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Research Article | Open Access

Quasi-resolving subcategories in triangulated categories

Weili Gu1, Zhaoyong Huang1, Lingling Tan2( ), Tiwei Zhao2
School of Mathematics, Nanjing University, Nanjing 210093, China
School of Artificial Intelligence, Jianghan University, Wuhan 430056, China
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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.

Keywords

triangulated categoryproper class of trianglequasi-resolving subcategoryresolution dimensionAuslander-Buchweitz approximation

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Electronic Research Archive
Volume 34 Issue 3,
March 2026
Pages 2038-2065
DOI: 10.3934/era.2026091

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Cite this article:
Gu W, Huang Z, Tan L, et al. Quasi-resolving subcategories in triangulated categories. Electronic Research Archive, 2026, 34(3): 2038-2065. https://doi.org/10.3934/era.2026091

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Received: 28 November 2025
Revised: 18 February 2026
Accepted: 28 February 2026
Published: 06 March 2026
©2026 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)