Theorems · Definition · linear algebra

TensorProduct.lidOfCompatibleSMul

(R : Type u_1) →
  [inst : CommSemiring R] →
    (A : Type u_4) →
      (M : Type u_5) →
        [inst_1 : AddCommMonoid M] →
          [inst_2 : Module R M] →
            [inst_3 : CommSemiring A] →
              [inst_4 : Module A M] →
                [inst_5 : Module R A] →
                  [inst_6 : SMulCommClass R A A] →
                    [TensorProduct.CompatibleSMul R A A M] →
                      [TensorProduct.CompatibleSMul A R A M] → TensorProduct R A M ≃ₗ[A] M

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

Defined in

Mathlib.LinearAlgebra.TensorProduct.Associator

Cited by

1 results in Mathlib

Foundations

Depth 64 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringAddCommMonoidModuleCommSemiringModuleModuleSMulCommClassTensorProduct.CompatibleSMulTensorProduct.CompatibleSMul