{ι : Type u_1} →
  {ι' : Type u_2} →
    {c : ComplexShape ι} →
      {c' : ComplexShape ι'} →
        {C : Type u_3} →
          [inst : CategoryTheory.Category.{v_1, u_3} C] →
            [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
              [inst_2 : CategoryTheory.Limits.HasZeroObject C] →
                (K : HomologicalComplex C c) →
                  (e : c.Embedding c') →
                    {j k : ι} →
                      {j' k' : ι'} →
                        (hj' : e.f j = j') →
                          (hk : c.next j = k) →
                            (hk' : c'.next j' = k') →
                              (cone : CategoryTheory.Limits.KernelFork (K.d j k)) →
                                CategoryTheory.Limits.IsLimit cone →
                                  CategoryTheory.Limits.IsLimit
                                    (HomologicalComplex.extend.leftHomologyData.kernelFork K e hj' hk hk' cone)