Theorems · Definition · algebraic geometry
AlgebraicGeometry.morphismRestrict
{X Y : AlgebraicGeometry.Scheme} → (f : X ⟶ Y) → (U : Y.Opens) → ↑((TopologicalSpace.Opens.map f.base).obj U) ⟶ ↑UThe restriction of a morphism X ⟶ Y onto X |_{f ⁻¹ U} ⟶ Y |_ U.
- Defined in
- Mathlib.AlgebraicGeometry.Restrict
- Cited by
- 90 results in Mathlib
- Foundations
- Depth 143 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objstatement · cited by 19,642
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Iso.invproof · cited by 6,514
- TopCat.carrierstatement · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CommRingCatstatement · cited by 2,333
- TopologicalSpace.Opensstatement · cited by 2,040
- 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
Cited by104
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.resLEproof · cited by 45
- AlgebraicGeometry.morphismRestrict_ιstatement · cited by 25
- AlgebraicGeometry.image_morphismRestrict_preimagestatement · cited by 20
- AlgebraicGeometry.Scheme.Hom.resLE_comp_ιproof · cited by 15
- AlgebraicGeometry.Scheme.PartialMap.compproof · cited by 15
- AlgebraicGeometry.targetAffineLocallyproof · cited by 12
- AlgebraicGeometry.IsZariskiLocalAtTarget.iff_of_iSup_eq_topstatement · cited by 10
- AlgebraicGeometry.isPullback_morphismRestrictstatement and proof · cited by 10
- AlgebraicGeometry.morphismRestrict_ι_assocstatement and proof · cited by 10
- AlgebraicGeometry.IsZariskiLocalAtTarget.restrictstatement · cited by 8
- AlgebraicGeometry.IsAffineOpen.SpecMap_appLE_fromSpecproof · cited by 8
- AlgebraicGeometry.morphismRestrict_compstatement · cited by 8