Theorems · Theorem · commutative algebra

KaehlerDifferential.map_compDer

∀ (R : Type u) (S : Type v) [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] (A : Type u_2)
  (B : Type u_3) [inst_3 : CommRing A] [inst_4 : CommRing B] [inst_5 : Algebra R A] [inst_6 : Algebra A B]
  [inst_7 : Algebra S B] [inst_8 : Algebra R B] [inst_9 : IsScalarTower R A B] [inst_10 : IsScalarTower R S B]
  [inst_11 : SMulCommClass S A B],
  (KaehlerDifferential.map R S A B).compDer (KaehlerDifferential.D R A) =
    Derivation.compAlgebraMap A (Derivation.restrictScalars R (KaehlerDifferential.D S B))

Defined in

Mathlib.RingTheory.Kaehler.Basic

Cited by

1 results in Mathlib

Foundations

Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraCommRingCommRingAlgebraAlgebraAlgebraAlgebraIsScalarTowerIsScalarTowerSMulCommClass