Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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TWO DESCRIPTIONS OF RELATIVE DERIVED CATEGORIES

  • Bahiraei, Payam (Department of Pure Mathematics Faculty of Mathematical Sciences University of Guilan)
  • Received : 2017.03.26
  • Accepted : 2017.11.29
  • Published : 2018.01.31
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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.

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References

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