Models for functor categories over self-injective quivers

Abstract

Let [Formula: see text] be a ring, [Formula: see text] a small [Formula: see text]-preadditive category, and let [Formula: see text] be the category of [Formula: see text]-linear functors from [Formula: see text] to the left [Formula: see text]-module category [Formula: see text]. Given a cotorsion pair [Formula: see text] in [Formula: see text], we construct four cotorsion pairs [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] in [Formula: see text] and investigate when these cotorsion pairs are hereditary and complete. Moreover, under few assumptions, we show that there exist a recollement of homotopy categories induced by these cotorsion pairs. Finally, some applications are given in the category of [Formula: see text]-periodic chain complexes of [Formula: see text]-modules.