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Homological Dimensions of Extriangulated Categories and Recollements

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arxiv 2104.06042 v1 pith:TWLUVSB2 submitted 2021-04-13 math.RT

Weili Gu , Xin Ma , Lingling Tan This is my paper · ORCID
classification math.RT
keywords categoriesmathcaldimensionsextriangulateddimensionextensiongiveglobal
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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.

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