  Algebraic topological methods have been used successfully in concurrency
theory, the domain of theoretical computer science that deals with distributed
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.
