Theorems · Definition · linear algebra

TensorProduct.dualDistrib

(R : Type u_1) →
  (M : Type u_3) →
    (N : Type u_4) →
      [inst : CommSemiring R] →
        [inst_1 : AddCommMonoid M] →
          [inst_2 : AddCommMonoid N] →
            [inst_3 : Module R M] →
              [inst_4 : Module R N] →
                TensorProduct R (Module.Dual R M) (Module.Dual R N) →ₗ[R] Module.Dual R (TensorProduct R M N)

The canonical linear map from Dual M ⊗ Dual N to Dual (M ⊗ N), sending f ⊗ g to the composition of TensorProduct.map f g with the natural isomorphism R ⊗ R ≃ R.

Defined in

Mathlib.LinearAlgebra.Dual.Lemmas

Cited by

10 results in Mathlib

Foundations

Depth 65 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringAddCommMonoidAddCommMonoidModuleModule