Theorems · Definition · algebraic geometry

AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.toSheafedSpace

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {X : AlgebraicGeometry.PresheafedSpace C} →
      (Y : AlgebraicGeometry.SheafedSpace C) →
        (f : X ⟶ Y.toPresheafedSpace) →
          [H : AlgebraicGeometry.PresheafedSpace.IsOpenImmersion f] → AlgebraicGeometry.SheafedSpace C

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

Defined in

Mathlib.Geometry.RingedSpace.OpenImmersion

Cited by

5 results in Mathlib

Foundations

Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryAlgebraicGeometry.PresheafedSpace.IsOpenImmersion