Theorems · Theorem · linear algebra

TensorProduct.AlgebraTensorModule.tensorQuotientEquiv_apply_tmul

∀ {R : Type u_1} (A : Type u_2) (B : Type u_3) [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A]
  [inst_3 : CommRing B] [inst_4 : Algebra R B] (M : Type u_4) [inst_5 : AddCommGroup M] [inst_6 : Module R M]
  [inst_7 : Module A M] [inst_8 : IsScalarTower R A M] {N : Type u_5} [inst_9 : AddCommGroup N] [inst_10 : Module R N]
  [inst_11 : Module B N] [inst_12 : IsScalarTower R B N] (n : Submodule B N) (x : M) (y : N),
  (TensorProduct.AlgebraTensorModule.tensorQuotientEquiv A B M n) (x ⊗ₜ[R] Submodule.Quotient.mk y) =
    Submodule.Quotient.mk (x ⊗ₜ[R] y)

Defined in

Mathlib.LinearAlgebra.TensorProduct.Quotient

Cited by

0 results in Mathlib

Foundations

Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraCommRingAlgebraAddCommGroupModuleModuleIsScalarTowerAddCommGroupModuleModuleIsScalarTower