nLab
hypercrossed complex

Idea

The Moore complex of a simplicial group (or, more generally, any simplicially enriched groupoid), carries a lot more structure that just a chain complex of group(oid)s. This structure is its structure as a hypercrossed complex. The notion was introduced by Pilar Carrasco in her thesis.

Related concepts

• group

• 2-group, crossed module, differential crossed module

• 3-group, 2-crossed module / crossed square, differential 2-crossed module

• n-group

• ∞-group, simplicial group, crossed complex, hypercrossed complex

References

• Pilar Carrasco, 1987, Complejos Hipercruzados, Cohomologia y Extensiones, Ph.D. thesis, Universidad de Granada.

• P. Carrasco and A. M. Cegarra, Group-theoretic Algebraic Models for Homotopy Types, J. Pure Appl. Alg., 75, (1991), 195 – 235.