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Theorems · Definition · algebraic geometry

AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.toLocallyRingedSpace

{X : AlgebraicGeometry.PresheafedSpace CommRingCat} →
  (Y : AlgebraicGeometry.LocallyRingedSpace) →
    (f : X ⟶ Y.toPresheafedSpace) →
      [H : AlgebraicGeometry.PresheafedSpace.IsOpenImmersion f] → AlgebraicGeometry.LocallyRingedSpace

If X ⟶ Y is an open immersion, and Y is a LocallyRingedSpace, then so is X.

Defined in
Mathlib.Geometry.RingedSpace.OpenImmersion
Cited by
5 results in Mathlib
Foundations
Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AlgebraicGeometry.PresheafedSpace.IsOpenImmersion
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.toScheme · cited by 4IsOpenImmersion.toSchemeAlgebraicGeometry.PresheafedSpace.IsOpenImmersion.locallyRingedSpace_toLocallyRingedSpace · cited by 1IsOpenImmersion.locallyRi…AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.toLocallyRingedSpaceHom · cited by 1IsOpenImmersion.toLocally…AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.toLocallyRingedSpace_toSheafedSpace · cited by 0IsOpenImmersion.toLocally…AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.toScheme_toLocallyRingedSpace · cited by 0IsOpenImmersion.toScheme_…AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.toLocallyRingedSpace.congr_simp · cited by 0toLocallyRingedSpace.cong…AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.toLocallyRingedSpaceHom_val · cited by 0IsOpenImmersion.toLocally…Quiver.Hom · cited by 32603Quiver.HomCommRingCat · cited by 2333CommRingCatAlgebraicGeometry.SheafedSpace.toPresheafedSpace · cited by 1988SheafedSpace.toPresheafed…AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace · cited by 1892LocallyRingedSpace.toShea…AlgebraicGeometry.PresheafedSpace · cited by 260AlgebraicGeometry.Preshea…AlgebraicGeometry.LocallyRingedSpace · cited by 205AlgebraicGeometry.Locally…AlgebraicGeometry.SheafedSpace · cited by 142AlgebraicGeometry.Sheafed…AlgebraicGeometry.PresheafedSpace.IsOpenImmersion · cited by 44PresheafedSpace.IsOpenImm…AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.toSheafedSpace · cited by 5IsOpenImmersion.toSheafed…IsOpenImmersion.toLocallyRing…CITED BYCITES

Cites9

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Cited by7

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