Resolving resolution dimensions in triangulated categories
Resolving resolution dimensions in triangulated categories
复制标题
解析三角类别中的分辨率维度
DOI：
10.1515/math-2021-0013
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发表时间：
2021-01
期刊：
影响因子：
1.7
通讯作者：
Tiwei Zhao
中科院分区：
文献类型：
--
作者：
Xin Ma;Tiwei Zhao
Abstract. Let . T. {mathcal{T}}. be a triangulated category with a proper class . ξ. xi . of triangles and . X. {mathcal{X}}. be a subcategory of . T. {mathcal{T}}. . We first introduce the notion of . X. {mathcal{X}}. -resolution dimensions for a resolving subcategory of . T. {mathcal{T}}. and then give some descriptions of objects having finite . X. {mathcal{X}}. -resolution dimensions. In particular, we obtain Auslander-Buchweitz approximations for these objects. As applications, we construct adjoint pairs for two kinds of inclusion functors and characterize objects having finite . X. {mathcal{X}}. -resolution dimensions in terms of a notion of . ξ. xi . -cellular towers. We also construct a new resolving subcategory from a given resolving subcategory and reformulate some known results.
Abstract. Let . T. {mathcal{T}}. be a triangulated category with a proper class . ξ. xi . of triangles and . X. {mathcal{X}}. be a subcategory of . T. {mathcal{T}}. . We first introduce the notion of . X. {mathcal{X}}. -resolution dimensions for a resolving subcategory of . T. {mathcal{T}}. and then give some descriptions of objects having finite . X. {mathcal{X}}. -resolution dimensions. In particular, we obtain Auslander-Buchweitz approximations for these objects. As applications, we construct adjoint pairs for two kinds of inclusion functors and characterize objects having finite . X. {mathcal{X}}. -resolution dimensions in terms of a notion of . ξ. xi . -cellular towers. We also construct a new resolving subcategory from a given resolving subcategory and reformulate some known results.
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