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Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.Hom.singleton_mem_propQCPrecoverage

∀ {P : CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme} {X Y : AlgebraicGeometry.Scheme} {f : X ⟶ Y},
  P f →
    ∀ [AlgebraicGeometry.Surjective f] [AlgebraicGeometry.QuasiCompact f],
      CategoryTheory.Presieve.singleton f ∈ (AlgebraicGeometry.Scheme.propQCPrecoverage P).coverings Y
Defined in
Mathlib.AlgebraicGeometry.Sites.QuasiCompact
Cited by
2 results in Mathlib
Foundations
Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AlgebraicGeometry.SurjectiveAlgebraicGeometry.QuasiCompact
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AlgebraicGeometry.Scheme.Hom.generate_singleton_mem_propQCTopology · cited by 0Hom.generate_singleton_me…AlgebraicGeometry.Scheme.Hom.singleton_mem_fpqcPrecoverage · cited by 0Hom.singleton_mem_fpqcPre…Set · cited by 53352SetQuiver.Hom · cited by 32603Quiver.HomAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeCategoryTheory.MorphismProperty · cited by 2179CategoryTheory.MorphismPr…CategoryTheory.Presieve · cited by 449CategoryTheory.PresieveCategoryTheory.Precoverage.coverings · cited by 194Precoverage.coveringsAlgebraicGeometry.QuasiCompact · cited by 102AlgebraicGeometry.QuasiCo…CategoryTheory.Presieve.singleton · cited by 57Presieve.singletonAlgebraicGeometry.Surjective · cited by 48AlgebraicGeometry.Surject…AlgebraicGeometry.Scheme.propQCPrecoverage · cited by 10Scheme.propQCPrecoverageAlgebraicGeometry.Scheme.Hom.singleton_mem_qcPrecoverage · cited by 1Hom.singleton_mem_qcPreco…Hom.singleton_mem_propQCPreco…CITED BYCITES

Cites11

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Cited by2

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