Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.homOfLE
(X : AlgebraicGeometry.Scheme) → {U V : X.Opens} → U ≤ V → (↑U ⟶ ↑V)If U ≤ V, then U is also a subscheme of V.
- Defined in
- Mathlib.AlgebraicGeometry.Restrict
- Cited by
- 103 results in Mathlib
- Foundations
- Depth 140 from the axioms, rests on 5,518 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement · cited by 32,603
- TopCat.carrierstatement · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CommRingCatstatement · cited by 2,333
- AlgebraicGeometry.PresheafedSpace.carrierstatement · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement · cited by 1,892
- AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement · cited by 1,734
- AlgebraicGeometry.Scheme.Opensstatement and proof · cited by 1,149
- AlgebraicGeometry.Scheme.Opens.toSchemestatement · cited by 433
- AlgebraicGeometry.Scheme.Opens.ιproof · cited by 275
- AlgebraicGeometry.IsOpenImmersion.liftproof · cited by 20
Cited by113
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.resLEproof · cited by 45
- AlgebraicGeometry.Scheme.PartialMap.restrictproof · cited by 31
- AlgebraicGeometry.Scheme.homOfLE_ιstatement · cited by 31
- AlgebraicGeometry.Scheme.Hom.resLE_comp_ιproof · cited by 15
- AlgebraicGeometry.Scheme.ι_image_homOfLE_le_ι_imagestatement · cited by 15
- AlgebraicGeometry.Scheme.homOfLE_ι_assocstatement and proof · cited by 9
- AlgebraicGeometry.Scheme.IdealSheafData.glueDataproof · cited by 8
- AlgebraicGeometry.IsAffineOpen.SpecMap_appLE_fromSpecproof · cited by 8
- AlgebraicGeometry.Scheme.restrictFunctorproof · cited by 7
- AlgebraicGeometry.Scheme.homOfLE_appstatement and proof · cited by 7
- AlgebraicGeometry.Scheme.Opens.toSpecΓ_SpecMap_presheaf_map_assocstatement and proof · cited by 6
- AlgebraicGeometry.Scheme.homOfLE_homOfLE_assocstatement and proof · cited by 6