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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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참고문헌 (32)
참고문헌 신청
J. Asadollahi / 2016 / On relative derived categories / Comm. Algebra 44(12):5454~5477
J. Asadollahi / 2014 / Gorenstein derived equivalences and their in-variants / J. Pure Appl. Algebra 218(5):888~903
M. Auslander / 1974 / Representation theory of Artin algebras. I, II / Comm. Algebra 1:177~268
M. Auslander / 1974 / Representation theory of Artin algebras. I, II / Comm. Algebra 1:269~310
A. A. Beilinson / 1981 / Faisceaux pervers, in Analysis and topology on singular spaces, I (Luminy) / Asterisque 100:5~171
J. Asadollahi / 2014 / Gorenstein derived equivalences and their in-variants / J. Pure Appl. Algebra 218(5):888~903
M. Auslander / 1974 / Representation theory of Artin algebras. I, II / Comm. Algebra 1:177~268
M. Auslander / 1974 / Representation theory of Artin algebras. I, II / Comm. Algebra 1:269~310
A. A. Beilinson / 1981 / Faisceaux pervers, in Analysis and topology on singular spaces, I (Luminy) / Asterisque 100:5~171
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