Quasi-resolving subcategories in triangulated categories

Weili Gu; Zhaoyong Huang; Lingling Tan; Tiwei Zhao; Weili Gu; Zhaoyong Huang; Lingling Tan; Tiwei Zhao

doi:10.3934/era.2026091

Electronic Research Archive

2026, Volume 34, Issue 3: 2038-2065. doi: 10.3934/era.2026091

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Research article

Quasi-resolving subcategories in triangulated categories

1.
School of Mathematics, Nanjing University, Nanjing 210093, China
2.
School of Artificial Intelligence, Jianghan University, Wuhan 430056, China

Received: 28 November 2025 Revised: 18 February 2026 Accepted: 28 February 2026 Published: 06 March 2026

We have introduced the notion of quasi-resolving subcategories in a triangulated category with a proper class of triangles. We provided some criteria for computing the resolution dimension of objects relative to a quasi-resolving subcategory. We also provided a method to construct quasi-resolving subcategories from given ones.
- triangulated category,
- proper class of triangle,
- quasi-resolving subcategory,
- resolution dimension,
- Auslander-Buchweitz approximation
Citation: Weili Gu, Zhaoyong Huang, Lingling Tan, Tiwei Zhao. Quasi-resolving subcategories in triangulated categories[J]. Electronic Research Archive, 2026, 34(3): 2038-2065. doi: 10.3934/era.2026091

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Abstract

We have introduced the notion of quasi-resolving subcategories in a triangulated category with a proper class of triangles. We provided some criteria for computing the resolution dimension of objects relative to a quasi-resolving subcategory. We also provided a method to construct quasi-resolving subcategories from given ones.

References

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