Homology, Homotopy and Applications
Volume 12 (2010)
Path categories and resolutions
Pages: 231 – 244
Path categories are defined, and their basic properties are described, for simplicial and cubical sets. A calculational method for describing the path category $P(K)$ of a finite oriented simplicial complex $K$ is introduced, which involves a finite $2$-category which can be specified by generators and relations. This method specializes to higher dimensional automata via the triangulation functor from cubical to simplicial sets, and leads to calculations of their associated execution paths.
path category; 2-category; resolutions; higher dimensional automata
2010 Mathematics Subject Classification
18D05, 55U10, 68Q85