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Relative Tilting Classes in Extriangulated Categories

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Abstract

In this paper, we study the relative tilting theory in extriangulated categories. We introduce the notion of relative tilting classes in an extriangulated category and then give some equivalent characterizations. On the above basis, we discuss the relations between relative homological dimensions and relative (co)resolution dimensions in the context of relative tilting classes. We also introduce the notion of relative tilting triples, and then discuss the relations between them.

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Acknowledgements

This work is supported by NSFC (No. 12271292), and Youth Innovation Team of Universities of Shandong Province (No. 2022KJ314).

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Authors and Affiliations

  1. School of Mathematical Sciences, Qufu Normal University, Qufu, 273165, China

    Dingguo Wang, Yuanhui Yu & Tiwei Zhao

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  1. Dingguo Wang
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  2. Yuanhui Yu
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  3. Tiwei Zhao
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Correspondence to Tiwei Zhao.

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Communicated by Shi** Liu.

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Wang, D., Yu, Y. & Zhao, T. Relative Tilting Classes in Extriangulated Categories. Bull. Malays. Math. Sci. Soc. 47, 50 (2024). https://doi.org/10.1007/s40840-023-01645-5

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