English

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}
}

Comments

24 pages

R2 v1 2026-06-23T16:59:03.139Z