Theorems · Theorem · commutative algebra

KaehlerDifferential.tensorKaehlerEquiv_tmul_D

∀ (R : Type u_1) (S : Type u_2) (A : Type u_3) (B : Type u_4) [inst : CommRing R] [inst_1 : CommRing S]
  [inst_2 : Algebra R S] [inst_3 : CommRing A] [inst_4 : CommRing B] [inst_5 : Algebra R A] [inst_6 : Algebra R B]
  [inst_7 : Algebra A B] [inst_8 : Algebra S B] [inst_9 : IsScalarTower R A B] [inst_10 : IsScalarTower R S B]
  [inst_11 : Algebra.IsPushout R S A B] (b : B) (a : A),
  (KaehlerDifferential.tensorKaehlerEquiv R S A B) (b ⊗ₜ[A] (KaehlerDifferential.D R A) a) =
    b • (KaehlerDifferential.D S B) ((algebraMap A B) a)

Defined in

Mathlib.RingTheory.Kaehler.TensorProduct

Cited by

3 results in Mathlib

Foundations

Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraCommRingCommRingAlgebraAlgebraAlgebraAlgebraIsScalarTowerIsScalarTowerAlgebra.IsPushout