New York Journal of Mathematics
Volume 21 (2015) 1117-1151


Philippe Gaucher

The choice of cofibrations of higher dimensional transition systems

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Published: November 6, 2015
Keywords: left determined model category, combinatorial model category, higher dimensional transition system, causal structure
Subject: 18C35,18G55,55U35,68Q85

It is proved that there exists a left determined model structure of weak transition systems with respect to the class of monomorphisms and that it restricts to left determined model structures on cubical 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 does not preserve the causal structure. As a conclusion, we explain why working with star-shaped transition systems is a solution to this problem.

Author information

Laboratoire PPS (CNRS UMR 7126), Univ Paris Diderot, Sorbonne Paris Cité, Case 7014, 75205 PARIS Cedex 13, France