The algebraic structure of the universal complicial sets

TL;DR

This paper provides an algebraic framework for understanding complicial sets by describing morphisms between orientals, which represent strict omega-categories, using operators and axioms.

Contribution

It offers a detailed algebraic description of morphisms between orientals, advancing the algebraic understanding of complicial sets.

Findings

Algebraic description of morphisms between orientals

Operators and axioms characterize complicial sets

Enhanced algebraic understanding of strict omega-categories

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.