Theorems · Theorem · commutative algebra
Algebra.Extension.H1Cotangent.map_toInfinitesimal_bijective
∀ {R : Type u_1} {S : Type u_3} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S]
(P : Algebra.Extension R S), Function.Bijective ⇑(Algebra.Extension.H1Cotangent.map P.toInfinitesimal)- Defined in
- Mathlib.RingTheory.Smooth.Kaehler
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · 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
- Function.Bijectivestatement · cited by 863
- LinearMap.kerproof · cited by 848
- Algebra.Extensionstatement and proof · cited by 138
- Algebra.Extension.Cotangentproof · cited by 121
- Function.Bijective.injectiveproof · cited by 115
- Algebra.Extension.CotangentSpaceproof · cited by 73
- map_eq_zero_iffproof · cited by 62
Cited by2
Results whose statement or proof uses this declaration.
- Algebra.Extension.H1Cotangent.equivOfFormallySmoothproof · cited by 5
- Algebra.Extension.H1Cotangent.equivOfFormallySmooth_toLinearMapproof · cited by 1