Definition:Étalé Space of Presheaf

Definition
Let $X$ be a topological space.

Let $\mathbf C$ be a category.

Let $\FF$ be a $\mathbf C$-valued presheaf on $X$.

The étalé space of $\FF$ is the pair $\struct {\map {\operatorname {\acute Et} } \FF, \pi}$ where:
 * $\map {\operatorname {\acute Et} } \FF$ is the disjoint union $\ds \bigsqcup_{x \mathop \in X} \FF_x$ of stalks of $\FF$
 * $\pi: \map {\operatorname {\acute Et} } \FF \to X$ is the canonical projection.

Also denoted as
The étalé space of $\FF$ is also denoted $\map {\operatorname {Sp\acute e} } \FF$.

Also see

 * Definition:Section of Étalé Space
 * Definition:Sheafification