Theorems · Definition · commutative algebra
Algebra.SubmersivePresentation.coeffs
{R : Type u_1} →
{S : Type u_2} →
{ι : Type u_3} →
{σ : Type u_4} →
[inst : CommRing R] →
[inst_1 : CommRing S] →
[inst_2 : Algebra R S] → [inst_3 : Finite σ] → Algebra.SubmersivePresentation R S ι σ → Set RThe set of coefficients that is enough to descend a submersive presentation P.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 135 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- SetLike.coeproof · cited by 8,199
- Finitestatement and proof · cited by 3,029
- Set.iUnionproof · cited by 2,483
- Units.valproof · cited by 1,966
- IsUnit.unitproof · cited by 252
- Algebra.Presentation.toGeneratorsproof · cited by 104
- Algebra.PreSubmersivePresentation.toPresentationproof · cited by 84
- Algebra.SubmersivePresentationstatement and proof · cited by 52
- Algebra.SubmersivePresentation.toPreSubmersivePresentationproof · cited by 47
Cited by6
Results whose statement or proof uses this declaration.
- Algebra.SubmersivePresentation.HasCoeffs.coeffs_subset_rangestatement · cited by 2
- Algebra.SubmersivePresentation.finite_coeffsstatement · cited by 1
- Algebra.IsStandardSmoothOfRelativeDimension.exists_subalgebra_fgproof · cited by 1
- Algebra.SubmersivePresentation.coeffs_toPresentation_subset_coeffsstatement · cited by 0
- Algebra.SubmersivePresentation.HasCoeffs.casesOnstatement and proof · cited by 0
- Algebra.SubmersivePresentation.HasCoeffs.recOnstatement and proof · cited by 0