Theorems · Definition · algebraic geometry

AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.isoOfRangeEq

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {X Y Z : AlgebraicGeometry.PresheafedSpace C} →
      (f : X ⟶ Z) →
        [hf : AlgebraicGeometry.PresheafedSpace.IsOpenImmersion f] →
          (g : Y ⟶ Z) →
            [AlgebraicGeometry.PresheafedSpace.IsOpenImmersion g] →
              Set.range ⇑(CategoryTheory.ConcreteCategory.hom f.base) =
                  Set.range ⇑(CategoryTheory.ConcreteCategory.hom g.base) →
                (X ≅ Y)

Two open immersions with equal range is isomorphic.

Defined in

Mathlib.Geometry.RingedSpace.OpenImmersion

Cited by

2 results in Mathlib

Foundations

Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryAlgebraicGeometry.PresheafedSpace.IsOpenImmersionAlgebraicGeometry.PresheafedSpace.IsOpenImmersion