{P : TopCat → Prop} →
  [∀ (S : CompHausLike P) (p : ↑S.toTop → Prop), CompHausLike.HasProp P (Subtype p)] →
    [inst : CompHausLike.HasProp P PUnit.{u + 1}] →
      (S : CompHausLike P) →
        (Y : CategoryTheory.Functor (CompHausLike P)ᵒᵖ (Type (max u w))) →
          [CategoryTheory.Limits.PreservesFiniteProducts Y] →
            [CompHausLike.HasExplicitFiniteCoproducts P] →
              LocallyConstant (↑S.toTop) (Y.obj (Opposite.op (CompHausLike.of P PUnit.{u + 1}))) ⟶ Y.obj (Opposite.op S)