Theorems · Theorem · algebraic geometry

AlgebraicGeometry.LocallyRingedSpace.residue_comp_residueFieldMap_eq_stalkMap_comp_residue

∀ {X Y : AlgebraicGeometry.LocallyRingedSpace} (f : X ⟶ Y) (x : ↑X.toTopCat),
  CategoryTheory.CategoryStruct.comp (Y.residue ((CategoryTheory.ConcreteCategory.hom f.base) x))
      (AlgebraicGeometry.LocallyRingedSpace.residueFieldMap f x) =
    CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.LocallyRingedSpace.Hom.stalkMap f x) (X.residue x)

Defined in: Mathlib.Geometry.RingedSpace.LocallyRingedSpace.ResidueField
Cited by: 1 results in Mathlib
Foundations: Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites24

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.CategoryStruct.compstatement and proof · cited by 17,999
CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
TopCat.carrierstatement and proof · cited by 3,184
ContinuousMapstatement · cited by 2,491
CommRingCatstatement · cited by 2,333
AlgebraicGeometry.PresheafedSpace.carrierstatement · cited by 2,020
AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement · cited by 1,988
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement · cited by 1,892
TopCatstatement · cited by 1,889
AlgebraicGeometry.PresheafedSpace.Hom.basestatement and proof · cited by 1,135

Cited by1

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AlgebraicGeometry.LocallyRingedSpace.residue_comp_residueFieldMap_eq_stalkMap_comp_residue_assocproof · cited by 0