Skip to content
DraconiticResearch
Search Sources API
194,161 studies31 sourcesUpdated 45 min ago
PreprintarXiv licencearXiv

Bounded t-structures on the category of strongly bounded objects

  • Hongxing Chen
  • Xiaohu Chen
  • Jinbi Zhang
Open at sourcePDFDOICite

Abstract

Strongly bounded objects in a weakly approximable triangulated category are known to relate closely to global dimension and to play a significant role in the uniqueness problem for triangulated enhancements. In this paper, we investigate when the full subcategory of strongly bounded objects admits a bounded t-structure. Our main result, under a finiteness condition termed the finite strong finitistic dimension, states that this happens exactly when the subcategory agrees with the full subcategory of bounded objects in the ambient triangulated category. In that case, the bounded t-structure is unique up to equivalence; even more, the uniqueness holds unconditionally on the full subcategory of bounded objects.

Related

  1. Examples of nontrivial presilting objects in a singularity category
    Changchang Xi, Jinbi Zhang
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  2. Kuranishi spaces in a category of fibrant objects and their homotopy fiber products
    Taesu Kim
    arXivPreprintarXiv licenceFull textGeometry & topologyarXiv
  3. Universal δ-functors and relative injective objects in the category of p-Banach spaces
    Nazaret Trejo-Arroyo
    arXivPreprintarXiv licenceFull textAlgebra & number theoryAnalysis & PDEsarXiv
  4. ON HOPFIAN AND CO-HOPFIAN OBJECTS IN AN ABELIAN CATEGORY AND IN THE CATEGORY OF ITS COMPLEX SEQUENCES OF MORPHISMS
    Ablaye Diallo, Mohamed Ben Maaouia, Mamadou Sanghare
    JP Journal of Algebra, Number Theory and ApplicationsPeer-reviewedCC BYFull textGeometry & topologyHAL
  5. Acyclic and totally acyclic objects in the Q-shaped derived category
    Henrik Holm, Peter Jorgensen
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{chen2026bounded,
  title = {{Bounded $t$-structures on the category of strongly bounded objects}},
  author = {Hongxing Chen and Xiaohu Chen and Jinbi Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.29031},
  eprint = {2608.29031},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.29031},
}
RIS
TY  - UNPB
TI  - Bounded t-structures on the category of strongly bounded objects
AU  - Hongxing Chen
AU  - Xiaohu Chen
AU  - Jinbi Zhang
PY  - 2026
DA  - 2026/08/29
PB  - arXiv
DO  - 10.48550/arxiv.2608.29031
UR  - https://arxiv.org/abs/2608.29031
AB  - Strongly bounded objects in a weakly approximable triangulated category are known to relate closely to global dimension and to play a significant role in the uniqueness problem for triangulated enhancements. In this paper, we investigate when the full subcategory of strongly bounded objects admits a bounded t-structure. Our main result, under a finiteness condition termed the finite strong finitistic dimension, states that this happens exactly when the subcategory agrees with the full subcategory of bounded objects in the ambient triangulated category. In that case, the bounded t-structure is unique up to equivalence; even more, the uniqueness holds unconditionally on the full subcategory of bounded objects.
ER  -