Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.OpenCover.affineRefinement
{X : AlgebraicGeometry.Scheme} → X.OpenCover → X.AffineOpenCoverGiven any open cover 𝓤, this is an affine open cover which refines it.
The morphism in the category of open covers which proves that this is indeed a refinement, see
AlgebraicGeometry.Scheme.OpenCover.fromAffineRefinement.
- Defined in
- Mathlib.AlgebraicGeometry.Cover.Open
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 144 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopCat.carrierproof · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- AlgebraicGeometry.Scheme.toLocallyRingedSpaceproof · cited by 1,734
- CategoryTheory.PreZeroHypercover.I₀proof · cited by 763
- CategoryTheory.PreZeroHypercover.Xproof · cited by 649
- CategoryTheory.PreZeroHypercover.fproof · cited by 542
- CategoryTheory.Precoverage.ZeroHypercover.toPreZeroHypercoverproof · cited by 469
- AlgebraicGeometry.Scheme.OpenCoverstatement and proof · cited by 207
- AlgebraicGeometry.LocallyRingedSpace.toTopCatproof · cited by 128
- AlgebraicGeometry.Scheme.affineCoverproof · cited by 61
- AlgebraicGeometry.Scheme.Cover.idxproof · cited by 28
- CategoryTheory.Precoverage.ZeroHypercover.bindproof · cited by 8
Cited by7
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.OpenCover.pullbackCoverAffineRefinementObjIsostatement and proof · cited by 4
- 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.OpenCover.pullbackCoverAffineRefinementObjIso_inv_map_assocstatement and proof · cited by 0
- AlgebraicGeometry.Scheme.OpenCover.pullbackCoverAffineRefinementObjIso_inv_pullbackHom_assocstatement and proof · cited by 0
- AlgebraicGeometry.Scheme.OpenCover.fromAffineRefinementstatement and proof · cited by 0