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Exact dg structures are classified intrinsically by bi-Serre subcategories

  • Yasuaki Ogawa
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Abstract

The aim of this article is to leverage Enomoto's classification of exact structures to the dg level. Let π’œ be a connective additive idempotent complete dg category. We establish an intrinsic Enomoto-type classification of exact dg structures on π’œ in terms of bi-Serre subcategories in tr(π’œ). Our proof is a direct dg argument based on dg totalizations of $3$-term complexes and dg duality, rather than a reduction to the greatest exact dg structure and the classification of its substructures. As a consequence, we establish a bijection between exact dg structures on π’œ and bi-Serre subcategories in tr(π’œ). Moreover, this bijection is an isomorphism of posets and yields a complete lattice structure on the class of exact dg structures on π’œ. In particular, we provide another construction of Rump--Chen's greatest exact dg structure on π’œ.

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Cite

BibTeXRIS
BibTeX
@misc{ogawa2026exact,
  title = {{Exact dg structures are classified intrinsically by bi-Serre subcategories}},
  author = {Yasuaki Ogawa},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.25583},
  eprint = {2609.25583},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.25583},
}
RIS
TY  - UNPB
TI  - Exact dg structures are classified intrinsically by bi-Serre subcategories
AU  - Yasuaki Ogawa
PY  - 2026
DA  - 2026/09/22
PB  - arXiv
DO  - 10.48550/arxiv.2609.25583
UR  - https://arxiv.org/abs/2609.25583
AB  - The aim of this article is to leverage Enomoto's classification of exact structures to the dg level. Let π’œ be a connective additive idempotent complete dg category. We establish an intrinsic Enomoto-type classification of exact dg structures on π’œ in terms of bi-Serre subcategories in tr(π’œ). Our proof is a direct dg argument based on dg totalizations of $3$-term complexes and dg duality, rather than a reduction to the greatest exact dg structure and the classification of its substructures. As a consequence, we establish a bijection between exact dg structures on π’œ and bi-Serre subcategories in tr(π’œ). Moreover, this bijection is an isomorphism of posets and yields a complete lattice structure on the class of exact dg structures on π’œ. In particular, we provide another construction of Rump--Chen's greatest exact dg structure on π’œ.
ER  -