Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.Hom.stalkSpecializes_stalkMap_apply

∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) (x x' : ↥X) (h : x ⤳ x')
  (y : ↑(Y.presheaf.stalk ((TopCat.Hom.hom f.base) x'))),
  (CategoryTheory.ConcreteCategory.hom (AlgebraicGeometry.Scheme.Hom.stalkMap f x))
      ((CategoryTheory.ConcreteCategory.hom (Y.presheaf.stalkSpecializes ⋯)) y) =
    (CategoryTheory.ConcreteCategory.hom (X.presheaf.stalkSpecializes h))
      ((CategoryTheory.ConcreteCategory.hom (AlgebraicGeometry.Scheme.Hom.stalkMap f x')) y)

Defined in: Mathlib.AlgebraicGeometry.Scheme
Cited by: 0 results in Mathlib
Foundations: Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites27

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
RingHomstatement · cited by 10,189
CategoryTheory.ConcreteCategory.homstatement · 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

Cited by0

Results whose statement or proof uses this declaration.

Nothing cites this yet.