Fixing the functoriality of Khovanov homology

@article{Clark2009FixingTF,
  title={Fixing the functoriality of Khovanov homology},
  author={David A. Clark and Scott Morrison and Kevin Walker},
  journal={Geometry \& Topology},
  year={2009},
  volume={13},
  pages={1499-1582}
}
We describe a modification of Khovanov homology [13], in the spirit of Bar-Natan [2], which makes the theory properly functorial with respect to link cobordisms. This requires introducing “disorientations” in the category of smoothings and abstract cobordisms between them used in Bar-Natan’s definition. Disorientations have “seams” separating oppositely oriented regions, coming with a preferred normal direction. The seams satisfy certain relations (just as the underlying cobordisms satisfy… 
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