n-group (category theory)
- n-group (category theory)
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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, n may be any natural number or infinity.
The general definition of n-group is a matter of ongoing research. However, it is expected that every topological space will have a homotopy n-group at every point, which will encapsulate the Postnikov tower of the space up to the homotopy group πn, or the entire Postnikov tower for n = ∞.
The definition and many properties of 2-groups are already known. A 1-group is simply a group, and the only 0-group is trivial.
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