Theorems · Definition · algebraic geometry

AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.pullbackConeOfLeft

{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) → CategoryTheory.Limits.PullbackCone f g

We construct the pullback along an open immersion via restricting along the pullback of the maps of underlying spaces (which is also an open embedding).

Defined in

Mathlib.Geometry.RingedSpace.OpenImmersion

Cited by

3 results in Mathlib

Foundations

Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryAlgebraicGeometry.PresheafedSpace.IsOpenImmersion