Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.ofRestrict
{U : TopCat} →
(X : AlgebraicGeometry.Scheme) →
{f : U ⟶ TopCat.of ↥X} → (h : Topology.IsOpenEmbedding ⇑(CategoryTheory.ConcreteCategory.hom f)) → X.restrict h ⟶ XThe canonical map from the restriction to the subspace.
- Defined in
- Mathlib.AlgebraicGeometry.OpenImmersion
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 136 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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 · 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 by11
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Opens.ιproof · cited by 275
- AlgebraicGeometry.isAffineOpen_opensRangeproof · cited by 13
- AlgebraicGeometry.Scheme.IdealSheafData.subschemeIsoproof · cited by 2
- 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 and proof · cited by 0
- AlgebraicGeometry.Scheme.ofRestrict_toLRSHom_c_appstatement and proof · cited by 0
- AlgebraicGeometry.Scheme.restrict_presheaf_mapstatement · cited by 0
- AlgebraicGeometry.Scheme.OpenCover.compactSpaceproof · cited by 0