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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 thesis of Alexander Grothendieck's student Hoàng Xuân Sính was an in-depth study of 2-groups under the monniker 'gr-category'. 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. 2-groups can be described using crossed modules. == References == * Hoàng Xuân Sính, (Gr-catégories ), PhD thesis, (1973) * John C. Baez and Aaron D. Lauda, (Higher-Dimensional Algebra V: 2-Groups ), Theory and Applications of Categories 12 (2004), 423–491. * David Michael Roberts and Urs Schreiber, (The inner automorphism 3-group of a strict 2-group ), Journal of Homotopy and Related Structures, vol. 3(1) (2008), pp.193–245. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「N-group (category theory)」の詳細全文を読む スポンサード リンク
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