Definition:Abelian Sheaf

Definition
Let $X$ be a topological space.

Definition 1
An abelian sheaf on $X$ is a sheaf on $X$ with values in the category of abelian groups.

Definition 2
An abelian sheaf on $X$ is a sheaf of $\underline{\mathbf{Z}}$-modules on $X$, where $\underline{\mathbf{Z}}$ is the constant sheaf with value the ring of integers $\Z$.

Also see

 * Equivalence of Definitions of Abelian Sheaf