Relative Auslander bijection in extriangulated categories
作者机构：School of Artificial Intelligence Jianghan University State Key Laboratory of Precision Blasting Jianghan University School of Mathematical Sciences Qufu Normal University
出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报(英文版))
年 卷 期：2024年
核心收录：
基 金：Supported by NSFC (Grant No. 11901341) Shandong Provincial Natural Science Foundation (Grant No.ZR2021QA001) Youth Innovation Team of Universities of Shandong Province (Grant No. 2022KJ314)
摘 要：Extriangulated categories were introduced by Nakaoka and Palu, which unify exact categories and extension-closed subcategories of triangulated categories. In this paper, we develop the relative homology aspect of Auslander bijection in extriangulated categories. Namely, we introduce the notion of generalized ARS-duality relative to an additive subfunctor, and prove that there is a bijective triangle which involves the generalized ARS-duality and the restricted Auslander bijection relative to the subfunctor. We give the Auslander’s defect formula in terms of the generalized ARS-duality, show the interplay of morphisms being determined by objects and a kind of extriangles, and characterize a class of objects which are somehow controlled by this kind of extriangles. We also give a realization for a functor relating the Auslander bijection and the generalized ARS-duality.
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