  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.

Algebraic Topology;Category Theory