Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.AffineZariskiSite.grothendieckTopology
(X : AlgebraicGeometry.Scheme) → CategoryTheory.GrothendieckTopology X.AffineZariskiSite
The Grothendieck topology on X.AffineZariskiSite induced from the topology on X.Opens.
Also see mem_grothendieckTopology_iff_sectionsOfPresieve.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 161 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopCat.carrierproof · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- AlgebraicGeometry.PresheafedSpace.carrierproof · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpaceproof · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpaceproof · cited by 1,892
- AlgebraicGeometry.Scheme.toLocallyRingedSpaceproof · cited by 1,734
- CategoryTheory.GrothendieckTopologystatement · cited by 1,415
- Opens.grothendieckTopologyproof · cited by 206
- AlgebraicGeometry.Scheme.AffineZariskiSitestatement · cited by 30
- CategoryTheory.Functor.inducedTopologyproof · cited by 19
- AlgebraicGeometry.Scheme.AffineZariskiSite.toOpensFunctorproof · cited by 17
Cited by4
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.AffineZariskiSite.generate_presieveOfSections_mem_grothendieckTopologystatement and proof · cited by 1
- AlgebraicGeometry.Scheme.AffineZariskiSite.mem_grothendieckTopologystatement · cited by 1
- AlgebraicGeometry.Scheme.AffineZariskiSite.mem_grothendieckTopology_iff_sectionsOfPresievestatement and proof · cited by 0
- AlgebraicGeometry.Scheme.AffineZariskiSite.sheafEquivstatement · cited by 0