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