Theorems · Definition · ring theory

Algebra.TensorProduct.cancelBaseChange

(R : Type uR) →
  (S : Type uS) →
    [inst : CommSemiring R] →
      [inst_1 : CommSemiring S] →
        [inst_2 : Algebra R S] →
          (T : Type u_3) →
            (A : Type u_4) →
              (B : Type u_5) →
                [inst_3 : CommSemiring T] →
                  [inst_4 : CommSemiring A] →
                    [inst_5 : CommSemiring B] →
                      [inst_6 : Algebra R T] →
                        [inst_7 : Algebra R A] →
                          [inst_8 : Algebra R B] →
                            [inst_9 : Algebra T A] →
                              [inst_10 : IsScalarTower R T A] →
                                [inst_11 : Algebra S A] →
                                  [IsScalarTower R S A] →
                                    [inst_13 : Algebra S T] →
                                      [inst_14 : IsScalarTower S T A] →
                                        TensorProduct S A (TensorProduct R S B) ≃ₐ[T] TensorProduct R A B

The natural isomorphism A ⊗[S] (S ⊗[R] B) ≃ₐ[T] A ⊗[R] B.

Defined in

Mathlib.RingTheory.TensorProduct.Maps

Cited by

10 results in Mathlib

Foundations

Depth 79 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringCommSemiringAlgebraCommSemiringCommSemiringCommSemiringAlgebraAlgebraAlgebraAlgebraIsScalarTowerAlgebraIsScalarTowerAlgebraIsScalarTower