Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.OpenCover.restrict
{X : AlgebraicGeometry.Scheme} → X.OpenCover → (U : X.Opens) → (↑U).OpenCoverThe restriction of an open cover to an open subset.
- Defined in
- Mathlib.AlgebraicGeometry.Restrict
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 147 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CategoryTheory.Functor.objproof · cited by 19,642
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- AlgebraicGeometry.Scheme.Opensstatement and proof · cited by 1,149
- AlgebraicGeometry.PresheafedSpace.Hom.baseproof · cited by 1,135
- AlgebraicGeometry.LocallyRingedSpace.Hom.toHomproof · cited by 995
- AlgebraicGeometry.Scheme.Hom.toLRSHom'proof · cited by 895
- CategoryTheory.PreZeroHypercover.I₀proof · cited by 763
- TopologicalSpace.Opens.mapproof · cited by 645
- CategoryTheory.Limits.pullback.sndproof · cited by 637
- CategoryTheory.PreZeroHypercover.fproof · cited by 542
- CategoryTheory.Precoverage.ZeroHypercover.toPreZeroHypercoverproof · cited by 469
Cited by4
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.HasAffineProperty.isZariskiLocalAtSourceproof · cited by 0
- AlgebraicGeometry.Scheme.OpenCover.restrict_I₀statement and proof · cited by 0
- AlgebraicGeometry.Scheme.OpenCover.restrict_Xstatement and proof · cited by 0
- AlgebraicGeometry.Scheme.OpenCover.restrict_fstatement and proof · cited by 0