Theorems · Definition · linear algebra

TensorProduct.comm

(R : Type u_1) →
  [inst : CommSemiring R] →
    (M : Type u_7) →
      (N : Type u_8) →
        [inst_1 : AddCommMonoid M] →
          [inst_2 : AddCommMonoid N] →
            [inst_3 : Module R M] → [inst_4 : Module R N] → TensorProduct R M N ≃ₗ[R] TensorProduct R N M

The tensor product of modules is commutative, up to linear equivalence.

Defined in

Mathlib.LinearAlgebra.TensorProduct.Basic

Cited by

108 results in Mathlib

Foundations

Depth 59 from the axioms, rests on 917 definitions · uses propext, Quot.sound

Assumes

CommSemiringAddCommMonoidAddCommMonoidModuleModule