Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.AffineOpenCover.openCover
{X : AlgebraicGeometry.Scheme} → X.AffineOpenCover → X.OpenCoverThe open cover associated to an affine open cover.
- Defined in
- Mathlib.AlgebraicGeometry.Cover.Open
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 133 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- AlgebraicGeometry.Scheme.OpenCoverstatement · cited by 207
- AlgebraicGeometry.Scheme.AffineCover.coverproof · cited by 5
- AlgebraicGeometry.Scheme.AffineOpenCoverstatement and proof · cited by 4
Cited by20
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.IdealSheafData.inclusionproof · cited by 12
- AlgebraicGeometry.Scheme.AffineOpenCover.openCover_fstatement and proof · cited by 5
- AlgebraicGeometry.Scheme.OpenCover.pullbackCoverAffineRefinementObjIsostatement and proof · cited by 4
- AlgebraicGeometry.Scheme.IdealSheafData.inclusion_subschemeιproof · cited by 3
- AlgebraicGeometry.Scheme.IdealSheafData.subSchemeCover_map_inclusionproof · cited by 3
- AlgebraicGeometry.isLocallyNoetherian_iff_openCoverproof · cited by 2
- AlgebraicGeometry.Scheme.OpenCover.pullbackCoverAffineRefinementObjIso_inv_mapstatement and proof · cited by 1
- AlgebraicGeometry.Scheme.OpenCover.pullbackCoverAffineRefinementObjIso_inv_pullbackHomstatement and proof · cited by 1
- AlgebraicGeometry.Scheme.IdealSheafData.inclusion_compproof · cited by 1
- AlgebraicGeometry.Scheme.IdealSheafData.inclusion_idproof · cited by 1
- AlgebraicGeometry.Scheme.OpenCover.pullbackCoverAffineRefinementObjIso_inv_map_assocstatement and proof · cited by 0