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Two descriptions of relative derived categories

Payam Bahiraei
대한수학회 (The Korean Mathematical Society)|2018.01|대한수학회논문집 (Communications of the KMS)|제33권 제1호|pp. 53-71

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키워드

relative derived categorymodel structurehomotopy categoryrecollement
주제분류수학

초록

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.

Abstract

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.

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