Homotopy Bisimilarity for Higher-Dimensional Automata
  We introduce a new category of higher-dimensional automata in which the morphisms are functional homotopy simulations, i.e. functional simulations up to concurrency of independent events. For this, we use unfoldings of higher-dimensional automata into higher-dimensional trees. Using a notion of open maps in this category, we define homotopy bisimilarity. We show that homotopy bisimilarity is equivalent to a straight-forward generalization of standard bisimilarity to higher dimensions, and that it is finer than split bisimilarity and incomparable with history-preserving bisimilarity. 
Uli Fahrenberg, Axel Legay
cs.LO math.CT