Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.AffineZariskiSite.PreservesLocalization.isLocallyDirected
Deprecated since 2026-02-01Mathlib marks this declaration as deprecated.
∀ {X : AlgebraicGeometry.Scheme} (F : CategoryTheory.Functor X.AffineZariskiSiteᵒᵖ CommRingCat)
(α : (AlgebraicGeometry.Scheme.AffineZariskiSite.toOpensFunctor X).op.comp X.presheaf ⟶ F),
CategoryTheory.NatTrans.Coequifibered α →
((F.rightOp.comp AlgebraicGeometry.Scheme.Spec).comp AlgebraicGeometry.Scheme.forget).IsLocallyDirected- Cited by
- 0 results in Mathlib
- Foundations
- Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- TopCat.carrierstatement · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CommRingCatstatement and proof · cited by 2,333
- 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
- AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement and proof · cited by 1,734
- AlgebraicGeometry.Scheme.Opensstatement · cited by 1,149
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