Abstract
In this article, we prove that if is a recollement of extriangulated categories, then torsion pairs in
and
can induce torsion pairs in
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.
Acknowledgments
The authors would like to thank the referee for reading the paper carefully and for many suggestions on mathematics and English expressions.