Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.AffineZariskiSite.relativeGluingData
{X : AlgebraicGeometry.Scheme} →
{F : CategoryTheory.Functor X.AffineZariskiSiteᵒᵖ CommRingCat} →
{α : (AlgebraicGeometry.Scheme.AffineZariskiSite.toOpensFunctor X).op.comp X.presheaf ⟶ F} →
CategoryTheory.NatTrans.Coequifibered α →
AlgebraicGeometry.Scheme.Cover.RelativeGluingData (AlgebraicGeometry.Scheme.AffineZariskiSite.directedCover X)The relative gluing data associated to a quasi-coherent 𝒪ₓ algebra.
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites30
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Functorstatement and proof · cited by 16,252
- Oppositestatement and proof · cited by 8,081
- CategoryTheory.Functor.compstatement and proof · cited by 6,529
- CategoryTheory.Iso.invproof · cited by 6,514
- 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
Cited by7
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.normalizationGlueDataproof · cited by 3
- AlgebraicGeometry.Scheme.AffineZariskiSite.opensRange_relativeGluingData_mapstatement · cited by 1
- AlgebraicGeometry.Scheme.AffineZariskiSite.PreservesLocalization.colimitDesc_preimagestatement and proof · cited by 0
- AlgebraicGeometry.Scheme.AffineZariskiSite.PreservesLocalization.opensRange_mapstatement · cited by 0
- AlgebraicGeometry.Scheme.AffineZariskiSite.isColimitCoconeproof · cited by 0