The algebraic structure of the universal complicial sets
arXiv:1009.3384 · doi:10.1016/j.jpaa.2012.02.036
Abstract
The nerve of a strict omega-category is a simplicial set with additional structure, making it into a so-called complicial set, and strict omega-categories are in fact equivalent to complicial sets. The nerve functor is represented by a sequence of strict omega-categories, called orientals, which are associated to simplexes. In this paper we give a detailed algebraic description of the morphisms between orientals. The aim is to describe complicial sets algebraically, by operators and equational axioms.
25 pages. As to appear in Journal of Pure and Applied Algebra. Minor corrections, addtional explanations, some propositions reclassified as lemmas