Torsion pairs, t-structures, and co-t-structures for completions of discrete cluster categories
Representation Theory
2025-06-23 v2 Category Theory
Abstract
We give a classification of torsion pairs, t-structures, and co-t-structures in the Paquette-Yildirim 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.
Keywords
Cite
@article{arxiv.2403.08735,
title = {Torsion pairs, t-structures, and co-t-structures for completions of discrete cluster categories},
author = {Sofia Franchini},
journal= {arXiv preprint arXiv:2403.08735},
year = {2025}
}
Comments
50 pages, 23 figures