Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.Cover.RelativeGluingData.cover
{S : AlgebraicGeometry.Scheme} →
{𝒰 : S.OpenCover} →
[inst : CategoryTheory.Category.{u_2, u_1} 𝒰.I₀] →
[inst_1 : AlgebraicGeometry.Scheme.Cover.LocallyDirected 𝒰] →
(d : AlgebraicGeometry.Scheme.Cover.RelativeGluingData 𝒰) →
[inst_2 : Small.{u, u_1} 𝒰.I₀] → [inst_3 : Quiver.IsThin 𝒰.I₀] → d.glued.OpenCoverThe cover of the glued Xᵢ given by the Xᵢ.
- Defined in
- Mathlib.AlgebraicGeometry.RelativeGluing
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CategoryTheory.PreZeroHypercover.I₀statement and proof · cited by 763
- AlgebraicGeometry.IsOpenImmersionstatement · cited by 476
- CategoryTheory.Precoverage.ZeroHypercover.toPreZeroHypercoverstatement and proof · cited by 469
- Smallstatement and proof · cited by 369
- AlgebraicGeometry.Scheme.precoveragestatement · cited by 336
- AlgebraicGeometry.Scheme.OpenCoverstatement and proof · cited by 207
- AlgebraicGeometry.Scheme.Cover.LocallyDirectedstatement and proof · cited by 63
- Quiver.IsThinstatement and proof · cited by 51
- AlgebraicGeometry.Scheme.Cover.RelativeGluingData.functorproof · cited by 18
- AlgebraicGeometry.Scheme.Cover.RelativeGluingDatastatement and proof · cited by 12
Cited by6
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.normalizationOpenCoverproof · cited by 9
- AlgebraicGeometry.Scheme.Cover.ColimitGluingData.isColimitGluedCoconeproof · cited by 1
- AlgebraicGeometry.Scheme.Cover.RelativeGluingData.cover_fstatement and proof · cited by 1
- AlgebraicGeometry.Scheme.AffineZariskiSite.PreservesLocalization.colimitDesc_preimagestatement and proof · cited by 0
- AlgebraicGeometry.Scheme.Cover.RelativeGluingData.cover_I₀statement and proof · cited by 0
- AlgebraicGeometry.Scheme.Cover.RelativeGluingData.cover_Xstatement and proof · cited by 0