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arXiv · 2405.01152

Relative cluster tilting theory and $\tau$-tilting theory

Yu Liu·Jixing Pan·Panyue Zhou
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Abstract

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.

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BibTeXRIS

Yu Liu, Jixing Pan, Panyue Zhou. 2024-05-02. Relative cluster tilting theory and $\tau$-tilting theory. https://arxiv.org/abs/2405.01152

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