Re: monoidal derived categories

From: Urs Schreiber (Urs.Schreiber_at_uni-essen.de)
Date: 03/19/05 

Date: 19 Mar 2005 10:15:01 -0500

Dan Christensen <jdc@uwo.ca> wrote in message news:<d1anet$2hn$1@dizzy.math.ohio-state.edu>...
> serge bouc <sergepointbouc@free.fr> writes:
>
> > Urs Schreiber a ecrit :
> >>
> >> Is anything known about (weak) multiplicative inverses in D(C)??
> >
> > It seems you're looking for "Derived Picard group". Google will
> > tell you more about this.
>
> Actually, I think the "derived Picard group" is different from
> the "Picard group of the derived category", and that it is the latter
> than Urs was asking about.

Thanks to Serge and Dan for pointing me to the (derived) Picard group.
This is indeed what I was looking for. I found particularly helpful a
couple of papers by Amnon Yekutieli on this subject.

One question remains: Yekutieli and others discuss only the group
structure on the objects. But the product is of course a functor and
hence also induces a product on the morphisms. Does anyone know if the
derived Picard group generalizes to a full 2-group? I.e. does it
generalize to a (possibly weakly) invertible product operation on
morphisms in a derived category, not just on objects?