n-cotorsion pairs in a recollement of extriangulated categories

2025/08/28 by Xin Ma, Ma, Xin, Panyue Zhou +1
Mathematics · #Algebraic structures and combinatorial models #Advanced Topics in Algebra #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2508.20331

Abstract

Let (A, B, C) be a recollement of extriangulated categories.In this paper, we first show how to obtain an n-cotorsion pair in B from given n-cotorsion pairs in A and C. Conversely, we prove that an n-cotorsion pair in B can induce n-cotorsion pairs in A and C under suitable conditions. As applications, several related results are provided to illustrate our construction.

Citations

• Mutation of n-cotorsion pairs in extriangulated categories
• Mutation of n-cotorsion pairs in triangulated categories
• n-cotorsion pairs and recollements of extriangulated categories
• Recollements and n-cotorsion pairs
• Dimensions and cotorsion pairs in recollements of extriangulated categories
• n-Extension closed subcategories of n-exangulated categories
• Resolving subcategories and dimensions in recollements of extriangulated categories
• Homological Dimensions of Extriangulated Categories and Recollements
• Positive and negative extensions in extriangulated categories
• Recollements of extriangulated categories
• On the relation between n-cotorsion pairs and (n+1)-cluster tilting subcategories
• Tilting subcategories in extriangulated categories
• Auslander--Reiten theory in extriangulated categories
• Triangulated quotient categories revisited
• Comparison of Abelian categories recollements

Related

• n-cotorsion pairs and recollements of extriangulated categories
• Recollements of extriangulated categories
• Recollements and n-cotorsion pairs
• Dimensions and cotorsion pairs in recollements of extriangulated categories
• Mutation of n-cotorsion pairs in extriangulated categories