Theorems · Definition · commutative algebra

Algebra.Extension.Hom.sub

{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'} →
              {S' : Type v'} →
                [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'] →
                              [IsScalarTower R R' S'] →
                                [IsScalarTower R S S'] → P.Hom P' → P.Hom P' → P.CotangentSpace →ₗ[S] P'.Cotangent

If f and g are two maps P → P' between presentations, their difference induces a map P.CotangentSpace →ₗ[S] P'.Cotangent that makes two maps between the cotangent complexes homotopic.

Defined in

Mathlib.RingTheory.Extension.Cotangent.Basic

Cited by

6 results in Mathlib

Foundations

Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraCommRingCommRingAlgebraAlgebraAlgebraAlgebraIsScalarTowerIsScalarTower