Wide Subcategories in Extriangulated Length Categories

Key Points

• The aim is to explore the connection between wide subcategories and torsion classes in extriangulated length categories.
• Established a bijection between wide subcategories and torsion classes under specific assumptions.
• Characterized wide intervals using principles from lattice theory.
• Generalized results on wide intervals from previous studies on abelian length categories.
• Successful establishment of the bijection between wide subcategories and torsion classes.
• Characterization of wide intervals provides insights into the structure of extriangulated length categories.
• Generalization of Asai-Pfeifer results highlights the relevance of wide intervals in broader contexts.