Theorems · Theorem · commutative algebra

TensorProduct.smul_tmul

∀ {R : Type u_1} {R' : Type u_4} [inst : CommSemiring R] [inst_1 : Monoid R'] {M : Type u_7} {N : Type u_8}
  [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid N] [inst_4 : DistribMulAction R' M] [inst_5 : Module R M]
  [inst_6 : Module R N] [inst_7 : DistribMulAction R' N] [TensorProduct.CompatibleSMul R R' M N] (r : R') (m : M)
  (n : N), (r • m) ⊗ₜ[R] n = m ⊗ₜ[R] (r • n)

smul can be moved from one side of the product to the other .

Defined in

Mathlib.LinearAlgebra.TensorProduct.Defs

Cited by

33 results in Mathlib

Foundations

Depth 42 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringMonoidAddCommMonoidAddCommMonoidDistribMulActionModuleModuleDistribMulActionTensorProduct.CompatibleSMul