Classifying substructures of extriangulated categories via Serre subcategories

Abstract

We give a classification of substructures (= closed subbifunctors) of a given skeletally small extriangulated category by using the category of defects, in a similar way to the author's classification of exact structures of a given additive category. More precisely, for an extriangulated category, possible substructures are in bijection with Serre subcategories of an abelian category consisting of defects of conflations. As a byproduct, we prove that for a given skeletally small additive category, the poset of exact structures on it is isomorphic to the poset of Serre subcategories of some abelian category.

12 pages, comments welcome

References in corpus (2)

• Auslander's defects over extriangulated categories: an application for the General Heart Construction
• Exact structures and degeneration of Hall algebras

Cited by in corpus (7)

• Auslander's formula and correspondence for exact categories
• On the lattices of exact and weakly exact structures
• Intervals of $s$-torsion pairs in extriangulated categories with negative first extensions
• Positive and negative extensions in extriangulated categories
• Localization of triangulated categories with respect to extension-closed subcategories
• Right triangulated categories: As extriangulated categories, aisles and co-aisles
• Higher Auslander's defect and classifying substructures of n-exangulated categories