Theorems · Theorem · commutative algebra

Algebra.Generators.CotangentSpace.fst_compEquiv

∀ {R : Type u₁} {S : Type u₂} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] {T : Type u₃}
  [inst_3 : CommRing T] [inst_4 : Algebra R T] [inst_5 : Algebra S T] [inst_6 : IsScalarTower R S T] {ι : Type w₁}
  {σ : Type w₂} (Q : Algebra.Generators S T ι) (P : Algebra.Generators R S σ),
  LinearMap.fst T Q.toExtension.CotangentSpace (TensorProduct S T P.toExtension.CotangentSpace) ∘ₗ
      ↑(Algebra.Generators.CotangentSpace.compEquiv Q P) =
    Algebra.Extension.CotangentSpace.map (Q.ofComp P).toExtensionHom

Defined in

Mathlib.RingTheory.Kaehler.JacobiZariski

Cited by

4 results in Mathlib

Foundations

Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraCommRingAlgebraAlgebraIsScalarTower