Theorems · Theorem · algebraic geometry

AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.invApp_app_apply

∀ {X Y : AlgebraicGeometry.LocallyRingedSpace} (f : X ⟶ Y) [H : AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion f]
  (U : TopologicalSpace.Opens ↑X.toTopCat) (x : ↑(X.presheaf.obj (Opposite.op U))),
  (CategoryTheory.ConcreteCategory.hom
        (f.c.app (Opposite.op ((AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.opensFunctor f).obj U))))
      ((CategoryTheory.ConcreteCategory.hom (AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.invApp f U)) x) =
    (CategoryTheory.ConcreteCategory.hom (X.presheaf.map (CategoryTheory.eqToHom ⋯))) x

Defined in

Mathlib.Geometry.RingedSpace.OpenImmersion

Cited by

0 results in Mathlib

Foundations

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

Assumes

AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion