 

Philippe Gaucher
Globular realization and cubical underlying homotopy type of time flow of process algebra


Published: 
February 10, 2008

Keywords: 
model category, Reedy category, homotopy colimit, precubical set, concurrency 
Subject: 
55U35, 18G55, 68Q85 


Abstract
We construct a small realization as flow of every precubical set
(modeling for example a process algebra). The realization is small
in the sense that the construction does not make use of any
cofibrant replacement functor and of any transfinite construction.
In particular, if the precubical set is finite, then the
corresponding flow has a finite globular decomposition. Two
applications are given. The first one presents a realization
functor from precubical sets to globular complexes which is
characterized up to a natural Shomotopy. The second one proves
that, for such flows, the underlying homotopy type is naturally
isomorphic to the homotopy type of the standard cubical complex
associated with the precubical set.


Author information
Laboratoire PPS (CNRS UMR 7126), Université Paris 7Denis Diderot, Site Chevaleret, Case 7012, 75205 PARIS Cedex 13, France
gaucher@pps.jussieu.fr
http://www.pps.jussieu.fr/~gaucher/

