hmmm, some interesting e-mail to todd from around january 2010 ... on stuff like :

as for the more general question of whether the cokernel of a
dualizable object by a dualizable subobject should be dualizable, i'm
beginning to wonder whether it might even be possible to find examples
"in nature" (in some loose sense) where this fails.

[end of quote]


and so forth ....

??hmm, but also (???less impressiely ... ??or something...) .... :

i suspect now that it _is_ easy within the original doctrine to show
that the cokernel of an n-dimensional object by an m-dimensional
subobject is [n-m]-dimensional, by using "categorified arithmetic of
chern classes" or something like that. (and this probably should have
been "obvious" in some sense.)

[end of quote]