Theorems · Definition · algebraic geometry

AlgebraicGeometry.SheafedSpace.IsOpenImmersion.invApp

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {X Y : AlgebraicGeometry.SheafedSpace C} →
      (f : X ⟶ Y) →
        [H : AlgebraicGeometry.SheafedSpace.IsOpenImmersion f] →
          (U : TopologicalSpace.Opens ↑↑X.toPresheafedSpace) →
            X.presheaf.obj (Opposite.op U) ⟶
              Y.presheaf.obj (Opposite.op ((AlgebraicGeometry.SheafedSpace.IsOpenImmersion.opensFunctor f).obj U))

For an open immersion f : X ⟶ Y and an open set U ⊆ X, we have the map X(U) ⟶ Y(U).

Defined in

Mathlib.Geometry.RingedSpace.OpenImmersion

Cited by

12 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryAlgebraicGeometry.SheafedSpace.IsOpenImmersion