-- Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform
/-- The associator isomorphism for categorical cospan transformations.  -/
CategoryTheory.Limits.CatCospanTransform.associator : {A : Type u₁} →
  {B : Type u₂} →
    {C : Type u₃} →
      {A' : Type u₄} →
        {B' : Type u₅} →
          {C' : Type u₆} →
            {A'' : Type u₇} →
              {B'' : Type u₈} →
                {C'' : Type u₉} →
                  [inst : CategoryTheory.Category.{v₁, u₁} A] →
                    [inst_1 : CategoryTheory.Category.{v₂, u₂} B] →
                      [inst_2 : CategoryTheory.Category.{v₃, u₃} C] →
                        {F : CategoryTheory.Functor A B} →
                          {G : CategoryTheory.Functor C B} →
                            [inst_3 : CategoryTheory.Category.{v₄, u₄} A'] →
                              [inst_4 : CategoryTheory.Category.{v₅, u₅} B'] →
                                [inst_5 : CategoryTheory.Category.{v₆, u₆} C'] →
                                  {F' : CategoryTheory.Functor A' B'} →
                                    {G' : CategoryTheory.Functor C' B'} →
                                      [inst_6 : CategoryTheory.Category.{v₇, u₇} A''] →
                                        [inst_7 : CategoryTheory.Category.{v₈, u₈} B''] →
                                          [inst_8 : CategoryTheory.Category.{v₉, u₉} C''] →
                                            {F'' : CategoryTheory.Functor A'' B''} →
                                              {G'' : CategoryTheory.Functor C'' B''} →
                                                {A''' : Type u₁₀} →
                                                  {B''' : Type u₁₁} →
                                                    {C''' : Type u₁₂} →
                                                      [inst_9 : CategoryTheory.Category.{v₁₀, u₁₀} A'''] →
                                                        [inst_10 : CategoryTheory.Category.{v₁₁, u₁₁} B'''] →
                                                          [inst_11 : CategoryTheory.Category.{v₁₂, u₁₂} C'''] →
                                                            {F''' : CategoryTheory.Functor A''' B'''} →
                                                              {G''' : CategoryTheory.Functor C''' B'''} →
                                                                (φ :
                                                                    CategoryTheory.Limits.CatCospanTransform F G F'
                                                                      G') →
                                                                  (φ' :
                                                                      CategoryTheory.Limits.CatCospanTransform F' G' F''
                                                                        G'') →
                                                                    (φ'' :
                                                                        CategoryTheory.Limits.CatCospanTransform F'' G''
                                                                          F''' G''') →
                                                                      (φ.comp φ').comp φ'' ≅ φ.comp (φ'.comp φ'')