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Resolution Dimension Relative to Resolving Subcategories in Extriangulated Categories

Author

Listed:
  • Lingling Tan

    (School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China)

  • Li Liu

    (School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China)

Abstract

Let ( C , E , s ) be an extriangulated category with a proper class ξ of E -triangles and X a resolving subcategory of C . In this paper, we introduce the notion of X -resolution dimension relative to the subcategory X in C , and then give some descriptions of objects with finite X -resolution dimension. In particular, we obtain Auslander-Buchweitz approximations for these objects. As applications, we construct adjoint pairs for two kinds of inclusion functors, and construct a new resolving subcategory from a given resolving subcategory which reformulates some known results.

Suggested Citation

  • Lingling Tan & Li Liu, 2021. "Resolution Dimension Relative to Resolving Subcategories in Extriangulated Categories," Mathematics, MDPI, vol. 9(9), pages 1-29, April.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:9:p:980-:d:544601
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    Cited by:

    1. Junfu Wang & Tiwei Zhao, 2022. "Tilting and Cotilting in Functor Categories," Mathematics, MDPI, vol. 10(17), pages 1-11, September.

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