Definition:Associated Z-Module Functor

Definition

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

• Associated Z-Module Functor is Functor
• Correspondence between Abelian Groups and Z-Modules