In Khovanov's categorification of the Jones polynomial, a polynomial
invariant of links is upgraded to an invariant with values in complexes
of graded vector spaces such that taking the graded Euler characteristics
 gives back the original polynomial. One would like to extend this
construction to other invariants like coloured Jones or Turaev-Viro
3-manifold invariants. The problem hereby is that the polynomial
invariant (or at least its construction) is not defined integrally
anymore, but rather over the rational numbers. Hence one would like to
interpret rational numbers as Euler characteristics and linear maps with
not necessarily integral matrix entries as maps induced by functors on
the Grothendieck group.  These questions and their relevance in existing
categorifications are addressed in the talk.