Theorems · Theorem · commutative algebra
Algebra.Generators.toKaehler_cotangentSpaceBasis
∀ {R : Type u} {S : Type v} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] {ι : Type w}
{P : Algebra.Generators R S ι} (i : ι),
P.toExtension.toKaehler (P.cotangentSpaceBasis i) = (KaehlerDifferential.D R S) (P.val i)- Cited by
- 6 results in Mathlib
- Foundations
- Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- LinearMapstatement · cited by 10,215
- Module.Basisstatement · cited by 1,477
- Derivationstatement · cited by 293
- KaehlerDifferentialstatement · cited by 204
- Algebra.Extension.Ringstatement · cited by 179
- Algebra.Generatorsstatement and proof · cited by 152
- Algebra.Generators.valstatement and proof · cited by 115
- Algebra.Generators.toExtensionstatement and proof · cited by 103
Cited by6
Results whose statement or proof uses this declaration.
- Algebra.Presentation.differentials.comm₂₃'proof · cited by 1
- Algebra.Generators.H1Cotangent.δAux_ofCompproof · cited by 1
- Algebra.Generators.disjoint_ker_toKaehler_of_linearIndependentproof · cited by 1
- Algebra.Generators.H1Cotangent.exact_δ_mapproof · cited by 1
- Algebra.SubmersivePresentation.basisKaehlerOfIsCompl_applyproof · cited by 1
- Algebra.Generators.cotangentRestrict_bijective_of_isComplproof · cited by 1