A new method to construct model structures from left Frobenius pairs in extriangulated categories

Yajun Ma; Haiyu Liu; Yuxian Geng; Yajun Ma; Haiyu Liu; Yuxian Geng

doi:10.3934/era.2022142

Electronic Research Archive

2022, Volume 30, Issue 8: 2774-2787. doi: 10.3934/era.2022142

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Research article

A new method to construct model structures from left Frobenius pairs in extriangulated categories

1.
Department of Mathematics, Nanjing University, Nanjing 210093, China
2.
School of Mathematics and Physics, Jiangsu University of Technology, Changzhou, Jiangsu 213001, China

Received: 25 July 2021 Revised: 12 March 2022 Accepted: 20 March 2022 Published: 23 May 2022

Extriangulated categories were introduced by Nakaoka and Palu as a simultaneous generalization of exact categories and triangulated categories. In this paper, we first introduce the concept of left Frobenius pairs on an extriangulated category $ \mathcal{C} $, and then establish a bijective correspondence between left Frobenius pairs and certain cotorsion pairs in $ \mathcal{C} $. As an application, some new admissible model structures are established from left Frobenius pairs under certain conditions, which generalizes a result of Hu et al. (J. Algebra 551 (2020) 23–60).
- extriangulated category,
- left Frobenius pair,
- cotorsion pair,
- model structure
Citation: Yajun Ma, Haiyu Liu, Yuxian Geng. A new method to construct model structures from left Frobenius pairs in extriangulated categories[J]. Electronic Research Archive, 2022, 30(8): 2774-2787. doi: 10.3934/era.2022142

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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 first introduce the concept of left Frobenius pairs on an extriangulated category $ \mathcal{C} $, and then establish a bijective correspondence between left Frobenius pairs and certain cotorsion pairs in $ \mathcal{C} $. As an application, some new admissible model structures are established from left Frobenius pairs under certain conditions, which generalizes a result of Hu et al. (J. Algebra 551 (2020) 23–60).

References

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