Theorems · Definition · algebraic geometry
AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.pullbackConeOfLeftIsLimit
{X Y Z : AlgebraicGeometry.LocallyRingedSpace} →
(f : X ⟶ Z) →
(g : Y ⟶ Z) →
[H : AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion f] →
CategoryTheory.Limits.IsLimit (AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.pullbackConeOfLeft f g)The constructed pullbackConeOfLeft is indeed limiting.
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Limits.WalkingPairstatement · cited by 1,319
- AlgebraicGeometry.LocallyRingedSpace.Hom.toHomproof · cited by 995
- CategoryTheory.Limits.IsLimitstatement · cited by 664
- CategoryTheory.Limits.WalkingCospanstatement · cited by 496
- CategoryTheory.Limits.cospanstatement · cited by 467
- AlgebraicGeometry.LocallyRingedSpacestatement and proof · cited by 205
- CategoryTheory.Limits.PullbackCone.mkproof · cited by 203
- CategoryTheory.Limits.PullbackConeproof · cited by 136
- CategoryTheory.Limits.PullbackCone.fstproof · cited by 118
- CategoryTheory.Limits.PullbackCone.sndproof · cited by 113
- AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersionstatement and proof · cited by 28
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.