Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.Hom.app_appIso_inv

∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) [H : AlgebraicGeometry.IsOpenImmersion f] (U : Y.Opens),
  CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Scheme.Hom.app f U)
      (AlgebraicGeometry.Scheme.Hom.appIso f ((TopologicalSpace.Opens.map f.base).obj U)).inv =
    Y.presheaf.map (CategoryTheory.homOfLE ⋯).op

Defined in: Mathlib.AlgebraicGeometry.OpenImmersion
Cited by: 1 results in Mathlib
Foundations: Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: AlgebraicGeometry.IsOpenImmersion

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites36

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement · cited by 62,936
Setstatement · cited by 53,352
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.Functor.objstatement · cited by 19,642
CategoryTheory.CategoryStruct.compstatement · cited by 17,999
CategoryTheory.Functor.mapstatement · cited by 8,698
Oppositestatement · cited by 8,081
CategoryTheory.Iso.invstatement · cited by 6,514
Set.imagestatement · cited by 5,609
Set.preimagestatement · cited by 4,946
CategoryTheory.ConcreteCategory.homstatement · cited by 4,022
TopCat.carrierstatement · cited by 3,184

Cited by1

Results whose statement or proof uses this declaration.

AlgebraicGeometry.Scheme.Hom.app_appIso_inv_assocproof · cited by 2