Theorems · Definition · commutative algebra
Algebra.Extension.Cotangent
{R : Type u} →
{S : Type v} → [inst : CommRing R] → [inst_1 : CommRing S] → [inst_2 : Algebra R S] → Algebra.Extension R S → Type wThe cotangent space of an extension.
This is a type synonym so that P.Ring can act on it through the action of S without creating
a diamond.
- Defined in
- Mathlib.RingTheory.Extension.Basic
- Cited by
- 121 results in Mathlib
- Foundations
- Depth 70 from the axioms, rests on 1,115 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Algebra.Extensionstatement and proof · cited by 138
- Algebra.Extension.kerproof · cited by 72
- Ideal.Cotangentproof · cited by 68
Cited by147
Results whose statement or proof uses this declaration.
- Algebra.Extension.Cotangent.mkstatement · cited by 49
- Algebra.Extension.H1Cotangentproof · cited by 49
- Algebra.Extension.cotangentComplexstatement and proof · cited by 48
- Algebra.Extension.Cotangent.mapstatement and proof · cited by 40
- Algebra.Extension.Cotangent.valstatement and proof · cited by 29
- Algebra.Extension.Cotangent.mk_surjectivestatement and proof · cited by 22
- Algebra.Extension.Cotangent.extstatement and proof · cited by 15
- Algebra.Extension.h1Cotangentιstatement · cited by 13
- Algebra.Generators.cMulXSubOneCotangentstatement · cited by 11
- Algebra.PreSubmersivePresentation.cotangentComplexAuxstatement · cited by 9
- Algebra.Extension.h1Cotangentι_extstatement · cited by 7
- Algebra.Generators.cotangentCompLocalizationAwayEquivstatement and proof · cited by 6