Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.Cover.mem_pretopology
∀ {P : CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme} [inst : P.IsStableUnderBaseChange]
[inst_1 : P.IsMultiplicative] {X : AlgebraicGeometry.Scheme}
{𝒰 : AlgebraicGeometry.Scheme.Cover (AlgebraicGeometry.Scheme.precoverage P) X},
CategoryTheory.Presieve.ofArrows 𝒰.X 𝒰.f ∈ (AlgebraicGeometry.Scheme.pretopology P).coverings X- Cited by
- 1 results in Mathlib
- Foundations
- Depth 196 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
- CategoryTheory.PreZeroHypercover.I₀statement · cited by 763
- CategoryTheory.PreZeroHypercover.Xstatement · cited by 649
- CategoryTheory.PreZeroHypercover.fstatement · cited by 542
- CategoryTheory.Precoverage.ZeroHypercover.toPreZeroHypercoverstatement · cited by 469
- CategoryTheory.Presievestatement · cited by 449
- AlgebraicGeometry.Scheme.precoveragestatement and proof · cited by 336
- CategoryTheory.MorphismProperty.IsMultiplicativestatement and proof · cited by 332
- CategoryTheory.Precoverage.coveringsstatement · cited by 194
- CategoryTheory.Presieve.ofArrowsstatement · cited by 150
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.mem_grothendieckTopology_iffproof · cited by 2