Theorems · Definition · algebraic geometry

AlgebraicGeometry.GeometricallyConnected.casesOn

{X Y : AlgebraicGeometry.Scheme} →
  {f : X ⟶ Y} →
    {motive : AlgebraicGeometry.GeometricallyConnected f → Sort u} →
      (t : AlgebraicGeometry.GeometricallyConnected f) →
        ((geometrically_connectedSpace : AlgebraicGeometry.geometrically (fun x => ConnectedSpace ↥x) f) → motive ⋯) →
          motive t

Defined in: Mathlib.AlgebraicGeometry.Geometrically.Connected
Cited by: 1 results in Mathlib
Foundations: Depth 132 from the axioms · uses propext, Classical.choice, Quot.sound

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites11

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

Cited by1

Results whose statement or proof uses this declaration.

AlgebraicGeometry.geometricallyConnected_iffproof · cited by 1