Geodesic
Thin elements and commutative shells in cubical omega-categories
Theory and applications of categories, Tome 14 (2005), pp. 60-74

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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.

Classification : 18D05
Keywords: cubical omega-category, connections, thin elements, thin structure, folding operations, commutative shells 
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     author = {Philip J. Higgins},
     title = {Thin elements and commutative shells  in cubical omega-categories},
     journal = {Theory and applications of categories},
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     volume = {14},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2005_14_a3/}
}
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Philip J. Higgins. Thin elements and commutative shells  in cubical omega-categories. Theory and applications of categories, Tome 14 (2005), pp. 60-74. http://geodesic.mathdoc.fr/item/TAC_2005_14_a3/