Mathlib Map

Theorems · Definition · algebraic geometry

AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.toLocallyRingedSpaceHom

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

If X ⟶ Y is an open immersion of PresheafedSpaces, and Y is a LocallyRingedSpace, we can upgrade it into a morphism of LocallyRingedSpace.

Defined in
Mathlib.Geometry.RingedSpace.OpenImmersion
Cited by
1 results in Mathlib
Foundations
Depth 97 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.toSchemeHom · cited by 1IsOpenImmersion.toSchemeH…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.PresheafedSpace.IsOpenImmersion · cited by 44PresheafedSpace.IsOpenImm…AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.toLocallyRingedSpace · cited by 5IsOpenImmersion.toLocally…IsOpenImmersion.toLocallyRing…CITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.