Abstract:In this paper, we study ideal quotients of triangulated categories by higher cluster tilting subcategories. Koenig and Zhu proved that the ideal quotient by a $2$-cluster tilting subcategory is an abelian category; moreover, by Morita's theorem, it is equivalent to the module category over the $2$-cluster tilting subcategory. We generalize this result to higher cluster tilting subcategories. More precisely, we show that the natural DG-enhancement of the ideal quotient of a triangulated category by a $(d+1)$-cluster tilting subcategory is an abelian $d$-truncated DG-category. In the appendix, we prove a Morita-type theorem for abelian $d$-truncated DG-categories, which asserts that an abelian $d$-truncated DG-category with enough projectives is equivalent to a $d$-extended module category over a $d$-truncated DG-category. As an application, we show that the ideal quotient of a triangulated category by a $(d+1)$-cluster tilting subcategory is equivalent to a $d$-extended module category over a $d$-truncated DG-category.
| Comments: | 32 pages |
| Subjects: | Representation Theory (math.RT); Category Theory (math.CT) |
| Cite as: | arXiv:2605.24607 [math.RT] |
| (or arXiv:2605.24607v1 [math.RT] for this version) | |
| https://doi.org/10.48550/arXiv.2605.24607 arXiv-issued DOI via DataCite (pending registration) |
From: Nao Mochizuki [view email]
[v1]
Sat, 23 May 2026 14:43:45 UTC (46 KB)
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