4.5 Article

Resolving resolution dimensions in triangulated categories

期刊

OPEN MATHEMATICS
卷 19, 期 1, 页码 121-143

出版社

DE GRUYTER POLAND SP Z O O
DOI: 10.1515/math-2021-0013

关键词

triangulated categories; a proper class of triangles; resolving resolution dimensions; resolving subcategories; Auslander-Buchweitz approximations

资金

  1. NSF of China [11901341, 11971225, 12001168]
  2. Henan University of Engineering [DKJ2019010]
  3. Key Research Project of Education Department of Henan Province [21A110006, ZR2019QA015]
  4. Shandong Provincial Natural Science Foundation - China Postdoctoral Science Foundation [2020M682141]
  5. Young Talents Invitation Program of Shandong Province

向作者/读者索取更多资源

In this paper, the concept of chi-resolution dimensions for a resolving subcategory chi of a triangulated category T is introduced, with descriptions of objects having finite chi-resolution dimensions and the derivation of Auslander-Buchweitz approximations for these objects. The construction of adjoint pairs for inclusion functors and the characterization of objects with finite chi-resolution dimensions using xi-cellular towers are discussed. Additionally, a new resolving subcategory is constructed from a given one with the reformulation of some known results.
Let T be a triangulated category with a proper class xi of triangles and chi be a subcategory of T. We first introduce the notion of chi-resolution dimensions for a resolving subcategory of T and then give some descriptions of objects having finite chi-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 chi-resolution dimensions in terms of a notion of xi-cellular towers. We also construct a new resolving subcategory from a given resolving subcategory and reformulate some known results.

作者

我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。

评论

主要评分

4.5
评分不足

次要评分

新颖性
-
重要性
-
科学严谨性
-
评价这篇论文

推荐

暂无数据
暂无数据