AlgebraicGeometry.Scheme.Hom.stalkMap

{X Y : AlgebraicGeometry.Scheme} → (f : X ⟶ Y) → (x : ↥X) → Y.presheaf.stalk (f x) ⟶ X.presheaf.stalk x

A morphism of schemes f : X ⟶ Y induces a local ring homomorphism from Y.presheaf.stalk (f x) to X.presheaf.stalk x for any x : X.

Defined in: Mathlib.AlgebraicGeometry.Scheme
Cited by: 82 results in Mathlib
Foundations: Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound

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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.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
AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement and proof · cited by 1,734

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