Theorems · Definition · commutative algebra
Algebra.Generators.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) → Module.Basis ι S P.toExtension.CotangentSpaceThe canonical basis on the CotangentSpace.
- Cited by
- 22 results in Mathlib
- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Module.Basisstatement · cited by 1,477
- KaehlerDifferentialstatement · cited by 204
- Algebra.Extension.Ringstatement · cited by 179
- Algebra.Generatorsstatement and proof · cited by 152
- Algebra.Generators.toExtensionstatement · cited by 103
- Algebra.Extension.CotangentSpacestatement · cited by 73
- KaehlerDifferential.mvPolynomialBasisproof · cited by 9
- Module.Basis.baseChangeproof · cited by 9
Cited by27
Results whose statement or proof uses this declaration.
- Algebra.Generators.CotangentSpace.compEquivproof · cited by 9
- Algebra.PreSubmersivePresentation.cotangentComplexAuxproof · cited by 9
- Algebra.Generators.cotangentRestrictproof · cited by 6
- Algebra.Generators.toKaehler_cotangentSpaceBasisstatement · cited by 6
- Algebra.Generators.cotangentSpaceBasis_repr_tmulstatement · cited by 4
- Algebra.Generators.CotangentSpace.compEquiv_symm_inrproof · cited by 4
- Algebra.Generators.CotangentSpace.fst_compEquivproof · cited by 4
- Algebra.SubmersivePresentation.sectionCotangentproof · cited by 3
- Algebra.Generators.cotangentSpaceBasis_applystatement · cited by 3
- Algebra.SubmersivePresentation.sectionCotangent_eq_iffstatement and proof · cited by 2
- Algebra.SubmersivePresentation.basisKaehlerOfIsComplproof · cited by 2
- Algebra.Generators.repr_CotangentSpaceMapstatement and proof · cited by 2