Direct sum of sheaves
= Direct sum of sheaves
{title2=$\bigoplus_i\mathcal F_i$}
= Direct sums of sheaves
{synonym}
The direct sum of sheaves of abelian groups is the sheafification of the presheaf $U\mapsto\bigoplus_i\mathcal F_i(U)$. It need not equal that presheaf: sections are locally represented using finitely many summands, while globally infinitely many can occur. For point-supported <skyscraper sheaves> at closed points, allowable point supports are a <locally finite family of subsets>.