Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.Hom.asFiber
{X Y : AlgebraicGeometry.Scheme} → (f : X ⟶ Y) → (x : ↥X) → ↥(AlgebraicGeometry.Scheme.Hom.fiber f (f x))A point x as a point in the fiber of f at f x.
- Defined in
- Mathlib.AlgebraicGeometry.Fiber
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 195 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
- TopCat.carrierstatement and proof · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- ContinuousMapstatement · cited by 2,491
- CommRingCatstatement · cited by 2,333
- AlgebraicGeometry.PresheafedSpace.carrierstatement and proof · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement and proof · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement and proof · cited by 1,892
- TopCatstatement · cited by 1,889
- AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement and proof · cited by 1,734
Cited by6
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.quasiFiniteAt_iff_isOpen_singleton_asFiberstatement and proof · cited by 2
- AlgebraicGeometry.Scheme.Hom.QuasiFiniteAt.isClopen_singleton_asFiberstatement and proof · cited by 1
- AlgebraicGeometry.Scheme.Hom.fiberι_asFiberstatement · cited by 1
- AlgebraicGeometry.Scheme.Hom.asFiberHom_applystatement and proof · cited by 1
- AlgebraicGeometry.Scheme.Hom.range_asFiberHomstatement and proof · cited by 0