Definition:Associated Z-Module Functor

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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

Object functor:         sends an abelian group to its associated Z-module
Morphism functor: sends a mapping to itself

Also see