Theorems · Definition · linear algebra

TensorProduct.AlgebraTensorModule.uliftEquiv

(R : Type uR) →
  (A : Type uA) →
    (M : Type uM) →
      (N : Type uN) →
        [inst : CommSemiring R] →
          [inst_1 : CommSemiring 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] →
                          ULift.{u₁, max uN uM} (TensorProduct R M N) ≃ₗ[A]
                            TensorProduct (ULift.{u₃, uR} R) (ULift.{u₂, uM} M) (ULift.{u₄, uN} N)

ULift commutes with tensor products.

Defined in

Mathlib.LinearAlgebra.TensorProduct.Tower

Cited by

2 results in Mathlib

Foundations

Depth 74 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringCommSemiringAlgebraAddCommMonoidModuleModuleIsScalarTowerAddCommMonoidModule