The Karoubi Envelope and Lee's Degeneration of Khovanov Homology

We give a simple proof of Lee's result from \cite{MR2173845}, that the dimension of the Lee variant of the Khovanov homology of an $c$-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.