∀ {X Y Z : TopCat} (f : X ⟶ Y) (g : Y ⟶ Z) (U : Set ↑Z) (p : IsOpen U),
  (TopologicalSpace.Opens.map (CategoryTheory.CategoryStruct.comp f g)).obj { carrier := U, is_open' := p } =
    (TopologicalSpace.Opens.map f).obj ((TopologicalSpace.Opens.map g).obj { carrier := U, is_open' := p })