We consider behavioural pseudo-metrics (a robust variant on bisimulations) for probabilistic transition systems coalgebraically. Our approach relies on Makkai-Pare's theory of accessible categories, which ensures that the free-mean-algebra functor on complete metric spaces admits a final coalgebra. In this talk, I will review the basics of the categorical theory and outline some of the results. Joint with Franck van Breugel, Michael Makkai and James Worrel.