N-group (category theory)

In mathematics, an n-group, or n-dimensional higher group, is a special kind of n-category that generalises the concept of group to higher-dimensional algebra. Here, ${\displaystyle n}$ may be any natural number or infinity. The thesis of Alexander Grothendieck's student Hoàng Xuân Sính was an in-depth study of 2-groups under the moniker 'gr-category'.

The general definition of ${\displaystyle n}$-group is a matter of ongoing research. However, it is expected that every topological space will have a homotopy ${\displaystyle n}$-group at every point, which will encapsulate the Postnikov tower of the space up to the homotopy group ${\displaystyle \pi _{n}}$, or the entire Postnikov tower for ${\displaystyle n=\infty }$.