Homology, Homotopy and Applications

Volume 16 (2014)

Number 1

The homology graph of a precubical set

Pages: 119 – 138

DOI: https://dx.doi.org/10.4310/HHA.2014.v16.n1.a7


Thomas Kahl (Centro de Matemática, Universidade do Minho, Braga, Portugal)


Precubical sets are used to model concurrent systems. We introduce the homology graph of a precubical set, which is a directed graph whose nodes are the homology classes of the precubical set. We show that the homology graph is invariant under weak morphisms that are homeomorphisms.


higher dimensional automata, precubical set, homology graph, directed homology, homeomorphic abstraction

2010 Mathematics Subject Classification

55N99, 55U10, 68Q45, 68Q85

Published 2 June 2014