New York Journal of Mathematics
Volume 12 (2006) 63-95


Philippe Gaucher

T-homotopy and refinement of observation. IV. Invariance of the underlying homotopy type

Published: June 4, 2006
Keywords: concurrency, homotopy, directed homotopy, model category, refinement of observation, poset, cofibration, Reedy category, homotopy colimit
Subject: 55U35, 55P99, 68Q85

This series explores a new notion of T-homotopy equivalence of flows. The new definition involves embeddings of finite bounded posets preserving the bottom and the top elements and the associated cofibrations of flows. In this fourth part, it is proved that the generalized T-homotopy equivalences preserve the underlying homotopy type of a flow. The proof is based on Reedy model category techniques.

Author information

Preuves Programmes et Systèmes, Université Paris 7-Denis Diderot, Case 7014,2 Place Jussieu, 75251 PARIS Cedex 05, France