Theorems · Theorem · commutative algebra
Algebra.Extension.cotangentComplex_injective_iff
∀ {R : Type u} {A : Type v} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A] (P : Algebra.Extension R A)
[Algebra.FormallySmooth R P.Ring], Function.Injective ⇑P.cotangentComplex ↔ Subsingleton (Algebra.H1Cotangent R A)- Defined in
- Mathlib.RingTheory.Smooth.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 125 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 · 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
- KaehlerDifferentialstatement · cited by 204
- Algebra.Extension.Ringstatement and proof · cited by 179
- AddEquiv.toEquivproof · cited by 174
- Algebra.Extensionstatement and proof · cited by 138
- Algebra.Extension.Cotangentstatement · cited by 121
- Algebra.Extension.CotangentSpacestatement · cited by 73
- Algebra.FormallySmoothstatement and proof · cited by 60
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.FormallySmooth.kerCotangentToTensor_injective_iffproof · cited by 1