Relationship between groupspaces and n-groups

Determine the exact relationship between groupspaces, as defined by cube-structures satisfying the groupspace axioms, and n-groups (higher groups) from higher category theory, in order to clarify whether and how these frameworks correspond or interrelate.

Background

The paper introduces groupspaces as a higher-order generalization of group theory that includes both nilspaces and non-commutative groups. The author notes similarities between groupspaces and n-groups from higher category theory but states that the precise relationship is not clear.

Clarifying this relationship would connect the algebraic-combinatorial framework of groupspaces with established higher categorical and homotopical notions, potentially enabling transfer of methods and results between the two areas.