Skew categories, smash product categories and quasi-Koszul categories

Abstract

Let A \mathscr {A} be a small additive Krull-Schmidt locally radical finite category over a field K K and let G G be a finite group. We show that if A \mathscr {A} is a free G G -category (resp. G G -graded category), then A \mathscr {A} is quasi-Koszul if and only if the skew (resp. smash product) category G ∗ A G*\mathscr {A} (resp. A # G \mathscr {A}\#G ) is.