Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.Hom.stalkMap_congr_hom

∀ {X Y : AlgebraicGeometry.Scheme} (f g : X ⟶ Y) (hfg : f = g) (x : ↥X),
  AlgebraicGeometry.Scheme.Hom.stalkMap f x =
    CategoryTheory.CategoryStruct.comp (Y.presheaf.stalkCongr ⋯).hom (AlgebraicGeometry.Scheme.Hom.stalkMap g x)

Defined in: Mathlib.AlgebraicGeometry.Scheme
Cited by: 3 results in Mathlib
Foundations: Depth 100 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 · cited by 62,936
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.CategoryStruct.compstatement · cited by 17,999
CategoryTheory.Iso.homstatement · cited by 7,684
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

Cited by3

Results whose statement or proof uses this declaration.

AlgebraicGeometry.Scheme.PartialMap.fromSpecStalkOfMem_restrictproof · cited by 2
AlgebraicGeometry.Scheme.Hom.stalkMap_congr_hom_assocproof · cited by 0
AlgebraicGeometry.isIso_stalkMap_coprodSpecproof · cited by 0