Definition hset_struct_with_smash_data (P : hset_cartesian_struct) (Pt : pointed_hset_struct P) : UU := P boolset × (∏ (X Y : hSet) (PX : P X) (PY : P Y), P (setquotinset (smash_eqrel P Pt PX 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.