Relative Derived Category with respect to a Subcategory

preprint2014arXivOpen access

Abstract

The notion of relative derived category with respect to a subcategory is introduced. A triangle-equivalence, which extends a theorem of Gao and Zhang [Gorenstein derived categories, \emph{J. Algebra} \textbf{323} (2010) 2041-2057] to the bounded below case, is obtained. Moreover, we interpret the relative derived functor ExtXA(−,−)\mathrm{Ext}_{\mathcal{X}\mathcal {A}}(-,-) as the morphisms in such derived category and give two applications.

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