∀ {C : Type u_3} [inst : CategoryTheory.Category.{u_2, u_3} C] [inst_1 : CategoryTheory.Abelian C]
  [CategoryTheory.IsGrothendieckAbelian.{u_1, u_2, u_3} C] {X : C} {J : Type u_1}
  [inst_3 : CategoryTheory.SmallCategory J] {Y : CategoryTheory.Functor J C} {j₀ : J} (y : X ⟶ Y.obj j₀),
  CategoryTheory.Limits.HasColimit
    (CategoryTheory.Limits.kernel (CategoryTheory.IsGrothendieckAbelian.IsPresentable.injectivity₀.g y))