Theorems · Definition · commutative algebra

IsTensorProduct.equiv

{R : Type u_1} →
  [inst : CommSemiring R] →
    {M₁ : Type u_2} →
      {M₂ : Type u_3} →
        {M : Type u_4} →
          [inst_1 : AddCommMonoid M₁] →
            [inst_2 : AddCommMonoid M₂] →
              [inst_3 : AddCommMonoid M] →
                [inst_4 : Module R M₁] →
                  [inst_5 : Module R M₂] →
                    [inst_6 : Module R M] →
                      {f : M₁ →ₗ[R] M₂ →ₗ[R] M} → IsTensorProduct f → TensorProduct R M₁ M₂ ≃ₗ[R] M

If M is the tensor product of M₁ and M₂, it is linearly equivalent to M₁ ⊗[R] M₂.

Defined in

Mathlib.RingTheory.IsTensorProduct

Cited by

9 results in Mathlib

Foundations

Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidAddCommMonoidAddCommMonoidModuleModuleModule