Re: monoidal derived categories

From: Dan Christensen (jdc_at_uwo.ca)
Date: 03/16/05 

Date: 16 Mar 2005 13:45:00 -0500

"Urs Schreiber" <Urs.Schreiber@uni-essen.de> writes:

> Is anything known about (weak) multiplicative inverses in D(C)??

I believe you are asking what the invertible objects are, where
a complex E is invertible if there is another complex F such that
E \otimes F is quasi-isomorphic to the identity.

If this is what you are asking, the keyword to search under is "Picard
group" of the derived category, as this is what the group of
quasi-isomorphism classes of invertible objects is called. In many
cases, this group consists of just the suspensions (and desuspensions)
of the identity, and so is isomorphic to the integers. But there are
other cases is which it is much more subtle.

Google/arxiv/MathSciNet will all turn up lots of references now that
you know what to look for! :-)

Dan 

-- 
Dan Christensen
jdc@uwo.ca
.