Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.Hom.germ_stalkMap_apply

∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) (U : Y.Opens) (x : ↥X) (hx : f x ∈ U)
  (y : ↑(Y.presheaf.obj (Opposite.op U))),
  (CategoryTheory.ConcreteCategory.hom (AlgebraicGeometry.Scheme.Hom.stalkMap f x))
      ((CategoryTheory.ConcreteCategory.hom (Y.presheaf.germ U (f x) hx)) y) =
    (CategoryTheory.ConcreteCategory.hom (X.presheaf.germ ((TopologicalSpace.Opens.map f.base).obj U) x hx))
      ((CategoryTheory.ConcreteCategory.hom (AlgebraicGeometry.Scheme.Hom.app f U)) y)

Defined in: Mathlib.AlgebraicGeometry.Scheme
Cited by: 2 results in Mathlib
Foundations: Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites29

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.Functor.objstatement and proof · cited by 19,642
RingHomstatement · cited by 10,189
Oppositestatement · cited by 8,081
CategoryTheory.ConcreteCategory.homstatement and proof · 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
TopologicalSpace.Opensstatement · cited by 2,040
AlgebraicGeometry.PresheafedSpace.carrierstatement and proof · cited by 2,020

Cited by2

Results whose statement or proof uses this declaration.

AlgebraicGeometry.eq_zero_of_basicOpen_eq_botproof · cited by 1
AlgebraicGeometry.stalkMap_injective_of_isOpenMap_of_injectiveproof · cited by 0