Path categories and resolutions

J.F. Jardine

doi:hha/1296223883

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Home > Journals > Homology Homotopy Appl. > Volume 12 > Issue 2 > Article

2010 Path categories and resolutions

J.F. Jardine

Homology Homotopy Appl. 12(2): 231-244 (2010).

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Abstract

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.