∀ {X Y : CompactlyGenerated} (f : ↑X.toTop ≃ₜ ↑Y.toTop),
  CategoryTheory.CategoryStruct.comp (CompactlyGenerated.ofHom { toFun := ⇑f.symm, continuous_toFun := ⋯ })
      (CompactlyGenerated.ofHom { toFun := ⇑f, continuous_toFun := ⋯ }) =
    CategoryTheory.CategoryStruct.id Y