A note on equivariantization of additive categories and triangulated categories

Abstract

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.

Many errors corrected

References in corpus (3)

• On equivariant triangulated categories
• McKay correspondence and equivariant sheaves on $P^1$
• The derived category of a graded Gorenstein ring