The choice of cofibrations of higher dimensional transition systems

Philippe Gaucher
2015 New York Journal of Mathematics New York J. Math   unpublished
It is proved that there exists a left determined model structure of weak transition systems with respect to the class of monomor-phisms and that it restricts to left determined model structures on cubi-cal and regular transition systems. Then it is proved that, in these three model structures, for any higher dimensional transition system containing at least one transition, the fibrant replacement contains a transition between each pair of states. This means that the fibrant replacement functor
more » ... eplacement functor does not preserve the causal structure. As a conclusion, we explain why working with star-shaped transition systems is a solution to this problem.