Relative cluster tilting theory and $\tau$-tilting theory
| Autor: | Liu, Yu, Pan, Jixing, Zhou, Panyue |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | Let $\mathcal C$ be a Krull-Schmidt triangulated category with shift functor $[1]$ and $\mathcal R$ be a rigid subcategory of $\mathcal C$. We are concerned with the mutation of two-term weak $\mathcal R[1]$-cluster tilting subcategories. We show that any almost complete two-term weak $\mathcal R[1]$-cluster tilting subcategory has exactly two completions. Then we apply the results on relative cluster tilting subcategories to the domain of $\tau$-tilting theory in functor categories and abelian categories. Comment: 35 pages.In this version, we have added many new results |
| Databáze: | arXiv |
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