Homological Dimensions of Extriangulated Categories and Recollements

Weili Gu; Xin Ma; Lingling Tan

Homological Dimensions of Extriangulated Categories and Recollements

Representation Theory 2021-04-14 v1

Authors: Weili Gu , Xin Ma , Lingling Tan

Abstract

In this paper, let $(\mathcal{A},\mathcal{B},\mathcal{C})$ be a recollement of extriangulated categories. We introduce the global dimension and extension dimension of extriangulated categories, and give some upper bounds of global dimensions (resp. extension dimensions) of the categories involved in $(\mathcal{A},\mathcal{B},\mathcal{C})$ , which give a simultaneous generalization of some results in the recollement of abelian categories and triangulated categories.

Keywords

extriangulated categories recollements global dimension extension dimension abelian categories triangulated categories

Cite

@article{arxiv.2104.06042,
  title  = {Homological Dimensions of Extriangulated Categories and Recollements},
  author = {Weili Gu and Xin Ma and Lingling Tan},
  journal= {arXiv preprint arXiv:2104.06042},
  year   = {2021}
}

Comments

18 pages. arXiv admin note: text overlap with arXiv:2012.03258 by other authors

Homological Dimensions of Extriangulated Categories and Recollements

Abstract

Keywords

Cite

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