Colimits over product categories
Essentially constant in additive categories

Here we show that if $F, G : \mathcal{I} \to \mathcal{A}$ are functors
from a filtered category to an additive category, then $F \oplus G$ is
essentially constant if and oly if $F$ and $G$ are essentially constant,
provided that $\mathcal{A}$ is Karoubian.

If $\mathcal{A}$ is not Karoubian, then we cannot even start the
"obvious" proof as we don't know that \colim (F \oplus G)$ can be split
into two parts! Presumably this result is actually false if
$\mathcal{A}$ is not Karoubian.

Thanks to Nuno Cardoso for pointing out this difficulty (see also next
commit).
Fix an error in derived.tex

It is not clear that if RF is defined a X + Y then it is defined at both
X and Y. This is true when the target triangulated category is Karoubian
but presumably not in general (see also previous commit).

Thanks to Nuno Cardoso for pointing out this difficulty.
http://stacks.math.columbia.edu/tag/05SD#comment-524
http://stacks.math.columbia.edu/tag/05SD#comment-526
http://stacks.math.columbia.edu/tag/05SD#comment-527
http://stacks.math.columbia.edu/tag/05SD#comment-528
http://stacks.math.columbia.edu/tag/05SD#comment-529