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n-group

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Definition

An nn-group is a group object internal to (n1)(n-1)-groupoids.

If it is deloopable, an nn-group GG is the hom-object G=Aut BG(*)G = Aut_{\mathbf{B}G}({*}) of an n-groupoid BG\mathbf{B}G with a single object *{*}.

If BG\mathbf{B}G is a strict n-groupoid, then the corresponding nn-group is called a strict nn-group. Strict nn-groups are equivalent to crossed complexes of groups, of length nn.

Under the homotopy hypothesis nn-groups correspond to pointed connected homotopy n-types.

Examples

See also

References

The homotopy theory of k-tuply groupal n-groupoids is discussed in

  • A.R. Garzón, J.G. Miranda, Serre homotopy theory in subcategories of simplicial groups Journal of Pure and Applied Algebra Volume 147, Issue 2, 24 March 2000, Pages 107-123

Revised on February 25, 2013 21:54:04 by Tim Porter (95.147.236.96)