Theorems · Definition · algebraic geometry

AlgebraicGeometry.Scheme.Hom.cover

{P : CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme} →
  {X S : AlgebraicGeometry.Scheme} →
    (f : X ⟶ S) →
      P f → [AlgebraicGeometry.Surjective f] → AlgebraicGeometry.Scheme.Cover (AlgebraicGeometry.Scheme.precoverage P) S

The single object covering by one surjective morphism satisfying P.

Defined in: Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap
Cited by: 8 results in Mathlib
Foundations: Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: AlgebraicGeometry.Surjective

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Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites7

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
AlgebraicGeometry.Schemestatement and proof · cited by 2,540
CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
AlgebraicGeometry.Scheme.precoveragestatement · cited by 336
AlgebraicGeometry.Scheme.Coverstatement · cited by 88
AlgebraicGeometry.Surjectivestatement and proof · cited by 48
CategoryTheory.Precoverage.ZeroHypercover.singletonproof · cited by 2

Cited by8

Results whose statement or proof uses this declaration.

AlgebraicGeometry.Scheme.Hom.presieve₀_coverstatement · cited by 2
AlgebraicGeometry.Scheme.Hom.singleton_mem_qcPrecoverageproof · cited by 1
AlgebraicGeometry.isSheaf_type_propQCTopology_iffproof · cited by 1
AlgebraicGeometry.Scheme.Hom.cover.congr_simpstatement and proof · cited by 0
AlgebraicGeometry.Scheme.Hom.singleton_mem_fppfPrecoverageproof · cited by 0
AlgebraicGeometry.Scheme.Hom.cover_I₀statement and proof · cited by 0
AlgebraicGeometry.Scheme.Hom.cover_Xstatement and proof · cited by 0
AlgebraicGeometry.Scheme.Hom.cover_fstatement and proof · cited by 0