Theorems · Definition · algebraic geometry
AlgebraicGeometry.PresheafedSpace.GlueData.vPullbackConeIsLimit
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
(D : AlgebraicGeometry.PresheafedSpace.GlueData C) →
[inst_1 : CategoryTheory.Limits.HasLimits C] → (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
``
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- Foundations
- Depth 124 from the axioms · uses propext, Classical.choice, Quot.sound
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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
- Oppositestatement · cited by 8,081
- TopCatstatement · cited by 1,889
- 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.PresheafedSpacestatement · cited by 260
- CategoryTheory.Limits.WalkingMultispanstatement · cited by 151
- CategoryTheory.GlueData.Jstatement and proof · cited by 141
- CategoryTheory.Limits.MultispanIndex.multispanstatement · cited by 139
- CategoryTheory.Limits.PullbackConeproof · cited by 136
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- AlgebraicGeometry.SheafedSpace.GlueData.vPullbackConeIsLimitproof · cited by 0