---- > [!definition] Definition. ([[direct sum of sheaves]]) > The **direct sum** $\bigoplus_{i \in I} \mathcal{F}_{i}$ of a family of [[sheaf|sheaves]] $\{ \mathcal{F}_{i} \}_{i \in I}$ on a [[topological space]] $X$ is defined as the [[sheafification]] of the [[presheaf]] $U \mapsto \bigoplus_{i \in I}\mathcal{F}_{i}(U).$ ^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 > ```