Torsion pairs, t-structures, and co-t-structures for completions of discrete cluster categories

Franchini, Sofia (2025) Torsion pairs, t-structures, and co-t-structures for completions of discrete cluster categories. Mathematische Zeitschrift, 310 (4): 86. ISSN 0025-5874

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Abstract

We give a classification of torsion pairs, t-structures, and co-t-structures in the Paquette–Yıldırım completion of the Igusa–Todorov discrete cluster category. We prove that the aisles of t-structures and co-t-structures are in bijection with non-crossing partitions enriched with some additional data. We also observe that recollements exist in the completion and we classify them.