Theorems · Definition · commutative algebra

Algebra.Extension.homInfinitesimal

{R : Type u} →
  {A : Type v} →
    [inst : CommRing R] →
      [inst_1 : CommRing A] →
        [inst_2 : Algebra R A] →
          (P₁ : Algebra.Extension R A) →
            (P₂ : Algebra.Extension R A) → [Algebra.FormallySmooth R P₁.Ring] → P₁.infinitesimal.Hom P₂.infinitesimal

Given extensions 0 → I₁ → P₁ → A → 0 and 0 → I₂ → P₂ → A → 0 with P₁ formally smooth, this is an arbitrarily chosen map P₁/I₁² → P₂/I₂² of extensions.

Defined in

Mathlib.RingTheory.Smooth.Basic

Cited by

1 results in Mathlib

Foundations

Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraAlgebra.FormallySmooth