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Theorems · Definition · commutative algebra

KaehlerDifferential.D

(R : Type u) →
  (S : Type v) → [inst : CommRing R] → [inst_1 : CommRing S] → [inst_2 : Algebra R S] → Derivation R S Ω[S⁄R]

The universal derivation into Ω[S⁄R].

Defined in
Mathlib.RingTheory.Kaehler.Basic
Cited by
92 results in Mathlib
Foundations
Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingCommRingAlgebra

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

KaehlerDifferential.map · cited by 33KaehlerDifferential.mapKaehlerDifferential.map_D · cited by 15KaehlerDifferential.map_DKaehlerDifferential.kerToTensor · cited by 11KaehlerDifferential.kerTo…Algebra.Generators.H1Cotangent.δAux · cited by 10H1Cotangent.δAuxDerivation.liftKaehlerDifferential_comp_D · cited by 7Derivation.liftKaehlerDif…Algebra.Extension.CotangentSpace.map_tmul · cited by 7CotangentSpace.map_tmulKaehlerDifferential.span_range_derivation · cited by 7KaehlerDifferential.span_…Derivation.liftKaehlerDifferential_comp · cited by 6Derivation.liftKaehlerDif…Algebra.Presentation.differentialsRelations · cited by 6Presentation.differential…Algebra.Generators.toKaehler_cotangentSpaceBasis · cited by 6Generators.toKaehler_cota…Derivation.liftKaehlerDifferential_unique · cited by 5Derivation.liftKaehlerDif…Algebra.Generators.cotangentSpaceBasis_repr_tmul · cited by 4Generators.cotangentSpace…Algebra.Extension.CotangentSpace.map_cotangentComplex · cited by 4CotangentSpace.map_cotang…KaehlerDifferential.kerToTensor_apply · cited by 4KaehlerDifferential.kerTo…sectionOfRetractionKerToTensorAux · cited by 3sectionOfRetractionKerToT…RingHom.id · cited by 18349RingHom.idCommRing · cited by 17173CommRingAlgebra · cited by 11388AlgebraLinearMap · cited by 10215LinearMapDerivation · cited by 293DerivationKaehlerDifferential · cited by 204KaehlerDifferentialKaehlerDifferential.DLinearMap · cited by 1KaehlerDifferential.DLine…KaehlerDifferential.DCITED BYCITES

Cites7

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Cited by106

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