Theorems · Definition · algebraic geometry

AlgebraicGeometry.Scheme.Pullback.p2

{X Y Z : AlgebraicGeometry.Scheme} →
  (𝒰 : X.OpenCover) →
    (f : X ⟶ Z) →
      (g : Y ⟶ Z) →
        [inst : ∀ (i : 𝒰.I₀), CategoryTheory.Limits.HasPullback (CategoryTheory.CategoryStruct.comp (𝒰.f i) f) g] →
          (AlgebraicGeometry.Scheme.Pullback.gluing 𝒰 f g).glued ⟶ Y

The second projection from the glued scheme into Y.

Defined in: Mathlib.AlgebraicGeometry.Pullbacks
Cited by: 7 results in Mathlib
Foundations: Depth 150 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Limits.HasPullback

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Cites20

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.CategoryStruct.compstatement and proof · cited by 17,999
AlgebraicGeometry.Schemestatement and proof · cited by 2,540
CategoryTheory.PreZeroHypercover.I₀statement and proof · cited by 763
CategoryTheory.PreZeroHypercover.Xstatement · cited by 649
CategoryTheory.Limits.pullback.sndproof · cited by 637
CategoryTheory.PreZeroHypercover.fstatement and proof · cited by 542
AlgebraicGeometry.IsOpenImmersionstatement · cited by 476
CategoryTheory.Precoverage.ZeroHypercover.toPreZeroHypercoverstatement and proof · cited by 469
CategoryTheory.Limits.HasPullbackstatement and proof · cited by 434
AlgebraicGeometry.Scheme.precoveragestatement · cited by 336
AlgebraicGeometry.Scheme.OpenCoverstatement and proof · cited by 207

Cited by9

Results whose statement or proof uses this declaration.

AlgebraicGeometry.Scheme.Pullback.pullbackP1Isoproof · cited by 10
AlgebraicGeometry.Scheme.Pullback.pullbackP1Iso_hom_fstproof · cited by 1
AlgebraicGeometry.Scheme.Pullback.pullbackP1Iso_hom_sndstatement and proof · cited by 1
AlgebraicGeometry.Scheme.Pullback.gluedIsLimitstatement and proof · cited by 1
AlgebraicGeometry.Scheme.Pullback.p_commstatement and proof · cited by 1
AlgebraicGeometry.Scheme.Pullback.hasPullback_of_coverproof · cited by 1
AlgebraicGeometry.Scheme.Pullback.lift_comp_ιstatement and proof · cited by 0
AlgebraicGeometry.Scheme.Pullback.pullbackP1Iso_hom_snd_assocstatement and proof · cited by 0
AlgebraicGeometry.Scheme.Pullback.gluedLift_p2statement and proof · cited by 0