Theorems · Theorem · commutative algebra

Algebra.Extension.Cotangent.map_mk

∀ {R : Type u} {S : Type v} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] {P : Algebra.Extension R S}
  {R' : Type u_1} {S' : Type u_2} [inst_3 : CommRing R'] [inst_4 : CommRing S'] [inst_5 : Algebra R' S']
  {P' : Algebra.Extension R' S'} [inst_6 : Algebra R R'] [inst_7 : Algebra S S'] [inst_8 : Algebra R S']
  [inst_9 : IsScalarTower R R' S'] (f : P.Hom P') (x : ↥P.ker),
  (Algebra.Extension.Cotangent.map f) (Algebra.Extension.Cotangent.mk x) =
    Algebra.Extension.Cotangent.mk ⟨f.toAlgHom ↑x, ⋯⟩

Defined in

Mathlib.RingTheory.Extension.Basic

Cited by

3 results in Mathlib

Foundations

Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraCommRingCommRingAlgebraAlgebraAlgebraAlgebraIsScalarTower