Theorems · Theorem · algebraic geometry
AlgebraicGeometry.HasAffineProperty.of_iSup_eq_top
∀ {P : CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme} {Q : AlgebraicGeometry.AffineTargetMorphismProperty}
[AlgebraicGeometry.HasAffineProperty P Q] {X Y : AlgebraicGeometry.Scheme} {f : X ⟶ Y} {ι : Sort u_1}
(U : ι → ↑Y.affineOpens), ⨆ i, ↑(U i) = ⊤ → (∀ (i : ι), Q (f ∣_ ↑(U i))) → P f- Cited by
- 3 results in Mathlib
- Foundations
- Depth 159 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites54
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- Top.topstatement and proof · cited by 9,680
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- CategoryTheory.ConcreteCategory.homproof · cited by 4,022
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Cited by3
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.HasAffineProperty.of_openCoverproof · cited by 3
- AlgebraicGeometry.isAffine_of_isAffineOpen_basicOpenproof · cited by 2
- AlgebraicGeometry.HasAffineProperty.iff_of_iSup_eq_topproof · cited by 2