Theorems · Definition · algebraic geometry

AlgebraicGeometry.Scheme.AffineOpenCover.ofIsOpenCover

{X : AlgebraicGeometry.Scheme} →
  {ι : Type u_1} →
    (U : ι → X.Opens) →
      TopologicalSpace.IsOpenCover U → (∀ (i : ι), AlgebraicGeometry.IsAffineOpen (U i)) → X.AffineOpenCover

The affine open cover given by a covering family of affine opens.

Defined in: Mathlib.AlgebraicGeometry.AffineScheme
Cited by: 4 results in Mathlib
Foundations: Depth 148 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites14

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CategoryTheory.Functor.objproof · cited by 19,642
TopCat.carrierstatement and proof · cited by 3,184
AlgebraicGeometry.Schemestatement and proof · cited by 2,540
CommRingCatstatement · cited by 2,333
AlgebraicGeometry.PresheafedSpace.carrierstatement and proof · cited by 2,020
AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement and proof · cited by 1,988
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement and proof · cited by 1,892
AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement and proof · cited by 1,734
AlgebraicGeometry.Scheme.Opensstatement and proof · cited by 1,149
AlgebraicGeometry.PresheafedSpace.presheafproof · cited by 1,104
AlgebraicGeometry.IsAffineOpenstatement and proof · cited by 222
AlgebraicGeometry.IsAffineOpen.fromSpecproof · cited by 65

Cited by4

Results whose statement or proof uses this declaration.

AlgebraicGeometry.Scheme.AffineOpenCover.ofIsOpenCover_I₀statement and proof · cited by 0
AlgebraicGeometry.Scheme.AffineOpenCover.ofIsOpenCover_Xstatement and proof · cited by 0
AlgebraicGeometry.Scheme.AffineOpenCover.ofIsOpenCover_fstatement and proof · cited by 0
AlgebraicGeometry.Scheme.Modules.exists_affineOpenCover_presentationproof · cited by 0