Classifying substructures of extriangulated categories via Serre subcategories

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 catego...

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Veröffentlicht in:arXiv.org 2020-05
1. Verfasser: Enomoto, Haruhisa
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Sprache:eng
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Zusammenfassung: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2005.13381