Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.Opens.isoOfLE
{X : AlgebraicGeometry.Scheme} → {U V : X.Opens} → U ≤ V → (↑((TopologicalSpace.Opens.map V.ι.base).obj U) ≅ ↑U)If U ≤ V are opens of X, the restriction of U to V is isomorphic to U.
- Defined in
- Mathlib.AlgebraicGeometry.Restrict
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 142 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Isostatement · cited by 3,963
- 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
- AlgebraicGeometry.Scheme.Opensstatement and proof · cited by 1,149
Cited by10
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.PartialIso.restrictSourceproof · cited by 10
- AlgebraicGeometry.Scheme.PartialIso.IsOver.restrictSourceproof · cited by 2
- AlgebraicGeometry.Scheme.Opens.isoOfLE_hom_ιstatement · cited by 2
- AlgebraicGeometry.IsZariskiLocalAtTarget.of_range_subset_iSupproof · cited by 1
- AlgebraicGeometry.Scheme.Opens.isoOfLE_inv_ιstatement · cited by 1
- AlgebraicGeometry.Scheme.Opens.isoOfLE_inv_ι_assocstatement and proof · cited by 1
- AlgebraicGeometry.Scheme.Opens.isoOfLE_hom_ι_assocstatement and proof · cited by 0
- AlgebraicGeometry.Scheme.PartialIso.trans_isostatement · cited by 0
- AlgebraicGeometry.Scheme.PartialIso.restrictSource_isostatement · cited by 0
- AlgebraicGeometry.Scheme.Opens.isoOfLE.congr_simpstatement and proof · cited by 0