Cotorsion pairs in cluster categories of type $A_{\infty }^{\infty }$

Abstract

In this paper, we give a complete classification of cotorsion pairs in a cluster category $\mathcal{C}$ of type $A_{\infty }^{\infty }$ via certain configurations of arcs, called $\tau$-compact Ptolemy diagrams, in an infinite strip with marked points. As applications, we classify $t$-structures and functorially finite rigid subcategories in $\mathcal{C}$, respectively. We also deduce Liu-Paquette's classification of cluster tilting categories of $\mathcal{C}$ and Ng's classification of torsion pairs in the cluster category of type $A_{\infty }$.

Fix a typo in Definition 3.5

References in corpus (4)

• On triangulated orbit categories
• A characterization of torsion theories in the cluster category of Dynkin type A_{\infty}
• 2-Calabi-Yau categories with a directed cluster-tilting subcategory
• Torsion pairs in finite $2$-Calabi-Yau triangulated categories with maximal rigid objects