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

TL;DR

This paper establishes an equivalence between $Q$-shaped derived categories and derived categories of differential graded bimodules, leading to new invariance results and extending their descriptions over graded algebras.

Contribution

It proves the equivalence under mild assumptions and extends the understanding of $Q$-shaped derived categories as derived categories of differential graded bimodules.

Findings

$Q$-shaped derived categories are equivalent to derived categories of differential graded bimodules.

New invariance results for $Q$-shaped derived categories.

Extension of descriptions over graded algebras.

Abstract

We prove that, under mild assumptions, the $Q$-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 $Q$-shaped derived categories that allow us to extend known descriptions of such categories as derived categories of differential graded bimodules over (possibly graded) algebras.