  Let $k$ be a field. In this short note we give an example of a $2$-abelian
$k$-category, realized as a $2$-cluster-tilting subcategory of the category
$\operatorname{mod}\,A$ of finite dimensional (right) $A$-modules over a finite
dimensional $k$-algebra $A$, for which the naive idea for constructing its
"bounded derived category" as $2$-cluster-tilting subcategory of the bounded
derived category of $\operatorname{mod}\,A$ cannot work.
