  We generalize the notion of K\"ulshammer ideals to the setting of a graded
category. This allows us to define and study some properties of K\"ulshammer
type ideals in the graded center of a triangulated category and in the
Hochschild cohomology of an algebra, providing new derived invariants. Further
properties of K\"ulshammer ideals are studied in the case where the category is
$d$-Calabi-Yau.
