Definition:Stalk of Presheaf

Definition
Let $T = \left({S, \tau}\right)$ be a topological space.

Let $\mathbf C$ be a category which has all small inductive limits.

Let $\mathcal F$ be a $\mathbf C$-valued presheaf on $T$.

Let $x \in S$.

The stalk $\mathcal F_x$ of $\mathcal F$ at $x$ is the inductive limit:
 * $\displaystyle\varinjlim_{U \ni x} \mathcal F \left({U}\right)$

over all open $U \subseteq S$ containing $x$.

Also see

 * Definition:Stalk of Presheaf Functor