The algebra of the nerves of omega-categories

Richard Steiner

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.

Published 2013-09-01.

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