Definition:Canonical Mapping to Sections of Étalé Space
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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