About the globular homology of higher dimensional automata

TL;DR

This paper introduces a new simplicial nerve for higher dimensional automata that defines globular homology, resolving previous issues and enabling important morphisms to be represented as simplicial set morphisms.

Contribution

It presents a novel simplicial nerve construction that improves globular homology definition and morphism representation in higher dimensional automata.

Findings

Resolves drawbacks of previous globular homology definitions

Enables morphisms to be represented as simplicial set morphisms

Provides a new framework for analyzing higher dimensional automata

Abstract

We introduce a new simplicial nerve of higher dimensional automata whose homology groups yield a new definition of the globular homology. With this new definition, the drawbacks noticed with the construction of math.CT/9902151 disappear. Moreover the important morphisms which associate to every globe its corresponding branching area and merging area of execution paths become morphisms of simplicial sets.