Theorems · Definition · algebraic geometry

AlgebraicGeometry.Scheme.restrict

{U : TopCat} →
  (X : AlgebraicGeometry.Scheme) →
    {f : U ⟶ TopCat.of ↥X} →
      Topology.IsOpenEmbedding ⇑(CategoryTheory.ConcreteCategory.hom f) → AlgebraicGeometry.Scheme

The restriction of a Scheme along an open embedding.

Defined in: Mathlib.AlgebraicGeometry.OpenImmersion
Cited by: 10 results in Mathlib
Foundations: Depth 135 from the axioms · uses propext, Classical.choice, Quot.sound

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

Cites18

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement and proof · cited by 62,936
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
TopCat.carrierstatement and proof · cited by 3,184
AlgebraicGeometry.Schemestatement and proof · cited by 2,540
ContinuousMapstatement · cited by 2,491
CommRingCatstatement and proof · 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
TopCatstatement and proof · cited by 1,889
AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement and proof · cited by 1,734

Cited by14

Results whose statement or proof uses this declaration.

AlgebraicGeometry.Scheme.Opens.toSchemeproof · cited by 433
AlgebraicGeometry.Scheme.IdealSheafData.subschemeproof · cited by 36
AlgebraicGeometry.Scheme.ofRestrictstatement · cited by 9
AlgebraicGeometry.Scheme.Opens.ι_image_basicOpen'proof · cited by 2
AlgebraicGeometry.Scheme.ofRestrict_appIsostatement and proof · cited by 1
AlgebraicGeometry.Scheme.ofRestrict_appLEstatement and proof · cited by 1
AlgebraicGeometry.Scheme.ofRestrict_appstatement · cited by 0
AlgebraicGeometry.Scheme.ofRestrict_toLRSHom_basestatement · cited by 0
AlgebraicGeometry.Scheme.ofRestrict_toLRSHom_c_appstatement · cited by 0
AlgebraicGeometry.Scheme.restrict_carrierstatement and proof · cited by 0
AlgebraicGeometry.Scheme.restrict_presheaf_mapstatement and proof · cited by 0
AlgebraicGeometry.Scheme.restrict_presheaf_objstatement and proof · cited by 0