Theorems · Definition · algebraic geometry

AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.isoRestrict

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

An open immersion f : X ⟶ Y induces an isomorphism X ≅ Y|_{f(X)}.

Defined in

Mathlib.Geometry.RingedSpace.OpenImmersion

Cited by

5 results in Mathlib

Foundations

Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryAlgebraicGeometry.PresheafedSpace.IsOpenImmersion