Derived Hall algebras for stable homotopy theories (Q2837319)

Hall algebras, defined initially for abelian categories, play an important role in representation theory. Toën constructed derived Hall algebras associated to triangulated categories arising as homotopy categories of model categories whose objects are modules over a sufficiently finitary differential graded category over \(\mathbb{F}_q\). In this paper, the author modifies Toën's proofs to establish derived Hall algebras corresponding to triangulated categories arising as homotopy categories for more general stable homotopy theories, in particular stable complete Segal spaces satisfying appropriate finiteness assumptions.