Definition:Sheafification

Definition
Let $X$ be a topological space.

Let $\mathbf C$ be a category.

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

Definition 2
Let $\mathcal F$ be a presheaf of sets.

The sheafification of $\mathcal F$ is the sheaf of continuous sections of its étalé space $\operatorname{\acute Et}(\mathcal F)$.

Also see

 * Equivalence of Definitions of Sheafification
 * Sheafification Functor