Theorems · Theorem · algebraic geometry

AlgebraicGeometry.LocallyRingedSpace.stalkMap_congr_hom

∀ {X Y : AlgebraicGeometry.LocallyRingedSpace} (f g : X ⟶ Y) (hfg : f = g) (x : ↑X.toTopCat),
  AlgebraicGeometry.LocallyRingedSpace.Hom.stalkMap f x =
    CategoryTheory.CategoryStruct.comp (Y.presheaf.stalkSpecializes ⋯)
      (AlgebraicGeometry.LocallyRingedSpace.Hom.stalkMap g x)

Defined in: Mathlib.Geometry.RingedSpace.LocallyRingedSpace
Cited by: 4 results in Mathlib
Foundations: Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites22

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
CategoryTheory.Category.id_compproof · cited by 1,998
AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement and proof · cited by 1,988
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement and proof · cited by 1,892
TopCatstatement · cited by 1,889

Cited by4

Results whose statement or proof uses this declaration.

AlgebraicGeometry.Scheme.Hom.stalkMap_congr_homproof · cited by 3
AlgebraicGeometry.LocallyRingedSpace.stalkMap_hom_invproof · cited by 3
AlgebraicGeometry.LocallyRingedSpace.stalkMap_inv_homproof · cited by 3
AlgebraicGeometry.LocallyRingedSpace.stalkMap_congr_hom_assocproof · cited by 0