∀ {X : TopCat} {U : TopologicalSpace.Opens ↑X} (V : TopologicalSpace.Opens ↥U),
  ((TopologicalSpace.Opens.map U.inclusion').comp ⋯.functor).obj (⋯.functor.obj V) =
    (CategoryTheory.Functor.id (TopologicalSpace.Opens ↑X)).obj (⋯.functor.obj V)