Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.Hom.appIso
{X Y : AlgebraicGeometry.Scheme} →
(f : X ⟶ Y) →
[H : AlgebraicGeometry.IsOpenImmersion f] →
(U : X.Opens) →
Y.presheaf.obj (Opposite.op ((AlgebraicGeometry.Scheme.Hom.opensFunctor f).obj U)) ≅
X.presheaf.obj (Opposite.op U)The isomorphism Γ(Y, f(U)) ≅ Γ(X, U) induced by an open immersion f : X ⟶ Y.
- Defined in
- Mathlib.AlgebraicGeometry.OpenImmersion
- Cited by
- 48 results in Mathlib
- Foundations
- Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objstatement · cited by 19,642
- Oppositestatement · cited by 8,081
- CategoryTheory.Isostatement · cited by 3,963
- TopCat.carrierstatement · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CommRingCatstatement · cited by 2,333
- TopologicalSpace.Opensstatement · cited by 2,040
- AlgebraicGeometry.PresheafedSpace.carrierstatement · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement · cited by 1,892
- AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement · cited by 1,734
Cited by61
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Modules.restrictFunctorproof · cited by 11
- AlgebraicGeometry.IsOpenImmersion.ΓIsoproof · cited by 8
- AlgebraicGeometry.Scheme.Hom.appIso_homstatement · cited by 8
- AlgebraicGeometry.Scheme.IdealSheafData.subschemeObjIsoproof · cited by 6
- AlgebraicGeometry.Scheme.Hom.support_kerproof · cited by 6
- AlgebraicGeometry.Scheme.Hom.normalizationObjIsoproof · cited by 6
- AlgebraicGeometry.Scheme.IdealSheafData.subschemeι_appproof · cited by 5
- AlgebraicGeometry.Scheme.coprodPresheafObjIsoproof · cited by 5
- AlgebraicGeometry.Scheme.Hom.appIso_hom'statement · cited by 5
- AlgebraicGeometry.Scheme.Hom.appIso_inv_app_assocstatement and proof · cited by 5
- AlgebraicGeometry.Scheme.Modules.restrictFunctorCompproof · cited by 4
- AlgebraicGeometry.Scheme.Hom.appIso_inv_naturalitystatement · cited by 4