Theorems · Theorem · commutative algebra
Algebra.Extension.subsingleton_h1Cotangent
∀ {R : Type u} {S : Type v} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S]
(P : Algebra.Extension R S), Subsingleton P.H1Cotangent ↔ Function.Injective ⇑P.cotangentComplex- Cited by
- 3 results in Mathlib
- Foundations
- Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- LinearMap.kerproof · cited by 848
- KaehlerDifferentialstatement · cited by 204
- Algebra.Extension.Ringstatement · cited by 179
- Algebra.Extensionstatement and proof · cited by 138
- Algebra.Extension.Cotangentstatement and proof · cited by 121
- LinearMap.ker_eq_botproof · cited by 92
- Algebra.Extension.CotangentSpacestatement · cited by 73
Cited by3
Results whose statement or proof uses this declaration.
- Algebra.FormallySmooth.comp_surjectiveproof · cited by 6
- Algebra.Extension.cotangentComplex_injective_iffproof · cited by 1
- Algebra.Generators.cotangentRestrict_bijective_of_isComplproof · cited by 1