We show that the nerve of a strict omega-category can be described algebraically as a simplicial set with additional operations subject to certain identities. The resulting structures are called sets with complicial identities. We also construct an equivalence between the categories of strict omega-categories and of sets with complical identities.
Keywords: complicial identities, omega-category
2010 MSC: 18D05
Theory and Applications of Categories, Vol. 28, 2013, No. 23, pp 733-779.