Theorems · Theorem · linear algebra

TensorProduct.AlgebraTensorModule.map_add_left

∀ {R : Type uR} {A : Type uA} {M : Type uM} {N : Type uN} {P : Type uP} {Q : Type uQ} [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 Q]
  [inst_14 : Module R Q] (f₁ f₂ : M →ₗ[A] P) (g : N →ₗ[R] Q),
  TensorProduct.AlgebraTensorModule.map (f₁ + f₂) g =
    TensorProduct.AlgebraTensorModule.map f₁ g + TensorProduct.AlgebraTensorModule.map f₂ g

Defined in

Mathlib.LinearAlgebra.TensorProduct.Tower

Cited by

0 results in Mathlib

Foundations

Depth 71 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringSemiringAlgebraAddCommMonoidModuleModuleIsScalarTowerAddCommMonoidModuleAddCommMonoidModuleModuleIsScalarTowerAddCommMonoidModule