restrict — Mathlib

English

The limit of the identity map along the neighborhood filter at x is x.

Русский

Предел идентичности вдоль фильтра окрестностей x равен x.

LaTeX

$$$\limUnder (\mathcal{N}(x))\; \mathrm{id} = x$$$

Lean4

/-- The restriction of a section along an inclusion of open sets.
For `x : F.obj (op V)`, we provide the notation `x |_ₕ i` (`h` stands for `hom`) for `i : U ⟶ V`,
and the notation `x |_ₗ U ⟪i⟫` (`l` stands for `le`) for `i : U ≤ V`.
-/
def restrict {F : X.Presheaf C} {V : Opens X} (x : ToType (F.obj (op V))) {U : Opens X} (h : U ⟶ V) :
    ToType (F.obj (op U)) :=
  F.map h.op x

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