A simultaneous generalization of mutation and recollement on a triangulated category

Hiroyuki Nakaoka

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arXiv · 1512.02173

A simultaneous generalization of mutation and recollement on a triangulated category

Hiroyuki Nakaoka

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Abstract

In this article, we introduce the notion of {\it concentric twin cotorsion pair} on a triangulated category. This notion contains the notions of $t$-structure, cluster tilting subcategory, co-$t$-structure and functorally finite rigid subcategory as examples. Moreover, a recollement of triangulated categories can be regarded as a special case of concentric twin cotorsion pair. To any concentric twin cotorsion pair, we associate a pretriangulated subquotient category. This enables us to give a simultaneous generalization of the Iyama-Yoshino reduction and the recollement of cotorsion pairs. This allows us to give a generalized mutation on a set of cotorsion pairs defined by the concentric twin cotorsion pair.

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Hiroyuki Nakaoka. 2015-12-07. A simultaneous generalization of mutation and recollement on a triangulated category. https://arxiv.org/abs/1512.02173

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