title: A model category for local po-spaces

author: Peter Bubenik
email: p.bubenik@csuohio.edu
mailing address:  Department of Mathematics
  Cleveland State University
  2121 Euclid Ave. RT 1515
  Cleveland OH, 44115-221
  USA

author: Krzysztof Worytkiewicz
email: kworytki@uwo.ca
mailing address: Department of Mathematics
  University of Western Ontario
  Middlesex College
  London, Ontario N6A 5B7
  Canada

keywords: local po-spaces (local pospaces), abstract homotopy theory,
  model categories, concurrency, simplicial presheaves, sheaves,
  etale bundles, directed homotopy (dihomotopy), context.

AMS classification: Primary 55U35, 18G55, 68Q85; Secondary 18F20, 55U10}

arXiv submission number: math.AT/0506352

to appear in: Homology, Homotopy and Applications

abstract:
Locally partial-ordered spaces (local po-spaces) have been used to model
concurrent systems. We provide equivalences for these spaces by
constructing a model category containing the category of local
po-spaces. We show the category of simplicial presheaves on local
po-spaces can be given Jardine's model structure, in which we identify
the weak equivalences between local po-spaces. In the process we give an
equivalence between the category of sheaves on a local po-space and the
category of {\'e}tale bundles over a local po-space. Finally we describe
a localization that should provide a good framework for studying
concurrent systems.