Theorems · Definition · linear algebra

TensorProduct.piScalarRight

(R : Type u_1) →
  [inst : CommSemiring R] →
    (S : Type u_2) →
      [inst_1 : CommSemiring S] →
        [inst_2 : Algebra R S] →
          (N : Type u_3) →
            [inst_3 : AddCommMonoid N] →
              [inst_4 : Module R N] →
                [inst_5 : Module S N] →
                  [inst_6 : IsScalarTower R S N] →
                    (ι : Type u_4) → [Fintype ι] → [DecidableEq ι] → TensorProduct R N (ι → R) ≃ₗ[S] ι → N

For any R-module N and finite index type ι, N ⊗[R] (ι → R) is canonically isomorphic to ι → N.

Defined in

Mathlib.LinearAlgebra.TensorProduct.Pi

Cited by

7 results in Mathlib

Foundations

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

Assumes

CommSemiringCommSemiringAlgebraAddCommMonoidModuleModuleIsScalarTowerFintypeDecidableEq