English

Relative Derived Category with respect to a Subcategory

Category Theory 2014-10-15 v1

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.

Keywords

Cite

@article{arxiv.1410.3606,
  title  = {Relative Derived Category with respect to a Subcategory},
  author = {Zhenxing Di and Xiaoxiang Zhang and Wei Ren and Jianlong Chen},
  journal= {arXiv preprint arXiv:1410.3606},
  year   = {2014}
}
R2 v1 2026-06-22T06:22:36.825Z