∀ {C : Type u_3} [inst : CategoryTheory.Category.{u_2, u_3} C] [inst_1 : CategoryTheory.Abelian C] {X : C}
  {J : Type u_1} [inst_2 : CategoryTheory.SmallCategory J] {Y : CategoryTheory.Functor J C} {j₀ : J} (y : X ⟶ Y.obj j₀)
  (X_1 : CategoryTheory.Under j₀),
  CategoryTheory.MonoOver.homMk
      ((CategoryTheory.Limits.kernel (CategoryTheory.IsGrothendieckAbelian.IsPresentable.injectivity₀.g y)).map
        (CategoryTheory.CategoryStruct.id X_1))
      ⋯ =
    CategoryTheory.CategoryStruct.id
      (CategoryTheory.MonoOver.mk
        ((CategoryTheory.Limits.kernel.ι (CategoryTheory.IsGrothendieckAbelian.IsPresentable.injectivity₀.g y)).app
          X_1))