Theorems · Theorem · linear algebra

LinearMap.rTensor_baseChange

∀ {R : Type u_1} {A : Type u_2} {B : Type u_3} {M : Type u_4} {N : Type u_5} [inst : CommSemiring R]
  [inst_1 : Semiring A] [inst_2 : Algebra R A] [inst_3 : Semiring B] [inst_4 : Algebra R B] [inst_5 : AddCommMonoid M]
  [inst_6 : AddCommMonoid N] [inst_7 : Module R M] [inst_8 : Module R N] (φ : A →ₐ[R] B) (t : TensorProduct R A M)
  (f : M →ₗ[R] N),
  (LinearMap.rTensor N φ.toLinearMap) ((LinearMap.baseChange A f) t) =
    (LinearMap.baseChange B f) ((LinearMap.rTensor M φ.toLinearMap) t)

Defined in

Mathlib.LinearAlgebra.TensorProduct.Tower

Cited by

1 results in Mathlib

Foundations

Depth 62 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringSemiringAlgebraSemiringAlgebraAddCommMonoidAddCommMonoidModuleModule