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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 generalized cluster category associated to a surface, the coloured quivers coincide. We also show that compatible notions of mutation can be defined and we give an explicit description in the case of a disk. A partial description is given in the general 2‐Calabi–Yau case. We further show that Iyama–Yoshino reduction can be interpreted as cutting along an arc in the surface.

Coloured quivers for rigid objects and partial triangulations: the unpunctured case