Theorems · Definition · ring theory

Algebra.TensorProduct.assoc

(R : Type uR) →
  (S : Type uS) →
    (T : Type u_2) →
      (A : Type uA) →
        (C : Type uC) →
          (D : Type uD) →
            [inst : CommSemiring R] →
              [inst_1 : CommSemiring S] →
                [inst_2 : Algebra R S] →
                  [inst_3 : Semiring A] →
                    [inst_4 : Algebra R A] →
                      [inst_5 : Algebra S A] →
                        [inst_6 : IsScalarTower R S A] →
                          [inst_7 : Semiring C] →
                            [inst_8 : Algebra R C] →
                              [inst_9 : Algebra S C] →
                                [inst_10 : IsScalarTower R S C] →
                                  [inst_11 : Semiring D] →
                                    [inst_12 : Algebra R D] →
                                      [inst_13 : CommSemiring T] →
                                        [inst_14 : Algebra R T] →
                                          [inst_15 : Algebra S T] →
                                            [inst_16 : Algebra T A] →
                                              [inst_17 : IsScalarTower R T A] →
                                                [inst_18 : IsScalarTower S T A] →
                                                  TensorProduct R (TensorProduct S A C) D ≃ₐ[T]
                                                    TensorProduct S A (TensorProduct R C D)

The associator for tensor product of R-algebras, as an algebra isomorphism.

Defined in

Mathlib.RingTheory.TensorProduct.Maps

Cited by

8 results in Mathlib

Foundations

Depth 78 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringCommSemiringAlgebraSemiringAlgebraAlgebraIsScalarTowerSemiringAlgebraAlgebraIsScalarTowerSemiringAlgebraCommSemiringAlgebraAlgebraAlgebraIsScalarTowerIsScalarTower