\begin{definition}[Definition:Associated Z-Module Functor]
Let $\mathbf{Ab}$ be the category of abelian groups.
Let $\Z$ be the ring of integers and $\mathbf{Z-Mod}$ the category of unitary modules over $\Z$.
The '''associated Z-module functor''' $\mathbf{Ab} \to \mathbf{Z-Mod}$ is the covariant functor with
{{DefineFunctor
|ob = sends an abelian group to its associated Z-module
|mor = sends a mapping to itself
}}
\end{definition}