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∞-Tilting Subcategories in Extriangulated Categories

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Abstract

In this paper, the authors introduce a new definition of ∞-tilting (resp. cotilting) subcategories with infinite projective dimensions (resp. injective dimensions) in an extriangulated category. They give a Bazzoni characterization of ∞-tilting (resp. cotilting) subcategories. Also, they obtain a partial Auslander-Reiten correspondence between ∞-tilting (resp. cotilting) subcategories and coresolving (resp. resolving) subcategories with an \(\mathbb{E}\)-projective generator (resp. \(\mathbb{E}\)-injective cogenerator) in an extriangulated category.

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Acknowledgement

The authors would like to express their sincere thanks to the referee for his or her careful reading of the manuscript and helpful suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Qilu Normal University, Jinan, 250200, China

    Zhen Zhang & Shance Wang

  2. Institution of Mathematics, School of Mathematics Science, Nanjing Normal University, Nanjing, 210023, China

    Jiaqun Wei

Authors
  1. Zhen Zhang
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  2. Jiaqun Wei
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  3. Shance Wang
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Corresponding author

Correspondence to Shance Wang.

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Conflicsts of interest The authors declare no conflicts of interest.

Additional information

This work was supported by the National Natural Science Foundation of China (Nos. 12101344, 11371196) and the Shan Dong Provincial Natural Science Foundation of China (No. ZR2015PA001).

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Zhang, Z., Wei, J. & Wang, S. ∞-Tilting Subcategories in Extriangulated Categories. Chin. Ann. Math. Ser. B 45, 151–160 (2024). https://doi.org/10.1007/s11401-024-0008-6

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  • DOI: https://doi.org/10.1007/s11401-024-0008-6

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