Relative directed homotopy theory of partially ordered spaces

Details Relative directed homotopy theory of partially ordered spaces Relative directed homotopy theory of partially ordered spaces

2006-01-04

arxiv.org/abs/math/0601079v1

Mathematics

Algebraic Topology

20 pages

Scientific paper

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.

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