∀ {P : TopCat → Prop} [inst : CompHausLike.HasExplicitFiniteCoproducts P]
  (X : CategoryTheory.Functor (CompHausLike P)ᵒᵖ (Type (max u w))) [CategoryTheory.Limits.PreservesFiniteProducts X]
  {α : Type u} [inst_2 : Finite α] (σ : α → Type u) [inst_3 : (a : α) → TopologicalSpace (σ a)]
  [inst_4 : ∀ (a : α), CompactSpace (σ a)] [inst_5 : ∀ (a : α), T2Space (σ a)]
  [inst_6 : ∀ (a : α), CompHausLike.HasProp P (σ a)], CategoryTheory.IsIso (CompHausLike.sigmaComparison X σ)