Classical groups
Finite groups
Group schemes
Topological groups
Lie groups
Super-Lie groups
Higher groups
Cohomology and Extensions
Related concepts
homotopy hypothesis-theorem
delooping hypothesis-theorem
stabilization hypothesis-theorem
An -group is a group object internal to -groupoids.
If it is deloopable, an -group is the hom-object of an n-groupoid with a single object .
If is a strict n-groupoid, then the corresponding -group is called a strict -group. Strict -groups are equivalent to crossed complexes of groups, of length .
Under the homotopy hypothesis -groups correspond to pointed connected homotopy n-types.
For , there is a single -group, the point.
For arbitrary , there is a circle n-group.
In string theory, we have the string 2-group and the fivebrane 6-group.
See also
The homotopy theory of k-tuply groupal n-groupoids is discussed in
Last revised on June 9, 2022 at 16:57:38. See the history of this page for a list of all contributions to it.