  We introduce the Calabi-Yau (CY) objects in a Hom-finite Krull-Schmidt
triangulated $k$-category, and notice that the structure of the minimal,
consequently all the CY objects, can be described. The relation between
indecomposable CY objects and Auslander-Reiten triangles is provided. Finally
we classify all the CY modules of self-injective Nakayama algebras, determining
this way the self-injective Nakayama algebras admitting indecomposable CY
modules. In particular, this result recovers the algebras whose stable
categories are Calabi-Yau, which have been obtained in [BS].
