# 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}
}```
• Published 12 January 2007
• Mathematics
• Geometry & Topology
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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