Theorems · Theorem · algebraic geometry

AlgebraicGeometry.sourceLocalClosure.iff_forall_exists

∀ {P : CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme} {X Y : AlgebraicGeometry.Scheme} [P.RespectsIso]
  {f : X ⟶ Y},
  AlgebraicGeometry.sourceLocalClosure AlgebraicGeometry.IsOpenImmersion P f ↔
    ∀ (x : ↥X), ∃ U, x ∈ U ∧ P (CategoryTheory.CategoryStruct.comp U.ι f)

Defined in: Mathlib.AlgebraicGeometry.Morphisms.LocalClosure
Cited by: 1 results in Mathlib
Foundations: Depth 143 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.MorphismProperty.RespectsIso

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Cites31

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.CategoryStruct.compstatement and proof · cited by 17,999
CategoryTheory.Iso.invproof · cited by 6,514
CategoryTheory.Category.assocproof · cited by 6,433
TopCat.carrierstatement and proof · cited by 3,184
AlgebraicGeometry.Schemestatement and proof · cited by 2,540
CommRingCatstatement · cited by 2,333
CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
AlgebraicGeometry.PresheafedSpace.carrierstatement and proof · cited by 2,020
AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement and proof · cited by 1,988
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement and proof · cited by 1,892
AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement and proof · cited by 1,734

Cited by1

Results whose statement or proof uses this declaration.

AlgebraicGeometry.IsLocalIso.eq_sourceLocalClosure_isOpenImmersionproof · cited by 1