Theorems · Inductive type · algebraic geometry
AlgebraicGeometry.QuasiCompactCover
{S : AlgebraicGeometry.Scheme} → CategoryTheory.PreZeroHypercover S → PropA cover of a scheme is quasi-compact if every affine open of the base can be covered by a finite union of images of quasi-compact opens of the components.
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AlgebraicGeometry.Schemestatement · cited by 2,540
- CategoryTheory.PreZeroHypercoverstatement · cited by 256
Cited by21
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.presieve₀_mem_qcPrecoverage_iffstatement and proof · cited by 4
- AlgebraicGeometry.Scheme.quasiCompactCoverproof · cited by 2
- AlgebraicGeometry.IsAffineOpen.isCompactOpenCoveredstatement and proof · cited by 2
- AlgebraicGeometry.Scheme.Cover.ofQuasiCompactCoverstatement and proof · cited by 2
- AlgebraicGeometry.QuasiCompactCover.casesOnstatement and proof · cited by 1
- AlgebraicGeometry.QuasiCompactCover.exists_homstatement and proof · cited by 1
- AlgebraicGeometry.QuasiCompactCover.exists_isAffineOpen_of_isCompactstatement and proof · cited by 1
- AlgebraicGeometry.QuasiCompactCover.isCompactOpenCovered_of_isAffineOpenstatement and proof · cited by 1
- AlgebraicGeometry.QuasiCompactCover.isCompactOpenCovered_of_isCompactstatement and proof · cited by 1
- AlgebraicGeometry.QuasiCompactCover.of_homstatement and proof · cited by 1
- AlgebraicGeometry.QuasiCompactCover.of_isOpenMapstatement · cited by 1
- AlgebraicGeometry.Scheme.Cover.mem_propQCTopologystatement and proof · cited by 1