∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X Y : C} [inst_1 : CategoryTheory.Limits.HasInitial C]
  [inst_2 : CategoryTheory.Limits.InitialMonoClass C] (f : X ⟶ Y) [inst_3 : CategoryTheory.Mono f],
  (CategoryTheory.Subobject.map f).obj ⊥ = ⊥