 

Philippe Gaucher
The choice of cofibrations of higher dimensional transition systems view print


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


Abstract
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 starshaped
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
http://www.pps.univparisdiderot.fr/~gaucher/

