(P : TopCat → Prop) →
  [inst : CompHausLike.HasProp P PUnit.{u + 1}] →
    [inst_1 : CompHausLike.HasExplicitFiniteCoproducts P] →
      [inst_2 : CompHausLike.HasExplicitPullbacks P] →
        (hs :
            ∀ ⦃X Y : CompHausLike P⦄ (f : X ⟶ Y),
              CategoryTheory.EffectiveEpi f → Function.Surjective ⇑(CategoryTheory.ConcreteCategory.hom f)) →
          CategoryTheory.Functor.id (Type (max u w)) ≅
            (CompHausLike.LocallyConstant.functor P hs).comp
              ((CategoryTheory.sheafSections (CategoryTheory.coherentTopology (CompHausLike P)) (Type (max u w))).obj
                (Opposite.op (CompHausLike.of P PUnit.{u + 1})))