Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.IdealSheafData.glueDataObjMap
{X : AlgebraicGeometry.Scheme} →
(I : X.IdealSheafData) → {U V : ↑X.affineOpens} → U ≤ V → (I.glueDataObj U ⟶ I.glueDataObj V)The open immersion Spec Γ(𝒪ₓ/I, U) ⟶ Spec Γ(𝒪ₓ/I, V) if U ≤ V.
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Quiver.Homstatement · cited by 32,603
- CategoryTheory.Functor.mapproof · cited by 8,698
- Set.Elemstatement and proof · cited by 7,166
- TopCat.carrierstatement · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CommRingCatstatement · cited by 2,333
- AlgebraicGeometry.PresheafedSpace.carrierstatement · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement and proof · cited by 1,988
- Quiver.Hom.opproof · cited by 1,948
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement and proof · cited by 1,892
- AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement and proof · cited by 1,734
Cited by5
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.IdealSheafData.glueDataObjMap_glueDataObjιstatement · cited by 1
- AlgebraicGeometry.Scheme.IdealSheafData.glueDataObjMap_glueDataObjι_assocstatement and proof · cited by 1
- AlgebraicGeometry.Scheme.IdealSheafData.opensRange_glueDataObjMapstatement · cited by 1
- AlgebraicGeometry.Scheme.IdealSheafData.ideal_le_ker_glueDataObjιproof · cited by 0
- AlgebraicGeometry.Scheme.IdealSheafData.glueDataObjMap.congr_simpstatement and proof · cited by 0