$n$-cotorsion 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 $n$-cotorsion pairs in $\mathcal{A}$ and $\mathcal{C}$ can induce $n$-cotorsion pairs in $\mathcal{B}$. Conversely, this holds true under natural assumptions. Besides, we give mild conditions on a pseudo cluster tilting subcategory on the middle category of a recollement of extriangulated categories, for the corresponding additive quotients to form a recollement of semi-abelian categories.

18 pages