Cotorsion pairs in $(d+2)$-angulated categories

TL;DR

This paper introduces cotorsion pairs in $(d+2)$-angulated categories, generalizing classical concepts, and explores their properties and mutations, with applications to cluster categories of type A.

Contribution

It defines cotorsion pairs in $(d+2)$-angulated categories, provides geometric characterizations, and proves mutation invariance, extending classical results to higher angulated settings.

Findings

Defined cotorsion pairs in $(d+2)$-angulated categories

Characterized weak cotorsion pairs in cluster categories of type A

Proved mutation of cotorsion pairs preserves their structure

Abstract

Let $\mathcal C$ be a $(d+2)$-angulated category. In this paper, we define the notions of cotorsion pairs and weak cotorsion pairs in $\mathcal C$, which are generalizations of the classical cotorsion pairs in triangulated categories. As an application, we give a geometric characterization of weak cotorsion pairs in $(d+2)$-angulated cluster categories of type $A$. Moreover, we prove that any mutation of a (weak) cotorsion pair in $\mathcal C$ is again a (weak) cotorsion pair. When $d=1$, this result generalizes the work of Zhou and Zhu on classical cotorsion pairs in triangulated categories.