Definition pointed_hset_struct_unit_map {P : hset_struct} (Pt : pointed_hset_struct P) {X Y : hSet} (PY : P Y) (f : X → bool) (g : X → Y) (x : X) : Y := if f x then g x else hset_struct_point Pt 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.