{C₁ : Type u_1} →
  {C₂ : Type u_2} →
    {C₂₃ : Type u_4} →
      {C₃ : Type u_5} →
        {C₄ : Type u_6} →
          [inst : CategoryTheory.Category.{v_1, u_1} C₁] →
            [inst_1 : CategoryTheory.Category.{v_2, u_2} C₂] →
              [inst_2 : CategoryTheory.Category.{v_3, u_5} C₃] →
                [inst_3 : CategoryTheory.Category.{v_4, u_6} C₄] →
                  [inst_4 : CategoryTheory.Category.{v_6, u_4} C₂₃] →
                    [inst_5 : CategoryTheory.Limits.HasZeroMorphisms C₁] →
                      [inst_6 : CategoryTheory.Limits.HasZeroMorphisms C₂] →
                        [inst_7 : CategoryTheory.Limits.HasZeroMorphisms C₃] →
                          CategoryTheory.Functor C₁ (CategoryTheory.Functor C₂₃ C₄) →
                            CategoryTheory.Functor C₂ (CategoryTheory.Functor C₃ C₂₃) →
                              {ι₁ : Type u_7} →
                                {ι₂ : Type u_8} →
                                  {ι₃ : Type u_9} →
                                    {ι₁₂ : Type u_10} →
                                      {ι₂₃ : Type u_11} →
                                        {ι₄ : Type u_12} →
                                          {c₁ : ComplexShape ι₁} →
                                            {c₂ : ComplexShape ι₂} →
                                              {c₃ : ComplexShape ι₃} →
                                                HomologicalComplex C₁ c₁ →
                                                  HomologicalComplex C₂ c₂ →
                                                    HomologicalComplex C₃ c₃ →
                                                      (c₁₂ : ComplexShape ι₁₂) →
                                                        (c₂₃ : ComplexShape ι₂₃) →
                                                          (c₄ : ComplexShape ι₄) →
                                                            [inst : TotalComplexShape c₁ c₂ c₁₂] →
                                                              [inst_8 : TotalComplexShape c₁₂ c₃ c₄] →
                                                                [inst_9 : TotalComplexShape c₂ c₃ c₂₃] →
                                                                  [inst_10 : TotalComplexShape c₁ c₂₃ c₄] →
                                                                    [c₁.Associative c₂ c₃ c₁₂ c₂₃ c₄] → Prop