λ-pure derived categories of a Grothendieck category

Abstract

Let [Formula: see text] be a Grothendieck category, [Formula: see text] an infinite regular cardinal. We investigate the [Formula: see text]-purity of [Formula: see text], and the [Formula: see text]-pure acyclic complexes in [Formula: see text]. Using the [Formula: see text]-presentable objects, we verify that the class of [Formula: see text]-pure acyclic complexes is a thick subcategory of homotopy category. Then we construct [Formula: see text]-pure derived category naturally. Through some specific constructions, we get that bounded above [Formula: see text]-pure derived categories coincide with specific homotopy categories.