We discuss our approach to the Deligne conjecture for
higher monoidal abelian categories, based on a refined construction
of the Drinfeld dg quotient for dg categories. The main advantage
of the refined 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 refined Drinfeld dg quotient,
and the Segal monoids by their non-cartesian analogues introduced
by Leinster.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/6356