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http://dx.doi.org/10.4134/CKMS.c170124

TWO DESCRIPTIONS OF RELATIVE DERIVED CATEGORIES  

Bahiraei, Payam (Department of Pure Mathematics Faculty of Mathematical Sciences University of Guilan)
Publication Information
Communications of the Korean Mathematical Society / v.33, no.1, 2018 , pp. 53-71 More about this Journal
Abstract
In this paper, we provide two different descriptions for a relative derived category with respect to a subcategory ${\mathcal{X}}$ of an abelian category ${\mathcal{A}}$. First, we construct an exact model structure on certain exact category which has as its homotopy category the relative derived category of ${\mathcal{A}}$. 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;
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