\begin{definition}[Definition:Graded Abelian Group]
Let $\Delta$ be a set.
A '''graded abelian group of type $\Delta$''' is a pair $\struct {G, f}$ where:
:$G$ is an abelian group
:$f$ is a gradation on $G$ indexed by $\Delta$, the '''set of degrees'''.
\end{definition}