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
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHom.idproof · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- LinearMapproof · cited by 10,215
- Derivationstatement · cited by 293
- KaehlerDifferentialstatement and proof · cited by 204
- KaehlerDifferential.DLinearMapproof · cited by 1
Cited by106
Results whose statement or proof uses this declaration.
- KaehlerDifferential.mapproof · cited by 33
- KaehlerDifferential.map_Dstatement · cited by 15
- KaehlerDifferential.kerToTensorproof · cited by 11
- Algebra.Generators.H1Cotangent.δAuxproof · cited by 10
- Derivation.liftKaehlerDifferential_comp_Dstatement · cited by 7
- Algebra.Extension.CotangentSpace.map_tmulstatement and proof · cited by 7
- KaehlerDifferential.span_range_derivationstatement and proof · cited by 7
- Derivation.liftKaehlerDifferential_compstatement · cited by 6
- Algebra.Presentation.differentialsRelationsproof · cited by 6
- Algebra.Generators.toKaehler_cotangentSpaceBasisstatement and proof · cited by 6
- Derivation.liftKaehlerDifferential_uniquestatement and proof · cited by 5
- Algebra.Generators.cotangentSpaceBasis_repr_tmulstatement and proof · cited by 4