Theorems · Theorem · linear algebra

TensorProduct.AlgebraTensorModule.rTensor_comp

∀ {R : Type uR} {A : Type uA} {M : Type uM} {N : Type uN} {P : Type uP} {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] [inst_13 : AddCommMonoid P']
  [inst_14 : Module R P'] [inst_15 : Module A P'] [inst_16 : IsScalarTower R A P'] (f₂ : P →ₗ[A] P') (f₁ : M →ₗ[A] P),
  (TensorProduct.AlgebraTensorModule.rTensor R N) (f₂ ∘ₗ f₁) =
    (TensorProduct.AlgebraTensorModule.rTensor R N) f₂ ∘ₗ (TensorProduct.AlgebraTensorModule.rTensor R N) f₁

Defined in

Mathlib.LinearAlgebra.TensorProduct.Tower

Cited by

1 results in Mathlib

Foundations

Depth 74 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringSemiringAlgebraAddCommMonoidModuleModuleIsScalarTowerAddCommMonoidModuleAddCommMonoidModuleModuleIsScalarTowerAddCommMonoidModuleModuleIsScalarTower