  The decorated hypercube found in the construction of Khovanov homology for
links is an example of a Boolean lattice equipped with a presheaf of modules.
One can place this in a wider setting as an example of a coloured poset, that
is to say a poset with a unique maximal element equipped with a presheaf of
modules. In this paper we initiate the study of a bundle theory for coloured
posets, producing for a certain class of base posets a Leray-Serre type
spectral sequence. We then show how this theory finds application in Khovanov
homology by producing a new spectral sequence converging to the Khovanov
homology of a given link.
