  It is well known that the theory of coalgebras provides an abstract
definition of behavioural equivalence that coincides with strong bisimulation
across a wide variety of state-based systems. Unfortunately, the theory in the
presence of so-called silent actions is not yet fully developed. In this paper,
we give a coalgebraic characterisation of branching bisimulation in the context
of labelled transition systems and fully probabilistic systems. It is shown
that recording executions (up to a notion of stuttering), rather than the set
of successor states, from a state is sufficient to characterise branching
bisimulation in both cases.
