Deligne conjecture for Iterated monoidal categories

We discuss our approach to the Deligne conjecture for
higher monoidal abelian categories, based on a refined construction
of the Drinfeld dg quotient for dg categories. The main advantage
of the refined dg quotient is its nice monoidal behavior. It makes
possible to use the Kock-Toen approach to their "non-linear Deligne
conjecture", in the linear context. Following this idea, we replace
the Dwyer-Kan localization by our refined Drinfeld dg quotient,
and the Segal monoids by their non-cartesian analogues introduced
by Leinster.