It is known that strict omega-categories are equivalent through the nerve functor to complicial sets and to sets with complicial identities. It follows that complicial sets are equivalent to sets with complicial identities. We discuss these equivalences. In particular we give a conceptual proof that the nerves of omega-categories are complicial sets, and a direct proof that complicial sets are sets with complicial identities.
Keywords: complicial set,complicial identities, omega-category
2010 MSC: 18D05
Theory and Applications of Categories, Vol. 28, 2013, No. 24, pp 779-803.