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Relative cluster tilting theory and τ-tilting theory

2024/05/02 by Liu, Yu, Pan, Jixing, Zhou, Panyue
#Category Theory (math.CT) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2405.01152

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 τ-tilting theory in functor categories and abelian categories.

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