Theorems · Theorem · algebraic geometry

AlgebraicGeometry.stalkMap_toStalk

∀ {R S : CommRingCat} (f : R ⟶ S) (p : PrimeSpectrum ↑S),
  CategoryTheory.CategoryStruct.comp
      (AlgebraicGeometry.StructureSheaf.toStalk (↑R) (PrimeSpectrum.comap (CommRingCat.Hom.hom f) p))
      (AlgebraicGeometry.PresheafedSpace.Hom.stalkMap (AlgebraicGeometry.Spec.sheafedSpaceMap f).hom p) =
    CategoryTheory.CategoryStruct.comp f (AlgebraicGeometry.StructureSheaf.toStalk (↑S) p)

Defined in: Mathlib.AlgebraicGeometry.Spec
Cited by: 1 results in Mathlib
Foundations: Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites40

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coeproof · cited by 62,936
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.Functor.objproof · cited by 19,642
CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
Top.topproof · cited by 9,680
CategoryTheory.Category.assocproof · cited by 6,433
Algebra.algebraMapproof · cited by 4,706
CommRingCatstatement and proof · cited by 2,333
AlgebraicGeometry.PresheafedSpace.carrierstatement · cited by 2,020
AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement and proof · cited by 1,988
CategoryTheory.ObjectProperty.FullSubcategory.objproof · cited by 1,316
AlgebraicGeometry.PresheafedSpace.Hom.baseproof · cited by 1,135

Cited by1

Results whose statement or proof uses this declaration.

AlgebraicGeometry.stalkMap_toStalk_applyproof · cited by 1