Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.AffineZariskiSite.mem_grothendieckTopology_iff_sectionsOfPresieve
∀ {X : AlgebraicGeometry.Scheme} {U : X.AffineZariskiSite} {S : CategoryTheory.Sieve U},
S ∈ (AlgebraicGeometry.Scheme.AffineZariskiSite.grothendieckTopology X) U ↔
Ideal.span (AlgebraicGeometry.Scheme.AffineZariskiSite.sectionsOfPresieve S.arrows) = ⊤- Cited by
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- Foundations
- Depth 165 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites30
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- Setstatement · cited by 53,352
- CategoryTheory.Functor.objstatement · cited by 19,642
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- 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 · cited by 1,988
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