2024/11/27 by Huimin Chang, Chang, Huimin, Panyue Zhou +1
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.2411.17975
openalex publication_date 2024/11/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let \mathcal C be a (d+2)-angulated category. In this paper, we define the notions of cotorsion pairs and weak cotorsion pairs in \mathcal C, which are generalizations of the classical cotorsion pairs in triangulated categories. As an application, we give a geometric characterization of weak cotorsion pairs in (d+2)-angulated cluster categories of type A. Moreover, we prove that any mutation of a (weak) cotorsion pair in \mathcal C is again a (weak) cotorsion pair. When d=1, this result generalizes the work of Zhou and Zhu on classical cotorsion pairs in triangulated categories.