Theorems · Theorem · commutative algebra

TensorProduct.map_smul_left

∀ {R : Type u_1} {R₂ : Type u_2} [inst : CommSemiring R] [inst_1 : CommSemiring R₂] {σ₁₂ : R →+* R₂} {M : Type u_7}
  {N : Type u_8} {M₂ : Type u_12} {N₂ : Type u_14} [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid N]
  [inst_4 : AddCommMonoid M₂] [inst_5 : AddCommMonoid N₂] [inst_6 : Module R M] [inst_7 : Module R N]
  [inst_8 : Module R₂ M₂] [inst_9 : Module R₂ N₂] (r : R₂) (f : M →ₛₗ[σ₁₂] M₂) (g : N →ₛₗ[σ₁₂] N₂),
  TensorProduct.map (r • f) g = r • TensorProduct.map f g

Defined in

Mathlib.LinearAlgebra.TensorProduct.Map

Cited by

1 results in Mathlib

Foundations

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

Assumes

CommSemiringCommSemiringAddCommMonoidAddCommMonoidAddCommMonoidAddCommMonoidModuleModuleModuleModule