Theorems · Definition · linear algebra

TensorProduct.prodLeft

(R : Type u_1) →
  (S : Type u_2) →
    (M₁ : Type u_3) →
      (M₂ : Type u_4) →
        (M₃ : Type u_5) →
          [inst : CommSemiring R] →
            [inst_1 : Semiring S] →
              [inst_2 : AddCommMonoid M₁] →
                [inst_3 : AddCommMonoid M₂] →
                  [inst_4 : AddCommMonoid M₃] →
                    [inst_5 : Algebra R S] →
                      [inst_6 : Module R M₁] →
                        [inst_7 : Module S M₁] →
                          [inst_8 : IsScalarTower R S M₁] →
                            [inst_9 : Module R M₂] →
                              [inst_10 : Module R M₃] →
                                [inst_11 : Module S M₂] →
                                  [inst_12 : IsScalarTower R S M₂] →
                                    TensorProduct R (M₁ × M₂) M₃ ≃ₗ[S] TensorProduct R M₁ M₃ × TensorProduct R M₂ M₃

Tensor products distribute over a product on the left .

Defined in

Mathlib.LinearAlgebra.TensorProduct.Prod

Cited by

2 results in Mathlib

Foundations

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

Assumes

CommSemiringSemiringAddCommMonoidAddCommMonoidAddCommMonoidAlgebraModuleModuleIsScalarTowerModuleModuleModuleIsScalarTower