Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.Hom.isAffineOpen_iff_of_isOpenImmersion
∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) [H : AlgebraicGeometry.IsOpenImmersion f] {U : X.Opens},
AlgebraicGeometry.IsAffineOpen ((AlgebraicGeometry.Scheme.Hom.opensFunctor f).obj U) ↔
AlgebraicGeometry.IsAffineOpen U- Defined in
- Mathlib.AlgebraicGeometry.AffineScheme
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 145 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites29
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- SetLike.coeproof · cited by 8,199
- CategoryTheory.Iso.invproof · cited by 6,514
- Set.imageproof · cited by 5,609
- CategoryTheory.ConcreteCategory.homproof · cited by 4,022
- TopCat.carrierstatement and proof · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CommRingCatstatement · cited by 2,333
- AlgebraicGeometry.PresheafedSpace.carrierstatement and proof · cited by 2,020
Cited by7
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.IsAffineOpen.basicOpenproof · cited by 19
- AlgebraicGeometry.IsAffineOpen.image_of_isOpenImmersionproof · cited by 8
- AlgebraicGeometry.Scheme.IsQuasiAffine.isBasis_basicOpenproof · cited by 2
- AlgebraicGeometry.isAffineHom_diagonal_iffproof · cited by 1
- AlgebraicGeometry.IsAffineOpen.ι_basicOpen_preimageproof · cited by 0
- AlgebraicGeometry.IsAffineOpen.preimage_of_isOpenImmersionproof · cited by 0
- AlgebraicGeometry.isAffineOpen_of_isAffineOpen_basicOpenproof · cited by 0