  It is possible to translate a modified version of K. Worytkiewicz's
combinatorial semantics of CCS (Milner's Calculus of Communicating Systems) in
terms of labelled precubical sets into a categorical semantics of CCS in terms
of labelled flows using a geometric realization functor. It turns out that a
satisfactory semantics in terms of flows requires to work directly in their
homotopy category since such a semantics requires non-canonical choices for
constructing cofibrant replacements, homotopy limits and homotopy colimits. No
geometric information is lost since two precubical sets are isomorphic if and
only if the associated flows are weakly equivalent. The interest of the
categorical semantics is that combinatorics totally disappears. Last but not
least, a part of the categorical semantics of CCS goes down to a pure
homotopical semantics of CCS using A. Heller's privileged weak limits and
colimits. These results can be easily adapted to any other process algebra for
any synchronization algebra.
