Theorems · Theorem · algebraic geometry
AlgebraicGeometry.IsZariskiLocalAtSource.of_iSup_eq_top
∀ {P : CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme} [AlgebraicGeometry.IsZariskiLocalAtSource P]
{X Y : AlgebraicGeometry.Scheme} {f : X ⟶ Y} {ι : Sort u_1} (U : ι → X.Opens),
iSup U = ⊤ → (∀ (i : ι), P (CategoryTheory.CategoryStruct.comp (U i).ι f)) → P f- Cited by
- 2 results in Mathlib
- Foundations
- Depth 142 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites36
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
- Top.topstatement and proof · cited by 9,680
- SetLike.coeproof · cited by 8,199
- Set.Elemproof · cited by 7,166
- Set.rangeproof · cited by 4,705
- TopCat.carrierstatement and proof · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- Set.iUnionproof · cited by 2,483
- iSupstatement and proof · cited by 2,415
- CommRingCatstatement · cited by 2,333
- Set.extproof · cited by 2,266
Cited by2
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.IsZariskiLocalAtSource.iff_of_iSup_eq_topproof · cited by 3
- AlgebraicGeometry.IsZariskiLocalAtSource.of_openCoverproof · cited by 2