  We give a simple proof of Lee's result from [Adv. Math. 179 (2005) 554-586;
arXiv:math.GT/0210213], that the dimension of the Lee variant of the Khovanov
homology of a c-component link is 2^c, regardless of the number of crossings.
Our method of proof is entirely local and hence we can state a Lee-type theorem
for tangles as well as for knots and links. Our main tool is the "Karoubi
envelope of the cobordism category", a certain enlargement of the cobordism
category which is mild enough so that no information is lost yet strong enough
to allow for some simplifications that are otherwise unavailable.
