Theorems · Definition · linear algebra

LinearMap.baseChange

{R : Type u_1} →
  (A : Type u_2) →
    {M : Type u_4} →
      {N : Type u_5} →
        [inst : CommSemiring R] →
          [inst_1 : Semiring A] →
            [inst_2 : Algebra R A] →
              [inst_3 : AddCommMonoid M] →
                [inst_4 : AddCommMonoid N] →
                  [inst_5 : Module R M] →
                    [inst_6 : Module R N] → (M →ₗ[R] N) → TensorProduct R A M →ₗ[A] TensorProduct R A N

baseChange A f for f : M →ₗ[R] N is the A-linear map A ⊗[R] M →ₗ[A] A ⊗[R] N. This "base change" operation is also known as "extension of scalars".

Defined in

Mathlib.LinearAlgebra.TensorProduct.Tower

Cited by

62 results in Mathlib

Foundations

Depth 61 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringSemiringAlgebraAddCommMonoidAddCommMonoidModuleModule