---- > [!definition] Definition. ([[section functor]]) > Let $X$ be a [[topological space]] and $\mathsf{D}$ be a 'data category'. Each open set $U \subset X$ gives rise to a **section [[covariant functor|functor]]** $\Gamma(U, \cdot): \mathsf{Sh}(X, \mathsf{D}) \to \mathsf{D}$ assigning a $\mathsf{D}$-valued [[sheaf]] $\mathcal{F}$ on $X$ to the space of sections $\mathcal{F}(U)=\Gamma(U, \mathcal{F})$ and a [[morphism of (pre)sheaves|morphism]] $f:\mathcal{F} \to \mathcal{G}$ to its $U$-component $f_{U}:\mathcal{F}(U) \to \mathcal{G}(U)$. ^definition ---- #### ---- #### References > [!backlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM [[]] > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ``` > [!frontlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM outgoing([[]]) > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ```