Theorems · Theorem · algebraic geometry
AlgebraicGeometry.geometricallyConnected_iff
∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y),
AlgebraicGeometry.GeometricallyConnected f ↔ AlgebraicGeometry.geometrically (fun x => ConnectedSpace ↥x) f- Cited by
- 1 results in Mathlib
- Foundations
- Depth 133 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- TopCat.carrierstatement and proof · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CommRingCatstatement · cited by 2,333
- AlgebraicGeometry.PresheafedSpace.carrierstatement and proof · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement and proof · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement and proof · cited by 1,892
- AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement and proof · cited by 1,734
- ConnectedSpacestatement and proof · cited by 37
- AlgebraicGeometry.geometricallystatement and proof · cited by 26
- AlgebraicGeometry.GeometricallyConnectedstatement and proof · cited by 10
- AlgebraicGeometry.GeometricallyConnected.casesOnproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.GeometricallyConnected.eq_geometricallyproof · cited by 1