Definition:Canonical Mapping to Sections of Étalé Space

Definition

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 $\map {\FF'} U$.

Also see

• Canonical Mapping to Sections of Étalé Space is Natural, demonstrating that the canonical mapping is a natural transformation.
• Definition:Section of Étalé Space