English

Classifying substructures of extriangulated categories via Serre subcategories

Category Theory 2022-08-08 v1 Representation Theory

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.

Keywords

Cite

@article{arxiv.2005.13381,
  title  = {Classifying substructures of extriangulated categories via Serre subcategories},
  author = {Haruhisa Enomoto},
  journal= {arXiv preprint arXiv:2005.13381},
  year   = {2022}
}

Comments

12 pages, comments welcome

R2 v1 2026-06-23T15:51:14.844Z