T-homotopy and refinement of observation (II) : Adding new T-homotopy equivalences

Abstract

This paper is the second part of a series of papers about a new notion of T-homotopy of flows. It is proved that the old definition of T-homotopy equivalence does not allow the identification of the directed segment with the 3-dimensional cube. This contradicts a paradigm of dihomotopy theory. A new definition of T-homotopy equivalence is proposed, following the intuition of refinement of observation. And it is proved that up to weak S-homotopy, a old T-homotopy equivalence is a new T-homotopy equivalence. The left-properness of the weak S-homotopy model category of flows is also established in this second part. The latter fact is used several times in the next papers of this series.

20 pages, 3 figures

References in corpus (6)

• A model category for the homotopy theory of concurrency
• Topological Deformation of Higher Dimensional Automata
• Homological properties of non-deterministic branchings and mergings in higher dimensional automata
• T-homotopy and refinement of observation (IV) : Invariance of the underlying homotopy type
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• T-homotopy and refinement of observation (I) : Introduction

Cited by in corpus (5)

• Homotopical interpretation of globular complex by multipointed d-space
• T-homotopy and refinement of observation (IV) : Invariance of the underlying homotopy type
• Inverting weak dihomotopy equivalence using homotopy continuous flow
• Globular realization and cubical underlying homotopy type of time flow of process algebra
• Abstract homotopical methods for theoretical computer science