Theorems · Theorem · algebraic geometry
AlgebraicGeometry.IsAffineHom.isAffine_preimage
∀ {X Y : AlgebraicGeometry.Scheme} {f : X ⟶ Y} [self : AlgebraicGeometry.IsAffineHom f] (U : Y.Opens),
AlgebraicGeometry.IsAffineOpen U → AlgebraicGeometry.IsAffineOpen ((TopologicalSpace.Opens.map f.base).obj U)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 138 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- TopCat.carrierstatement · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CommRingCatstatement · cited by 2,333
- 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
- AlgebraicGeometry.Scheme.Opensstatement · cited by 1,149
- AlgebraicGeometry.PresheafedSpace.Hom.basestatement · cited by 1,135
- AlgebraicGeometry.LocallyRingedSpace.Hom.toHomstatement · cited by 995
Cited by2
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.IsAffineOpen.preimageproof · cited by 17
- AlgebraicGeometry.targetAffineLocally_affineAnd_iff_affineLocallyproof · cited by 1