nLab cubical group

A cubical group is a group object in the category of cubical sets.

Unlike in the category of simplicial sets, a cubical group need not be a fibrant cubical set. However a group object in the category of cubical sets with connections is a fibrant cubical set.

Reference

• Tonks, A.P., Cubical groups which are Kan, J. Pure Appl. Algebra, 81 (1992) 83–87.