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 Al-Agl, Brown and Steiner, Section 9). 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 in Brown, Kamps and Porter and Brown and Mosa.
Keywords: cubical omega-category, connections, thin elements, thin structure, folding operations, commutative shells
2000 MSC: 18D05
Theory and Applications of Categories,
Vol. 14, 2005,
No. 4, pp 60-74.