Communications of the
Korean Mathematical Society CKMS

In this paper, we provide two different descriptions for a relative derived category with respect to a subcategory $\CX$ of an abelian category $\CA$. First, we construct an exact model structure on certain exact category which has as its homotopy category the relative derived category of $\CA$. We also show that a relative derived category is equivalent to homotopy category of certain complexes. Moreover, we investigate the existence of certain recollements in such categories.

Keywords: relative derived category, model structure, homotopy category, recollement

MSC numbers: 18E30, 18G20, 55U35, 16E65, 16P10, 16G10