Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.PartialMap.restrict
{X Y : AlgebraicGeometry.Scheme} → (f : X.PartialMap Y) → (U : X.Opens) → Dense ↑U → U ≤ f.domain → X.PartialMap YThe restriction of a partial map to a smaller domain.
- Cited by
- 31 results in Mathlib
- Foundations
- Depth 141 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.
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- SetLike.coestatement and proof · cited by 8,199
- 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
- Densestatement and proof · cited by 359
- AlgebraicGeometry.Scheme.homOfLEproof · cited by 103
Cited by32
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.PartialMap.equivproof · cited by 18
- AlgebraicGeometry.Scheme.PartialMap.restrict_homstatement and proof · cited by 3
- AlgebraicGeometry.Scheme.PartialMap.comp_equiv_of_equiv_leftproof · cited by 3
- AlgebraicGeometry.Scheme.PartialMap.restrict_toRationalMapstatement · cited by 2
- AlgebraicGeometry.Scheme.PartialMap.equiv.transproof · cited by 2
- AlgebraicGeometry.Scheme.PartialMap.comp_equiv_of_equiv_rightproof · cited by 2
- AlgebraicGeometry.Scheme.PartialMap.equiv_iff_of_isSeparated_of_lestatement and proof · cited by 2
- AlgebraicGeometry.Scheme.PartialMap.equiv_of_restrict_eqstatement and proof · cited by 2
- AlgebraicGeometry.Scheme.PartialMap.fromSpecStalkOfMem_restrictstatement · cited by 2
- AlgebraicGeometry.Scheme.PartialMap.isDominant_hom_iff_of_equivproof · cited by 2
- AlgebraicGeometry.Scheme.PartialMap.isOver_iff_eq_restrictstatement and proof · cited by 1
- AlgebraicGeometry.Scheme.PartialMap.restrict_equivstatement · cited by 1