{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    {Φ : CategoryTheory.SmallObject.SuccStruct C} →
      {J : Type u} →
        [inst_1 : LinearOrder J] →
          [inst_2 : OrderBot J] →
            [inst_3 : SuccOrder J] →
              [inst_4 : WellFoundedLT J] →
                [inst_5 : CategoryTheory.Limits.HasIterationOfShape J C] →
                  {j : J} → ((i : J) → i < j → Φ.Iteration i) → CategoryTheory.Functor (↑(Set.Iio j)) C