Theorems · Theorem · linear algebra

TensorProduct.AlgebraTensorModule.map_mul

∀ {R : Type uR} {A : Type uA} {M : Type uM} {N : Type uN} [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] (f₁ f₂ : M →ₗ[A] M)
  (g₁ g₂ : N →ₗ[R] N),
  TensorProduct.AlgebraTensorModule.map (f₁ * f₂) (g₁ * g₂) =
    TensorProduct.AlgebraTensorModule.map f₁ g₁ * TensorProduct.AlgebraTensorModule.map f₂ g₂

Defined in

Mathlib.LinearAlgebra.TensorProduct.Tower

Cited by

0 results in Mathlib

Foundations

Depth 73 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringSemiringAlgebraAddCommMonoidModuleModuleIsScalarTowerAddCommMonoidModule