struct} {Pt : pointed_hset_struct P} (SP : hset_struct_with_smash P Pt) : UU := ∏ (X Y : hSet) (PX : P X) (PY : P Y), P (@homset (category_of_hset_struct P) (X ,, PX) (Y ,, PY)).
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Structures.CartesianStructure. Require Import UniMath.CategoryTheory.DisplayedCats.Structures.StructureLimitsAndColimits.