Theorems · Theorem · linear algebra

TensorProduct.mapOfCompatibleSMul_tmul

∀ (R : Type u_1) [inst : CommSemiring R] (A : Type u_22) (S : Type u_23) (M : Type u_24) (N : Type u_25)
  [inst_1 : AddCommMonoid M] [inst_2 : AddCommMonoid N] [inst_3 : Module R M] [inst_4 : Module R N]
  [inst_5 : CommSemiring A] [inst_6 : Module A M] [inst_7 : Module A N] [inst_8 : SMulCommClass R A M]
  [inst_9 : CommSemiring S] [inst_10 : Module S M] [inst_11 : SMulCommClass R S M] [inst_12 : SMulCommClass A S M]
  [inst_13 : TensorProduct.CompatibleSMul R A M N] (m : M) (n : N),
  (TensorProduct.mapOfCompatibleSMul R A S M N) (m ⊗ₜ[A] n) = m ⊗ₜ[R] n

Defined in

Mathlib.LinearAlgebra.TensorProduct.Basic

Cited by

1 results in Mathlib

Foundations

Depth 61 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringAddCommMonoidAddCommMonoidModuleModuleCommSemiringModuleModuleSMulCommClassCommSemiringModuleSMulCommClassSMulCommClassTensorProduct.CompatibleSMul