Theorems · Definition · algebraic geometry
AlgebraicGeometry.LocallyRingedSpace.ofRestrict
{U : TopCat} →
(X : AlgebraicGeometry.LocallyRingedSpace) →
{f : U ⟶ X.toTopCat} → (h : Topology.IsOpenEmbedding ⇑(CategoryTheory.ConcreteCategory.hom f)) → X.restrict h ⟶ XThe canonical map from the restriction to the subspace.
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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 · cited by 3,184
- ContinuousMapstatement · cited by 2,491
- AlgebraicGeometry.SheafedSpace.toPresheafedSpaceproof · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpaceproof · cited by 1,892
- TopCatstatement and proof · cited by 1,889
- Topology.IsOpenEmbeddingstatement and proof · cited by 231
- AlgebraicGeometry.LocallyRingedSpacestatement and proof · cited by 205
- AlgebraicGeometry.LocallyRingedSpace.toTopCatstatement and proof · cited by 128
- AlgebraicGeometry.LocallyRingedSpace.restrictstatement · cited by 55
Cited by14
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.affineCoverproof · cited by 61
- AlgebraicGeometry.Scheme.ofRestrictproof · cited by 9
- ChartedSpace.restrictLocallyRingedSpaceIsoproof · cited by 2
- AlgebraicGeometry.Scheme.exists_affine_mem_range_and_range_subsetproof · cited by 2
- AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.isoRestrict_hom_ofRestrictstatement and proof · cited by 2
- AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.ofRestrict_invAppstatement · cited by 1
- AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.isoRestrict_inv_ofRestrictstatement and proof · cited by 1
- ChartedSpace.restrictLocallyRingedSpaceIso_homstatement · cited by 0
- ChartedSpace.restrictLocallyRingedSpaceIso_invstatement · cited by 0
- AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.ofRestrict_invApp_applystatement · cited by 0
- AlgebraicGeometry.LocallyRingedSpace.restrictStalkIso_inv_eq_ofRestrictstatement · cited by 0
- AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.pullbackConeOfLeftproof · cited by 0