The algebraic structure of the universal complicial sets
Category Theory
2012-05-25 v2
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.
Keywords
Cite
@article{arxiv.1009.3384,
title = {The algebraic structure of the universal complicial sets},
author = {Richard Steiner},
journal= {arXiv preprint arXiv:1009.3384},
year = {2012}
}
Comments
25 pages. As to appear in Journal of Pure and Applied Algebra. Minor corrections, addtional explanations, some propositions reclassified as lemmas