Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.Hom.toLRSHom
{X Y : AlgebraicGeometry.Scheme} → X.Hom Y → (X.toLocallyRingedSpace ⟶ Y.toLocallyRingedSpace)Cast a morphism of schemes into morphisms of local ringed spaces.
- Defined in
- Mathlib.AlgebraicGeometry.Scheme
- Cited by
- 58 results in Mathlib
- Foundations
- Depth 3 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement · cited by 32,603
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement · cited by 1,734
- AlgebraicGeometry.Scheme.Hom.toLRSHom'proof · cited by 895
- AlgebraicGeometry.LocallyRingedSpacestatement · cited by 205
- AlgebraicGeometry.Scheme.Homstatement and proof · cited by 35
Cited by66
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.IsOpenImmersionproof · cited by 476
- AlgebraicGeometry.Scheme.Hom.opensFunctorproof · cited by 204
- AlgebraicGeometry.Scheme.Hom.stalkMapproof · cited by 82
- AlgebraicGeometry.Scheme.Hom.appIsoproof · cited by 48
- AlgebraicGeometry.IsOpenImmersion.liftproof · cited by 20
- AlgebraicGeometry.IsOpenImmersion.lift_facproof · cited by 18
- AlgebraicGeometry.Scheme.forgetToLocallyRingedSpaceproof · cited by 17
- AlgebraicGeometry.Scheme.preimage_basicOpenproof · cited by 16
- AlgebraicGeometry.Scheme.Hom.support_kerproof · cited by 6
- AlgebraicGeometry.Scheme.Hom.ext'statement and proof · cited by 5
- AlgebraicGeometry.Scheme.Hom.opensRange_of_isIsostatement · cited by 4
- AlgebraicGeometry.Scheme.Hom.appIso_inv_naturalityproof · cited by 4