The branching (resp. merging) space functor of a flow is a left Quillen functor. The associated derived functor allows to define the branching (resp. merging) homology of a flow. It is then proved that this homology theory is a dihomotopy invariant and that higher dimensional branchings (resp. mergings) satisfy a long exact sequence.
"Homological properties of non-deterministic branchings of mergings in higher dimensional automata." Homology Homotopy Appl. 7 (1) 51 - 76, 2005.