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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 aarXiv:1705.08715v2 fatcat:fppxof3gtvhdrcrkebtdwjkk4e