\begin{definition}[Definition:Canonical Mapping to Sections of Étalé Space]
Let $T = \struct {S, \tau}$ be a topological space.
Let $\FF$ be a presheaf of sets.
Let $\map {\operatorname {\acute Et} } \FF$ be its étalé space.
Let $\FF'$ be the sheaf of sections associated to $\map {\operatorname {\acute Et} } \FF \to T$.
The '''canonical mapping''' $c : \FF \to \FF'$ is defined as follows:
:Let $U \subseteq S$ be open in $T$.
:The mapping $c_U : \map \FF U \to \map {\FF'} U$ maps $s \in \map \FF U$ to the associated section $\overline s : U \to \map {\operatorname {\acute Et} } \FF$ in $\map {\FF'} U$.
\end{definition}