{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.HasZeroObject C] →
              [inst_2 : CategoryTheory.Limits.HasZeroMorphisms C] →
                [inst_3 : DecidableEq ι] →
                  (e : c.Embedding c') →
                    (X : C) →
                      [inst_4 : DecidableEq ι'] →
                        (i : ι) →
                          (i' : ι') →
                            e.f i = i' →
                              (((HomologicalComplex.single C c i).obj X).extend e ≅
                                (HomologicalComplex.single C c' i').obj X)