Theorems · Definition · commutative algebra
Algebra.Extension.toKaehler
{R : Type u} →
{S : Type v} →
[inst : CommRing R] →
[inst_1 : CommRing S] → [inst_2 : Algebra R S] → (P : Algebra.Extension R S) → P.CotangentSpace →ₗ[S] Ω[S⁄R]The projection map from the relative cotangent space to the module of differentials.
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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
- KaehlerDifferentialstatement · cited by 204
- Algebra.Extension.Ringstatement and proof · cited by 179
- Algebra.Extensionstatement and proof · cited by 138
- Algebra.Extension.CotangentSpacestatement · cited by 73
- KaehlerDifferential.mapBaseChangeproof · cited by 12
Cited by16
Results whose statement or proof uses this declaration.
- Algebra.Generators.H1Cotangent.δproof · cited by 11
- Algebra.FormallySmooth.comp_surjectiveproof · cited by 6
- Algebra.Generators.toKaehler_cotangentSpaceBasisstatement and proof · cited by 6
- Algebra.Extension.exact_cotangentComplex_toKaehlerstatement · cited by 4
- Algebra.Generators.H1Cotangent.δ_eq_δAuxproof · cited by 3
- Algebra.Extension.toKaehler_surjectivestatement · cited by 3
- Algebra.Presentation.differentials.comm₂₃statement · cited by 1
- Algebra.Presentation.differentials.comm₂₃'statement and proof · cited by 1
- Algebra.Generators.H1Cotangent.δAux_ofCompstatement and proof · cited by 1
- Algebra.Generators.H1Cotangent.δ_eqstatement and proof · cited by 1
- Algebra.Generators.cotangentRestrict_bijective_of_isComplstatement and proof · cited by 1
- Algebra.Generators.disjoint_ker_toKaehler_of_linearIndependentstatement and proof · cited by 1