Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.IdealSheafData.le_ofIdeals_iff
∀ {X : AlgebraicGeometry.Scheme} {I : X.IdealSheafData}
{J : (U : ↑X.affineOpens) → Ideal ↑(X.presheaf.obj (Opposite.op ↑U))},
I ≤ AlgebraicGeometry.Scheme.IdealSheafData.ofIdeals J ↔ I.ideal ≤ J- Cited by
- 2 results in Mathlib
- Foundations
- Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- Oppositestatement · cited by 8,081
- Set.Elemstatement and proof · cited by 7,166
- Idealstatement and proof · cited by 4,748
- TopCat.carrierstatement · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CommRingCatstatement · cited by 2,333
- TopologicalSpace.Opensstatement · cited by 2,040
- AlgebraicGeometry.PresheafedSpace.carrierstatement · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement and proof · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement and proof · cited by 1,892
Cited by2
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.ker_eq_top_of_isEmptyproof · cited by 2
- AlgebraicGeometry.Scheme.ker_of_isAffineproof · cited by 1