Definition:Stalk of Presheaf
(Redirected from Definition:Stalk of Sheaf)
Jump to navigation
Jump to search
Definition
Let $T = \struct{S, \tau}$ be a topological space.
Let $\mathbf C$ be a category which has all small inductive limits.
Let $\FF$ be a $\mathbf C$-valued presheaf on $T$.
Let $x \in S$.
The stalk $\FF_x$ of $\FF$ at $x$ is the inductive limit:
- $\ds \varinjlim_{U \ni x} \map \FF U$
over all open $U \subseteq S$ containing $x$.