 

Philippe Gaucher
Homotopy theory of labelled symmetric precubical sets view print


Published: 
January 28, 2014

Keywords: 
precubical set, higherdimensional transition system, locally presentable category, topological category, combinatorial model category, Bousfield localization 
Subject: 
18C35, 18G55, 55U35, 68Q85 


Abstract
This paper is the third paper of a series devoted to higherdimensional
transition systems. The preceding paper proved the
existence of a left determined model structure on the category of
cubical transition systems. In this sequel, it is proved that there
exists a model category of labelled symmetric precubical sets which
is Quillen equivalent to the Bousfield localization of this left
determined model category by the cubification functor. The
realization functor from labelled symmetric precubical sets to
cubical transition systems which was introduced in the first paper
of this series is used to establish this Quillen equivalence.
However, it is not a left Quillen functor. It is only a left
adjoint. It is proved that the two model categories are related to
each other by a zigzag of Quillen equivalences of length two. The
middle model category is still the model category of cubical
transition systems, but with an additional family of generating
cofibrations. The weak equivalences are closely related to
bisimulation. Similar results are obtained by restricting the
constructions to the labelled symmetric precubical sets satisfying
the HDA paradigm.


Author information
Laboratoire PPS (CNRS UMR 7126), Case 7014,Univ Paris Diderot. Sorbonne Paris Cité, F75205 PARIS, France

