Structures · Geometry
AlgebraicGeometry.GeometricallyConnected
We say that a morphism f : X ⟶ Y is geometrically connected if for all Spec K ⟶ Y with K
a field, X ×[Y] Spec K is connected.
- Shape
- One type argument · adds geometrically_connectedSpace
Extends0
Extends nothing: this is a root of the hierarchy.
Extended by0
Nothing extends this class yet.
Forgetful instances
Every AlgebraicGeometry.GeometricallyConnected is also a
Concrete types that are instances3
- CategoryTheory.Limits.pullback
- AlgebraicGeometry.Scheme.Hom.fiber
- AlgebraicGeometry.Scheme.Opens.toScheme
How is a type an instance?
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Assumed by16
- AlgebraicGeometry.Scheme.Hom.isConnected_preimage
- AlgebraicGeometry.Scheme.Hom.connectedComponentsHomeomorph
- AlgebraicGeometry.GeometricallyConnected.connectedSpace
- AlgebraicGeometry.Scheme.Hom.isConnected_preimage_singleton
- AlgebraicGeometry.instGeometricallyConnectedMorphismRestrict
- AlgebraicGeometry.GeometricallyConnected.geometrically_connectedSpace
- AlgebraicGeometry.GeometricallyConnected.connectedSpace_of_subsingleton
- AlgebraicGeometry.Scheme.Hom.connectedComponentsHomeomorph_apply
- AlgebraicGeometry.instConnectedSpaceCarrierCarrierCommRingCatPullbackSchemeOfGeometricallyConnectedOfUniversallyOpen_1
- AlgebraicGeometry.GeometricallyConnected.comp
- AlgebraicGeometry.instSurjectiveOfGeometricallyConnected
- AlgebraicGeometry.instGeometricallyConnectedFiberToSpecResidueField
- AlgebraicGeometry.instConnectedSpaceCarrierCarrierCommRingCatFiberOfGeometricallyConnected
- AlgebraicGeometry.instGeometricallyConnectedSndScheme
- AlgebraicGeometry.instGeometricallyConnectedFstScheme
- AlgebraicGeometry.instConnectedSpaceCarrierCarrierCommRingCatPullbackSchemeOfGeometricallyConnectedOfUniversallyOpen