Theorems · Definition · algebraic geometry

AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.pullbackConeOfLeftIsLimit

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {X Y Z : AlgebraicGeometry.PresheafedSpace C} →
      (f : X ⟶ Z) →
        [hf : AlgebraicGeometry.PresheafedSpace.IsOpenImmersion f] →
          (g : Y ⟶ Z) →
            CategoryTheory.Limits.IsLimit (AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.pullbackConeOfLeft f g)

The constructed pullback cone is indeed the pullback.

Defined in: Mathlib.Geometry.RingedSpace.OpenImmersion
Cited by: 1 results in Mathlib
Foundations: Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category AlgebraicGeometry.PresheafedSpace.IsOpenImmersion

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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
Quiver.Homstatement and proof · cited by 32,603
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 and proof · cited by 260
CategoryTheory.Limits.PullbackConeproof · cited by 136
AlgebraicGeometry.PresheafedSpace.IsOpenImmersionstatement and proof · cited by 44
AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.pullbackConeOfLeftstatement and proof · cited by 3
CategoryTheory.Limits.PullbackCone.isLimitAux'proof · cited by 2
AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.pullbackConeOfLeftLiftproof · cited by 2

Cited by1

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AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.pullback_snd_isIso_of_range_subsetproof · cited by 0