# $n$-cotorsion pairs in a recollement of extriangulated categories

## TL;DR

This paper explores how to construct and relate $n$-cotorsion pairs within a recollement of extriangulated categories, establishing methods to transfer these structures between the categories involved.

## Contribution

It introduces a framework to derive $n$-cotorsion pairs in one category from those in others within a recollement, and vice versa, under certain conditions.

## Key findings

- Constructs $n$-cotorsion pairs in $oldsymbol{ ext{B}}$ from those in $oldsymbol{ ext{A}}$ and $oldsymbol{ ext{C}}$.
- Provides conditions under which $n$-cotorsion pairs in $oldsymbol{ ext{B}}$ induce pairs in $oldsymbol{ ext{A}}$ and $oldsymbol{ ext{C}}$.
- Includes applications demonstrating the effectiveness of the construction.

## Abstract

Let $(\mathcal{A}, \mathcal{B}, \mathcal{C})$ be a recollement of extriangulated categories.In this paper, we first show how to obtain an $n$-cotorsion pair in $\mathcal{B}$ from given $n$-cotorsion pairs in $\mathcal{A}$ and $\mathcal{C}$. Conversely, we prove that an $n$-cotorsion pair in $\mathcal{B}$ can induce $n$-cotorsion pairs in $\mathcal{A}$ and $\mathcal{C}$ under suitable conditions. As applications, several related results are provided to illustrate our construction.