Theorems · Definition · commutative algebra

TensorProduct.mapBilinear

{R : Type u_1} →
  {R₂ : Type u_2} →
    [inst : CommSemiring R] →
      [inst_1 : CommSemiring R₂] →
        (σ₁₂ : R →+* R₂) →
          (M : Type u_7) →
            (N : Type u_8) →
              (M₂ : Type u_12) →
                (N₂ : Type u_14) →
                  [inst_2 : AddCommMonoid M] →
                    [inst_3 : AddCommMonoid N] →
                      [inst_4 : AddCommMonoid M₂] →
                        [inst_5 : AddCommMonoid N₂] →
                          [inst_6 : Module R M] →
                            [inst_7 : Module R N] →
                              [inst_8 : Module R₂ M₂] →
                                [inst_9 : Module R₂ N₂] →
                                  (M →ₛₗ[σ₁₂] M₂) →ₗ[R₂]
                                    (N →ₛₗ[σ₁₂] N₂) →ₗ[R₂] TensorProduct R M N →ₛₗ[σ₁₂] TensorProduct R₂ M₂ N₂

The tensor product of a pair of semilinear maps between modules, bilinear in both maps.

Defined in

Mathlib.LinearAlgebra.TensorProduct.Map

Cited by

7 results in Mathlib

Foundations

Depth 63 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringCommSemiringAddCommMonoidAddCommMonoidAddCommMonoidAddCommMonoidModuleModuleModuleModule