Theorems · Definition · linear algebra

TensorProduct.finsuppLeft

(R : Type u_1) →
  (S : Type u_2) →
    [inst : CommSemiring R] →
      [inst_1 : Semiring S] →
        [inst_2 : Algebra R S] →
          (M : Type u_3) →
            [inst_3 : AddCommMonoid M] →
              [inst_4 : Module R M] →
                [inst_5 : Module S M] →
                  [inst_6 : IsScalarTower R S M] →
                    (N : Type u_4) →
                      [inst_7 : AddCommMonoid N] →
                        [inst_8 : Module R N] →
                          (ι : Type u_5) → [DecidableEq ι] → TensorProduct R (ι →₀ M) N ≃ₗ[S] ι →₀ TensorProduct R M N

The tensor product of ι →₀ M and N is linearly equivalent to ι →₀ M ⊗[R] N

Defined in

Mathlib.LinearAlgebra.DirectSum.Finsupp

Cited by

9 results in Mathlib

Foundations

Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringSemiringAlgebraAddCommMonoidModuleModuleIsScalarTowerAddCommMonoidModuleDecidableEq