2024/04/29 by Huimin Chang, Chang, Huimin, Panyue Zhou +1 · 2 citations
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2404.18336
openalex publication_date 2024/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.