On the functoriality of Khovanov homology

We provide an overview of Blanchet’s oriented model of Khovanov homology, which resolves the sign ambiguity in functoriality. We give a detailed and self-contained exposition of the construction. We establish strict functoriality for the oriented model and briefly outline its extension to cobordisms with singularities recently studied by Scott Carter, Benjamin Cooper, Mikhail Khovanov and Vyacheslav Krushkal.