Theorems · Theorem · algebraic geometry
AlgebraicGeometry.HasAffineProperty.iff_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) = ⊤ → (P f ↔ ∀ (i : ι), Q (f ∣_ ↑(U i)))- Cited by
- 2 results in Mathlib
- Foundations
- Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites27
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- Top.topstatement and proof · cited by 9,680
- Set.Elemstatement and proof · cited by 7,166
- TopCat.carrierstatement · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- iSupstatement and proof · cited by 2,415
- CommRingCatstatement · cited by 2,333
- CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
- TopologicalSpace.Opensstatement · cited by 2,040
- AlgebraicGeometry.PresheafedSpace.carrierstatement · cited by 2,020
Cited by2
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.isAffineHom_of_forall_exists_isAffineOpenproof · cited by 1
- AlgebraicGeometry.HasAffineProperty.iff_of_openCoverproof · cited by 1