toStalk — Mathlib

English

The application of toOpen to the Γgerm yields the stalk value, aligning presheaf germs with stalks.

Русский

Применение toOpen к Γgerm даёт значение в стеке, согласуя гёрмы прес sheaf со стеклами.

LaTeX

$$$ toOpen R U \\ (Γ\\,\\mathrm{germ})(U,x, hx) = toStalk R x $$$

Lean4

/-- The canonical ring homomorphism interpreting an element of `R` as an element of
the stalk of `structureSheaf R` at `x`. -/
def toStalk (x : PrimeSpectrum.Top R) : CommRingCat.of R ⟶ (structureSheaf R).presheaf.stalk x :=
  (toOpen R ⊤ ≫ (structureSheaf R).presheaf.germ _ x (by trivial))

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