Theorems · Theorem · algebraic geometry
AlgebraicGeometry.IsAffineOpen.preimage
∀ {X Y : AlgebraicGeometry.Scheme} {U : Y.Opens},
AlgebraicGeometry.IsAffineOpen U →
∀ (f : X ⟶ Y) [AlgebraicGeometry.IsAffineHom f],
AlgebraicGeometry.IsAffineOpen ((TopologicalSpace.Opens.map f.base).obj U)- Cited by
- 17 results in Mathlib
- Foundations
- Depth 139 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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 and proof · cited by 1,149
- AlgebraicGeometry.PresheafedSpace.Hom.basestatement · cited by 1,135
- AlgebraicGeometry.LocallyRingedSpace.Hom.toHomstatement · cited by 995
Cited by17
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.toNormalization_normalizationDescproof · cited by 4
- AlgebraicGeometry.isAffineHom_π_appproof · cited by 3
- AlgebraicGeometry.exists_appTop_π_eq_of_isLimitproof · cited by 2
- AlgebraicGeometry.Scheme.IsQuasiAffine.of_isAffineHomproof · cited by 2
- AlgebraicGeometry.Scheme.exists_isOpenCover_and_isAffine_of_finiteproof · cited by 2
- AlgebraicGeometry.exists_appTop_map_eq_zero_of_isLimitproof · cited by 1
- AlgebraicGeometry.Scheme.isPullback_toSpecΓ_toSpecΓproof · cited by 1
- AlgebraicGeometry.Scheme.exists_isQuasiAffine_of_isLimitproof · cited by 1
- AlgebraicGeometry.exists_preimage_eqproof · cited by 1
- AlgebraicGeometry.isBasis_preimage_isAffineOpenproof · cited by 1
- AlgebraicGeometry.Scheme.IdealSheafData.ideal_map_of_isAffineHomstatement and proof · cited by 0