Theorems · Definition · ring theory

Algebra.TensorProduct.lidOfCompatibleSMul

(R : Type u_3) →
  (S : Type u_4) →
    (A : Type u_6) →
      [inst : CommSemiring R] →
        [inst_1 : CommSemiring S] →
          [inst_2 : Semiring A] →
            [inst_3 : Algebra R A] →
              [inst_4 : Algebra S A] →
                [inst_5 : Algebra R S] →
                  [TensorProduct.CompatibleSMul R S S A] →
                    [TensorProduct.CompatibleSMul S R S A] → TensorProduct R S A ≃ₐ[S] A

If the R- and S- action on S and A satisfy CompatibleSMul both ways, then S ⊗[R] A is canonically isomorphic to A.

Defined in

Mathlib.RingTheory.TensorProduct.Maps

Cited by

2 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringCommSemiringSemiringAlgebraAlgebraAlgebraTensorProduct.CompatibleSMulTensorProduct.CompatibleSMul