  The (usual) Caldero-Chapoton map is a map from the set of objects of a
category to a Laurent polynomial ring over the integers. In the case of a
cluster category, it maps "reachable" indecomposable objects to the
corresponding cluster variables in a cluster algebra. This formalises the idea
that the cluster category is a "categorification" of the cluster algebra.
  The definition of the Caldero-Chapoton map requires the category to be
2-Calabi-Yau, and the map depends on a cluster tilting object in the category.
  We study a modified version of the Caldero-Chapoton map which only requires
the category to have a Serre functor, and only depends on a rigid object in the
category.
  It is well-known that the usual Caldero-Chapoton map gives rise to so-called
friezes, for instance Conway-Coxeter friezes. We show that the modified
Caldero-Chapoton map gives rise to what we call generalised friezes, and that
for cluster categories of Dynkin type A, it recovers the generalised friezes
introduced by combinatorial means by Bessenrodt and us.
