  There are two categorifications of the Jones polynomial: "even" discovered by
M.Khovanov in 1999 and "odd" dicovered by P.Ozsvath, J.Rasmussen and Z.Szabo in
2007. The first one can be fully constructed in the category of cobordisms
(strictly: in the additive closure of that category), where we can build a
complex for a given tangle and show its invariance under Reidemeister moves.
The even link homology is given by a monoidal functor from cobordisms into
modules. However, odd link homology cannot be obtained in this way. In this
paper I fill this gap. I enrich cobordisms with chronologies (projections onto
intervals which are Morse separable functions) and show that they form a
category. Given a tangle diagram I take the cube of its resolutions and build a
complex in this new category. I show this complex is a tangle invariant and
applying appropriate functors I can recover both even and odd link homology
theories.
