Idempotent completion of extriangulated categories
Category Theory
2020-07-10 v1 Rings and Algebras
Representation Theory
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.
Keywords
Cite
@article{arxiv.2007.04788,
title = {Idempotent completion of extriangulated categories},
author = {Li Wang and Jiaqun Wei and Haicheng Zhang and Tiwei Zhao},
journal= {arXiv preprint arXiv:2007.04788},
year = {2020}
}
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24 pages