Theorems · Theorem · ring theory

Algebra.TensorProduct.tensorTensorTensorComm_toLinearEquiv

∀ {R : Type uR} {R' : Type u_1} {S : Type uS} {T : Type u_2} {A : Type uA} {B : Type uB} {C : Type uC} {D : Type uD}
  [inst : CommSemiring R] [inst_1 : CommSemiring S] [inst_2 : Algebra R S] [inst_3 : Semiring A] [inst_4 : Algebra R A]
  [inst_5 : Algebra S A] [inst_6 : IsScalarTower R S A] [inst_7 : Semiring B] [inst_8 : Algebra R B]
  [inst_9 : Semiring C] [inst_10 : Algebra R C] [inst_11 : Algebra S C] [inst_12 : IsScalarTower R S C]
  [inst_13 : Semiring D] [inst_14 : Algebra R D] [inst_15 : CommSemiring T] [inst_16 : Algebra R T]
  [inst_17 : Algebra T A] [inst_18 : IsScalarTower R T A] [inst_19 : SMulCommClass S T A] [inst_20 : Algebra S T]
  [inst_21 : IsScalarTower S T A] [inst_22 : CommSemiring R'] [inst_23 : Algebra R R'] [inst_24 : Algebra R' T]
  [inst_25 : Algebra R' A] [inst_26 : Algebra R' B] [inst_27 : IsScalarTower R R' A] [inst_28 : SMulCommClass S R' A]
  [inst_29 : SMulCommClass R' S A] [inst_30 : IsScalarTower R' T A] [inst_31 : IsScalarTower R R' B],
  ↑(Algebra.TensorProduct.tensorTensorTensorComm R R' S T A B C D) =
    TensorProduct.AlgebraTensorModule.tensorTensorTensorComm R R' S T A B C D

Defined in

Mathlib.RingTheory.TensorProduct.Maps

Cited by

0 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringCommSemiringAlgebraSemiringAlgebraAlgebraIsScalarTowerSemiringAlgebraSemiringAlgebraAlgebraIsScalarTowerSemiringAlgebraCommSemiringAlgebraAlgebraIsScalarTowerSMulCommClassAlgebraIsScalarTowerCommSemiringAlgebraAlgebraAlgebraAlgebraIsScalarTowerSMulCommClassSMulCommClassIsScalarTowerIsScalarTower