Opetopes and chain complexes

TL;DR

This paper presents an algebraic framework for opetopes using chain complexes, linking them to combinatorial treelike structures and higher category theory, simplifying calculations of their sources and targets.

Contribution

It introduces a novel algebraic description of opetopes via chain complexes, connecting different approaches in higher category theory.

Findings

Chain complexes effectively describe opetopes.

The algebraic approach simplifies source and target calculations.

Connections established between opetopic and other higher category models.

Abstract

We give a simple algebraic description of opetopes in terms of chain complexes, and we show how this description is related to combinatorial descriptions in terms of treelike structures. More generally, we show that the chain complexes associated to higher categories generate graphlike structures. The algebraic description gives a relationship between the opetopic approach and other approaches to higher category theory. It also gives an easy way to calculate the sources and targets of opetopes.