Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.Cover.RelativeGluingData.toBase
{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 ⟶ SThe structure map from the colimit of the Xᵢ to S.
- Defined in
- Mathlib.AlgebraicGeometry.RelativeGluing
- Cited by
- 8 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.
Cites18
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
- Quiver.Homstatement · cited by 32,603
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- 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
- CategoryTheory.Limits.colimit.descproof · cited by 63
Cited by10
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.fromNormalizationproof · cited by 28
- AlgebraicGeometry.Scheme.Cover.ColimitGluingData.gluedproof · cited by 7
- AlgebraicGeometry.Scheme.Hom.normalizationDesc_compproof · cited by 5
- AlgebraicGeometry.Scheme.Cover.RelativeGluingData.ι_toBasestatement · cited by 4
- AlgebraicGeometry.Scheme.Cover.RelativeGluingData.preimage_toBase_eq_range_ιstatement and proof · cited by 2
- AlgebraicGeometry.Scheme.Cover.RelativeGluingData.toBase_preimage_eq_opensRange_ιstatement · cited by 2
- AlgebraicGeometry.Scheme.Hom.fromNormalization_preimageproof · cited by 1
- AlgebraicGeometry.Scheme.Cover.RelativeGluingData.isPullback_natTrans_ι_toBasestatement and proof · cited by 0
- AlgebraicGeometry.Scheme.AffineZariskiSite.PreservesLocalization.colimitDesc_preimagestatement and proof · cited by 0
- AlgebraicGeometry.Scheme.Cover.RelativeGluingData.ι_toBase_assocstatement and proof · cited by 0