Mutation of n-cotorsion pairs in triangulated categories
arxiv(2024)
摘要
In this article, we define the notion of n-cotorsion pairs in triangulated
categories, which is a generalization of the classical cotorsion pairs. We
prove that any mutation of an n-cotorsion pair is again an n-cotorsion
pair. When n=1, this result generalizes the work of Zhou and Zhu for
classical cotorsion pairs. As applications, we give a geometric
characterization of n-cotorsion pairs in n-cluster categories of type A
and give a geometric realization of mutation of n-cotorsion pairs via
rotation of certain configurations of n-diagonals.
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