Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.Cover.mem_propQCTopology
∀ {P : CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme} {S : AlgebraicGeometry.Scheme}
(𝒰 : AlgebraicGeometry.Scheme.Cover (AlgebraicGeometry.Scheme.precoverage P) S)
[AlgebraicGeometry.QuasiCompactCover 𝒰.toPreZeroHypercover],
CategoryTheory.Sieve.ofArrows 𝒰.X 𝒰.f ∈ (AlgebraicGeometry.Scheme.propQCTopology P) S- Cited by
- 1 results in Mathlib
- Foundations
- Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement · cited by 53,352
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
- CategoryTheory.GrothendieckTopologystatement · cited by 1,415
- CategoryTheory.PreZeroHypercover.I₀statement · cited by 763
- CategoryTheory.PreZeroHypercover.Xstatement · cited by 649
- CategoryTheory.Sievestatement · cited by 552
- CategoryTheory.PreZeroHypercover.fstatement · cited by 542
- CategoryTheory.Precoverage.ZeroHypercover.toPreZeroHypercoverstatement and proof · cited by 469
- AlgebraicGeometry.Scheme.precoveragestatement and proof · cited by 336
- AlgebraicGeometry.Scheme.Coverstatement and proof · cited by 88
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.isSheaf_type_propQCTopology_iffproof · cited by 1