Homology, Homotopy and Applications

Volume 12 (2010)

Number 2

Path categories and resolutions

Pages: 231 – 244

DOI: http://dx.doi.org/10.4310/HHA.2010.v12.n2.a8


J.F. Jardine (Department of Mathematics, University of Western Ontario, London, Ontario, Canada)


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

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