Definition:Abelian Sheaf
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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 $\underline{\mathbb{Z}}$-modules on $X$, where $\underline{\mathbb{Z}}$ is the constant sheaf with value the ring of integers $\Z$.