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Relative directed homotopy theory of partially ordered spaces

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Thomas Kahl

Algebraic topological methods have been used successfully in concurrency
theory, the domain of theoretical computer science that deals with parallel
computing. L. Fajstrup, E. Goubault, and M. Raussen have introduced partially
ordered spaces (pospaces) as a model for concurrent systems. In this paper it
is shown that the category of pospaces under a fixed pospace is both a
fibration and a cofibration category in the sense of H. Baues. The homotopy
notion in this fibration and cofibration category is relative directed homotopy.
It is also shown that the category of pospaces is a closed model category such
that the homotopy notion is directed homotopy.

Journal of Homotopy and Related Structures, Vol. 1(2006), No. 1, pp. 79-100
http://jhrs.rmi.acnet.ge/volumes/2006/n1a4/