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arXiv · 2007.04788

Idempotent completion of extriangulated categories

Li Wang·Jiaqun Wei·Haicheng Zhang·Tiwei Zhao
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Abstract

Extriangulated categories were introduced by Nakaoka and Palu as a simultaneous generalization of exact categories and triangulated categories. In this paper, we show that the idempotent completion of an extriangulated category admits a natural extriangulated structure. As applications, we prove that cotorsion pairs in an extriangulated category induce cotorsion pairs in its idempotent completion under certain condition, and the idempotent completion of a recollement of extriangulated categories is still a recollement.

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Li Wang, Jiaqun Wei, Haicheng Zhang, Tiwei Zhao. 2020-07-08. Idempotent completion of extriangulated categories. https://arxiv.org/abs/2007.04788

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