English

$Q$-shaped derived categories as derived categories of differential graded bimodules

Representation Theory 2025-06-30 v3

Abstract

We prove that, under mild assumptions, the QQ-shaped derived categories introduced by Holm and J{\o}rgensen are equivalent to derived categories of differential graded bimodules over differential graded categories. This yields new derived invariance results for QQ-shaped derived categories that allow us to extend known descriptions of such categories as derived categories of differential graded bimodules over (possibly graded) algebras.

Keywords

Cite

@article{arxiv.2501.08255,
  title  = {$Q$-shaped derived categories as derived categories of differential graded bimodules},
  author = {Gustavo Jasso},
  journal= {arXiv preprint arXiv:2501.08255},
  year   = {2025}
}

Comments

30 pages. v2: Corrected several typos, improved introduction, added remark on relation to Lurie's k-linear tensor product. v3: Edits following referee report