Definition:Sheafification/Definition 2

Definition
Let $X$ be a topological space.

Let $\mathbf C$ be a category.

Let $\FF$ be a $\mathbf C$-valued presheaf on $X$.

Let $\FF$ be a presheaf of sets.

The sheafification of $\FF$ is the sheaf of continuous sections of its étalé space $\map {\operatorname {\acute Et} } \FF$.

Also see

 * Equivalence of Definitions of Sheafification