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Theorems · Definition · algebraic geometry

AlgebraicGeometry.Scheme.Cover.add

{P : CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme} →
  {X Y : AlgebraicGeometry.Scheme} →
    AlgebraicGeometry.Scheme.Cover (AlgebraicGeometry.Scheme.precoverage P) X →
      (f : Y ⟶ X) →
        autoParam (P f) AlgebraicGeometry.Scheme.Cover.add._auto_1 →
          AlgebraicGeometry.Scheme.Cover (AlgebraicGeometry.Scheme.precoverage P) X

Adding map satisfying P into a cover gives another cover.

Defined in
Mathlib.AlgebraicGeometry.Cover.MorphismProperty
Cited by
4 results in Mathlib
Foundations
Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

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AlgebraicGeometry.IsZariskiLocalAtSource.comp · cited by 10IsZariskiLocalAtSource.co…AlgebraicGeometry.IsZariskiLocalAtTarget.of_isPullback · cited by 6IsZariskiLocalAtTarget.of…AlgebraicGeometry.Scheme.Cover.add_toPreZeroHypercover · cited by 0Cover.add_toPreZeroHyperc…AlgebraicGeometry.HasAffineProperty.isZariskiLocalAtSource · cited by 0HasAffineProperty.isZaris…Quiver.Hom · cited by 32603Quiver.HomAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeCategoryTheory.MorphismProperty · cited by 2179CategoryTheory.MorphismPr…CategoryTheory.Precoverage.ZeroHypercover.toPreZeroHypercover · cited by 469ZeroHypercover.toPreZeroH…AlgebraicGeometry.Scheme.precoverage · cited by 336Scheme.precoverageCategoryTheory.PreZeroHypercover · cited by 256CategoryTheory.PreZeroHyp…AlgebraicGeometry.Scheme.Cover · cited by 88Scheme.CoverCategoryTheory.PreZeroHypercover.add · cited by 8PreZeroHypercover.addCover.addCITED BYCITES

Cites8

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Cited by4

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