Torsion pairs and recollements of extriangulated categories

Abstract

In this article, we prove that if $(\mathcal{A},\mathcal{B},\mathcal{C})$ is a recollement of extriangulated categories, then torsion pairs in $\mathcal{A}$ and $\mathcal{C}$ can induce torsion pairs in $\mathcal{B},$ and the converse holds under natural assumptions. Besides, we give mild conditions on a cluster tilting subcategory on the middle category of a recollement of extriangulated categories, for the corresponding abelian quotients to form a recollement of abelian categories.

Keywords:

• Extriangulated category
• recollement
• torsion pair

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 18G80
• 18E10
• 18E40

Acknowledgments

The authors would like to thank the referee for reading the paper carefully and for many suggestions on mathematics and English expressions.

Additional information

Funding

Jian He was supported by the National Natural Science Foundation of China (Grant No. 12171230). Yonggang Hu was supported by the National Natural Science Foundation of China (Grant Nos. 11671126 and 12071120). Panyue Zhou was supported by the National Natural Science Foundation of China (Grant No. 11901190) and the Scientific Research Fund of Hunan Provincial Education Department (Grant No. 19B239).