Theorems · Definition · linear algebra

TensorProduct.AlgebraTensorModule.lift

{R : Type uR} →
  {A : Type uA} →
    {M : Type uM} →
      {N : Type uN} →
        {P : Type uP} →
          [inst : CommSemiring R] →
            [inst_1 : Semiring A] →
              [inst_2 : Algebra R A] →
                [inst_3 : AddCommMonoid M] →
                  [inst_4 : Module R M] →
                    [inst_5 : Module A M] →
                      [inst_6 : IsScalarTower R A M] →
                        [inst_7 : AddCommMonoid N] →
                          [inst_8 : Module R N] →
                            [inst_9 : AddCommMonoid P] →
                              [inst_10 : Module R P] →
                                [inst_11 : Module A P] →
                                  [inst_12 : IsScalarTower R A P] → (M →ₗ[A] N →ₗ[R] P) → TensorProduct R M N →ₗ[A] P

Heterobasic version of TensorProduct.lift: Constructing a linear map M ⊗[R] N →[A] P given a bilinear map M →[A] N →[R] P with the property that its composition with the canonical bilinear map M →[A] N →[R] M ⊗[R] N is the given bilinear map M →[A] N →[R] P.

Defined in

Mathlib.LinearAlgebra.TensorProduct.Tower

Cited by

9 results in Mathlib

Foundations

Depth 59 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringSemiringAlgebraAddCommMonoidModuleModuleIsScalarTowerAddCommMonoidModuleAddCommMonoidModuleModuleIsScalarTower