Theorems · Definition · commutative algebra
Algebra.SubmersivePresentation.toPreSubmersivePresentation
{R : Type u} →
{S : Type v} →
{ι : Type w} →
{σ : Type t} →
[inst : CommRing R] →
[inst_1 : CommRing S] →
[inst_2 : Algebra R S] →
[inst_3 : Finite σ] → Algebra.SubmersivePresentation R S ι σ → Algebra.PreSubmersivePresentation R S ι σ- Cited by
- 47 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
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
- Finitestatement and proof · cited by 3,029
- Algebra.PreSubmersivePresentationstatement · cited by 54
- Algebra.SubmersivePresentationstatement and proof · cited by 52
Cited by63
Results whose statement or proof uses this declaration.
- Algebra.SubmersivePresentation.jacobian_isUnitstatement · cited by 7
- Algebra.SubmersivePresentation.coeffsproof · cited by 4
- Algebra.SubmersivePresentation.basisKaehlerstatement · cited by 4
- Algebra.SubmersivePresentation.jacobianOfHasCoeffsproof · cited by 4
- Algebra.SubmersivePresentation.reindexproof · cited by 3
- Algebra.SubmersivePresentation.sectionCotangentstatement and proof · cited by 3
- Algebra.IsStandardSmoothOfRelativeDimension.casesOnstatement and proof · cited by 3
- Algebra.IsStandardSmoothOfRelativeDimension.outstatement · cited by 3
- Algebra.SubmersivePresentation.cotangentEquivstatement and proof · cited by 3
- Algebra.SubmersivePresentation.ofAlgEquivproof · cited by 3
- Algebra.SubmersivePresentation.rank_kaehlerDifferentialstatement and proof · cited by 2
- Algebra.SubmersivePresentation.sectionCotangent_eq_iffstatement and proof · cited by 2