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arXiv · 2012.03258

Recollements of extriangulated categories

Li Wang·Jiaqun Wei·Haicheng Zhang
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Abstract

We give a simultaneous generalization of recollements of abelian categories and triangulated categories, which we call recollements of extriangulated categories. For a recollement $(\mathcal{A}$, $\mathcal{B}$, $\mathcal{C})$ of extriangulated categories, we show that cotorsion pairs in $\mathcal{A}$ and $\mathcal{C}$ induce cotorsion pairs in $\mathcal{B}$ under certain conditions. As an application, our main result recovers a result given by Chen for recollements of triangulated categories, and it also shows a new phenomena when it is applied to abelian categories.

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BibTeXRIS

Li Wang, Jiaqun Wei, Haicheng Zhang. 2020-12-06. Recollements of extriangulated categories. https://arxiv.org/abs/2012.03258

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