Resolution Dimension Relative to Resolving Subcategories in Extriangulated Categories

Lingling Tan and Li Liu
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Lingling Tan: School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China
Li Liu: School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China

Mathematics, 2021, vol. 9, issue 9, 1-29

Abstract: Let ( C , E , s ) be an extriangulated category with a proper class ? 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.

Keywords: extriangulated categories; a proper class of \({\mathbb{E}}\)-triangles; resolution dimension; resolving subcategories; Auslander-Buchweitz approximations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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