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arXiv · 1410.3606

Relative Derived Category with respect to a Subcategory

Zhenxing Di·Xiaoxiang Zhang·Wei Ren·Jianlong Chen
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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 $\mathrm{Ext}_{\mathcal{X}\mathcal {A}}(-,-)$ as the morphisms in such derived category and give two applications.

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Zhenxing Di, Xiaoxiang Zhang, Wei Ren, Jianlong Chen. 2014-10-14. Relative Derived Category with respect to a Subcategory. https://arxiv.org/abs/1410.3606

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