# On the relation between n-cotorsion pairs and (n+1)-cluster tilting subcategories

## TL;DR

This paper establishes a one-to-one correspondence between n-cotorsion pairs and (n+1)-cluster tilting subcategories in extriangulated categories, generalizing previous abelian case results and providing illustrative examples.

## Contribution

It introduces n-cotorsion pairs in extriangulated categories and links them to (n+1)-cluster tilting subcategories, extending prior work to a broader categorical context.

## Key findings

- One-to-one correspondence between n-cotorsion pairs and (n+1)-cluster tilting subcategories
- Generalization of previous abelian case results
- Examples illustrating the main theoretical result

## Abstract

A notion of $n$-cotorsion pairs in an extriangulated category with enough projectives and enough injectives is defined in this article. We show that there exists a one-to-one correspondence between $n$-cotorsion pairs and $(n+1)$-cluster tilting subcategories. As an application, this result generalizes the work by Huerta, Mendoza and P\'{e}rez in an abelian case. Finally, we give some examples illustrating our main result.