T-homotopy and refinement of observation (IV) : Invariance of the underlying homotopy type

Abstract

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.

arXiv comment33 pages ; 2 figures ; see http://nyjm.albany.edu:8000/j/2006/Vol12.htm

References in corpus (4)

• Comparing globular complex and flow
• Inverting weak dihomotopy equivalence using homotopy continuous flow
• T-homotopy and refinement of observation (I) : Introduction
• T-homotopy and refinement of observation (II) : Adding new T-homotopy equivalences

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• Homotopy theory of Moore flows (II)
• Comparing cubical and globular directed paths
• Globular realization and cubical underlying homotopy type of time flow of process algebra
• Homotopy theory of Moore flows (III)
• Abstract homotopical methods for theoretical computer science