Theorems · Definition · commutative algebra

DirectSum.decomposeTensorEquiv

{ι : Type u_1} →
  {R : Type u_2} →
    {M : Type u_3} →
      [inst : CommSemiring R] →
        [inst_1 : AddCommMonoid M] →
          [inst_2 : Module R M] →
            (ℳ : ι → Submodule R M) →
              (N : Type u_5) →
                [inst_3 : AddCommMonoid N] →
                  [inst_4 : Module R N] →
                    [inst_5 : DecidableEq ι] →
                      [DirectSum.Decomposition ℳ] →
                        (i : ι) → TensorProduct R (↥(ℳ i)) N ≃ₗ[R] ↥(DirectSum.decomposeTensor ℳ N i)

The linear isomorphism to the submodule from the tensor product with a summand.

Defined in

Mathlib.LinearAlgebra.TensorProduct.Decomposition

Cited by

4 results in Mathlib

Foundations

Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidModuleAddCommMonoidModuleDecidableEqDirectSum.Decomposition