Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.exists_cover_of_mem_pretopology
∀ {P : CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme} [inst : P.IsStableUnderBaseChange]
[inst_1 : P.IsMultiplicative] {X : AlgebraicGeometry.Scheme} {R : CategoryTheory.Presieve X},
R ∈ (AlgebraicGeometry.Scheme.pretopology P).coverings X → ∃ 𝒰, R = CategoryTheory.Presieve.ofArrows 𝒰.X 𝒰.fAlias of the forward direction of AlgebraicGeometry.Scheme.mem_pretopology_iff.
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- Foundations
- Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound
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- 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 and proof · cited by 449
- AlgebraicGeometry.Scheme.precoveragestatement · cited by 336
- CategoryTheory.MorphismProperty.IsMultiplicativestatement and proof · cited by 332
- CategoryTheory.Precoverage.coveringsstatement · cited by 194
- CategoryTheory.Presieve.ofArrowsstatement · cited by 150
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