Theorems · Definition · commutative algebra
Algebra.Extension.Cotangent.val
{R : Type u} →
{S : Type v} →
[inst : CommRing R] →
[inst_1 : CommRing S] → [inst_2 : Algebra R S] → {P : Algebra.Extension R S} → P.Cotangent → P.ker.CotangentThe identity map P.Cotangent → P.ker.Cotangent from the type synonym.
- Defined in
- Mathlib.RingTheory.Extension.Basic
- Cited by
- 29 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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.Extension.Ringstatement · cited by 179
- Algebra.Extensionstatement and proof · cited by 138
- Algebra.Extension.Cotangentstatement and proof · cited by 121
- Algebra.Extension.kerstatement · cited by 72
- Ideal.Cotangentstatement · cited by 68
Cited by31
Results whose statement or proof uses this declaration.
- Algebra.Extension.Cotangent.mapproof · cited by 40
- Algebra.Extension.Cotangent.mk_surjectiveproof · cited by 22
- Algebra.Extension.Cotangent.extstatement and proof · cited by 15
- Algebra.FormallySmooth.comp_surjectiveproof · cited by 6
- Algebra.Extension.H1Cotangent.map_compproof · cited by 6
- Algebra.Extension.H1Cotangent.map_eqproof · cited by 6
- Algebra.Generators.Cotangent.exactproof · cited by 6
- Algebra.Extension.Cotangent.val_smul'statement and proof · cited by 3
- Algebra.Extension.cotangentEquivCotangentKerproof · cited by 3
- Algebra.Extension.cotangentExtendScalarsEquiv_symm_toLinearMapproof · cited by 2
- Algebra.Extension.Cotangent.map_compproof · cited by 2
- Algebra.Extension.Cotangent.val_smul''statement and proof · cited by 1