Theorems · Definition · algebraic geometry
AlgebraicGeometry.sourceLocalClosure
CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme → CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme → CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme
The source (Zariski-)local closure of P is satisfied if there exists
an open cover of the source on which P is satisfied.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homproof · cited by 32,603
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
- CategoryTheory.PreZeroHypercover.I₀proof · cited by 763
- CategoryTheory.PreZeroHypercover.Xproof · cited by 649
- CategoryTheory.PreZeroHypercover.fproof · cited by 542
- CategoryTheory.Precoverage.ZeroHypercover.toPreZeroHypercoverproof · cited by 469
- AlgebraicGeometry.Scheme.precoverageproof · cited by 336
- AlgebraicGeometry.Scheme.Coverproof · cited by 88
Cited by5
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.IsLocalIso.eq_sourceLocalClosure_isOpenImmersionstatement and proof · cited by 1
- AlgebraicGeometry.sourceLocalClosure.coverstatement and proof · cited by 1
- AlgebraicGeometry.sourceLocalClosure.iff_forall_existsstatement and proof · cited by 1
- AlgebraicGeometry.sourceLocalClosure.lestatement · cited by 0
- AlgebraicGeometry.sourceLocalClosure.property_coverMap_compstatement and proof · cited by 0