Theorems · Definition · algebraic geometry
AlgebraicGeometry.LocallyRingedSpace.GlueData.vPullbackConeIsLimit
(D : AlgebraicGeometry.LocallyRingedSpace.GlueData) → (i j : D.J) → CategoryTheory.Limits.IsLimit (D.vPullbackCone i j)
The following diagram is a pullback, i.e. Vᵢⱼ is the intersection of Uᵢ and Uⱼ in X.
``
Vᵢⱼ ⟶ Uᵢ
| |
↓ ↓
Uⱼ ⟶ X
``
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 126 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Limits.WalkingPairstatement · cited by 1,319
- CategoryTheory.Limits.IsLimitstatement · cited by 664
- CategoryTheory.Limits.WalkingCospanstatement · cited by 496
- CategoryTheory.Limits.cospanstatement · cited by 467
- AlgebraicGeometry.LocallyRingedSpacestatement · cited by 205
- CategoryTheory.Limits.WalkingMultispanstatement · cited by 151
- CategoryTheory.GlueData.Jstatement and proof · cited by 141
- CategoryTheory.Limits.MultispanIndex.multispanstatement · cited by 139
- CategoryTheory.GlueData.Ustatement · cited by 121
- CategoryTheory.Limits.MultispanShape.prodstatement · cited by 93
- CategoryTheory.GlueData.diagramstatement · cited by 68
- CategoryTheory.GlueData.gluedstatement · cited by 44
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.GlueData.vPullbackConeIsLimitproof · cited by 0