Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.preimage_basicOpen
∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) {U : Y.Opens} (r : ↑(Y.presheaf.obj (Opposite.op U))),
(TopologicalSpace.Opens.map f.base).obj (Y.basicOpen r) =
X.basicOpen ((CategoryTheory.ConcreteCategory.hom (AlgebraicGeometry.Scheme.Hom.app f U)) r)- Defined in
- Mathlib.AlgebraicGeometry.Scheme
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- RingHomstatement · cited by 10,189
- Oppositestatement · cited by 8,081
- CategoryTheory.ConcreteCategory.homstatement · cited by 4,022
- 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 and proof · cited by 1,988
Cited by16
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.ker_applyproof · cited by 14
- AlgebraicGeometry.Scheme.toSpecΓ_preimage_basicOpenproof · cited by 7
- AlgebraicGeometry.Scheme.preimage_basicOpen_topproof · cited by 5
- AlgebraicGeometry.Scheme.Hom.range_subset_ker_supportproof · cited by 4
- AlgebraicGeometry.Scheme.Hom.preimage_basicOpenproof · cited by 3
- AlgebraicGeometry.Scheme.image_basicOpenproof · cited by 3
- AlgebraicGeometry.affineAnd_isLocalproof · cited by 2
- AlgebraicGeometry.exists_basicOpen_le_appLE_of_appLE_of_isAffineproof · cited by 1
- AlgebraicGeometry.Scheme.Opens.toSpecΓ_preimage_basicOpenproof · cited by 1
- AlgebraicGeometry.IsAffineOpen.fromSpec_preimage_basicOpen'proof · cited by 1
- AlgebraicGeometry.sourceAffineLocally_isLocalproof · cited by 1
- AlgebraicGeometry.eq_zero_of_basicOpen_eq_botproof · cited by 1