Cubical structures, homotopy theory (Q2568719)

In this paper the author studies the categories of semicubical complexes with or without degeneracies. The main result of the paper is a cubical approximation theorem for semicubical complexes with degenracies. The author also shows that unlike the simplicial case, Kan condition does not imply that a semicubical complex admits degeracies. It may be noted that a Kan semisimplicial set admits degeneracies.