Coloured quivers for rigid objects and partial triangulations: The unpunctured case.

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. We show further that Iyama-Yoshino reduction can be interpreted as cutting along an arc in the surface.