Why do knot cobordisms result in functoriality with respect to knot homologies so often?
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3$\begingroup$ mathoverflow.net/howtoask $\endgroup$– Neil StricklandCommented May 21, 2013 at 11:32
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3$\begingroup$ I think Neil is saying you should have some more backround information. Can you give some examples of this phenomenon? How did it arise in your work? You say often - can you explain some situations where it fails, and give your thoughts on how these situations are different? $\endgroup$– Steven GubkinCommented May 21, 2013 at 12:38
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Because the knot homology theories are TQFTs!
This definition is taken from [1]: 
Knot homology theories are (1+1)-dimensional TQFTs: links are 1-manifolds, and cobordisms between them are 2-manifolds.
