Cotorsion pairs in cluster categories of type A(infinity)(infinity)

摘要

In this paper, we give a complete classification of cotorsion pairs in a cluster category b of type A(infinity)(infinity) 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 b respectively. We also deduce Liu-Paquette's classification of cluster tilting categories of b and Ng's classification of torsion pairs in the cluster category of type A(infinity). (C) 2018 Elsevier Inc. All rights reserved.