  We associate a coloured quiver to a rigid object in a Hom-finite
2-Calabi--Yau triangulated category and to a partial triangulation on a marked
(unpunctured) Riemann surface. We show that, in the case where the category is
the generalised cluster category associated to a surface, the coloured quivers
coincide. We also show that compatible notions of mutation can be defined and
give an explicit description in the case of a disk. A partial description is
given in the general 2-Calabi-Yau case. We show further that Iyama-Yoshino
reduction can be interpreted as cutting along an arc in the surface.
