Idempotent completion of right suspended categories

Yutong Zhou; Yutong Zhou

doi:10.3934/math.2022743

AIMS Mathematics

2022, Volume 7, Issue 7: 13442-13453. doi: 10.3934/math.2022743

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Research article

Idempotent completion of right suspended categories

Yutong Zhou ^,

College of Mathematics, Hunan Institute of Science and Technology, 414006 Yueyang, China

Received: 09 March 2022 Revised: 12 May 2022 Accepted: 13 May 2022 Published: 19 May 2022
MSC : 18G80, 18E10

We show that the idempotent completion of a right suspended category has a natural structure of right suspended category and dually this is true for a left suspended category. This unifies and extends results of Balmer-Schlichting, Bühler and Liu-Sun for triangulated, exact and right triangulated categories, respectively.
- idempotent completion,
- suspended categories,
- triangulated categories,
- exact categories
Citation: Yutong Zhou. Idempotent completion of right suspended categories[J]. AIMS Mathematics, 2022, 7(7): 13442-13453. doi: 10.3934/math.2022743

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Abstract

We show that the idempotent completion of a right suspended category has a natural structure of right suspended category and dually this is true for a left suspended category. This unifies and extends results of Balmer-Schlichting, Bühler and Liu-Sun for triangulated, exact and right triangulated categories, respectively.

References

[1]	T. Bühler, Exact categories, Expo. Math., 28 (2020), 1–69. https://doi.org/10.1016/0021-8693(81)90214-3
[2]	P. Balmer, M. Schlichting, Idempotent completion of triangulated categories, J. Algebra, 236 (2001), 819–834. https://doi.org/10.1006/jabr.2000.8529 doi: 10.1006/jabr.2000.8529
[3]	Z. Li, Homotopy theory in additive categories with suspensions, Commun. Algebra, 49 (2021), 5137–5170. https://doi.org/10.1080/00927872.2021.1938102 doi: 10.1080/00927872.2021.1938102
[4]	J. Liu, L. Sun, Idempotent completion of pretriangulated categories, Czechoslovak Math. J., 64 (2014), 477–494. https://doi.org/10.1007/s10587-014-0114-9 doi: 10.1007/s10587-014-0114-9

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