Power APS of a group

Definition

Let $G$ be a group. The power APS of $G$, denoted $Power(G)$, has as its $n^{th}$ member the group $G^n$, and its concatenation map is the natural isomorphism from $G^m\times G^n$ to $G^{m+n}$.

The power APS of any group is an IAPS of groups. Some further important things about it are:

• The power APS defines a functor from the category of groups to the category of IAPSes of groups
• The power APS defines a functor from the category of groups to the category of APSes of groups