Theorems · Theorem · commutative algebra

IsLocalizedModule.map_lTensor

∀ {R : Type u_1} [inst : CommSemiring R] (A : Type u_2) [inst_1 : CommSemiring A] [inst_2 : Algebra R A] {M : Type u_3}
  [inst_3 : AddCommMonoid M] [inst_4 : Module R M] {M' : Type u_4} [inst_5 : AddCommMonoid M'] [inst_6 : Module R M']
  [inst_7 : Module A M'] [inst_8 : IsScalarTower R A M'] (S : Submonoid A) {N : Type u_7} [inst_9 : AddCommMonoid N]
  [inst_10 : Module R N] [inst_11 : Module A M] [inst_12 : IsScalarTower R A M] {P : Type u_8}
  [inst_13 : AddCommMonoid P] [inst_14 : Module R P] (f : N →ₗ[R] P) (g : M →ₗ[A] M') [h : IsLocalizedModule S g],
  (IsLocalizedModule.map S ((TensorProduct.AlgebraTensorModule.rTensor R N) g)
        ((TensorProduct.AlgebraTensorModule.rTensor R P) g))
      ((TensorProduct.AlgebraTensorModule.lTensor A M) f) =
    (TensorProduct.AlgebraTensorModule.lTensor A M') f

Defined in

Mathlib.RingTheory.Localization.BaseChange

Cited by

2 results in Mathlib

Foundations

Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringCommSemiringAlgebraAddCommMonoidModuleAddCommMonoidModuleModuleIsScalarTowerAddCommMonoidModuleModuleIsScalarTowerAddCommMonoidModuleIsLocalizedModule