  Let $G$ be a finite group. There is a standard theorem on the classification
of $G$-equivariant finite dimensional simple commutative, associative, and Lie
algebras (i.e., simple algebras of these types in the category of
representations of $G$). Namely, such an algebra is of the form $A={\rm
Fun}_H(G,B)$, where $H$ is a subgroup of $G$, and $B$ is a simple algebra of
the corresponding type with an $H$-action. We explain that such a result holds
in the generality of algebras over a linear operad. This allows one to extend
Theorem 5.5 of arXiv:1506.07565 on the classification of simple commutative
algebras in the Deligne category ${\rm Rep}(S_t)$ to algebras over any finitely
generated linear operad.
