  The relationships between thin elements, commutative shells and connections
in cubical omega-categories are explored by a method which does not involve the
use of pasting theory or nerves of omega-categories (both of which were
previously needed for this purpose; see previous work by Al-Agl/Brown/Steiner.
It is shown that composites of commutative shells are commutative and that thin
structures are equivalent to appropriate sets of connections; this work extends
to all dimensions the results proved in dimensions 2 and 3 by Brown/Mosa, and
Brown/Kamps/Porter.
