  In this article, we investigate the category $\mathcal{A}^G$ of equivariant
objects of an additive category $\mathcal{A}$ with respect to an action of a
finite group $G$. We show that if $G$ is solvable then we can reconstruct
$\mathcal{A}$ from $\mathcal{A}^G$ via a finite sequence of equivariantization.
We also consider the possibility of a triangulated structure on $\mathcal{A}^G$
canonical in certain sense when $\mathcal{A}$ is triangulated and give several
instances in which $\mathcal{A}^G$ is indeed canonically triangulated.
