Homology, Homotopy and Applications

Volume 8 (2006)

Number 1

A model category for local po-spaces

Pages: 263 – 292

DOI: http://dx.doi.org/10.4310/HHA.2006.v8.n1.a10

Authors

Peter Bubenik (Department of Mathematics, Cleveland State University, Cleveland Ohio, U.S.A.)

Krzysztof Worytkiewicz (Department of Mathematics, Middlesex College, University of Western Ontario, London, Ontario, Canada)

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 that 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 étale bundles over a local po-space. Finally, we describe a localization that should provide a good framework for studying concurrent systems.

Keywords

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

2010 Mathematics Subject Classification

Primary 18G55, 55U35, 68Q85. Secondary 18F20, 55U10.

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