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Why do knot cobordisms result in functoriality with respect to knot homologies so often?

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mathoverflow.net/howtoask –  Neil Strickland May 21 '13 at 11:32
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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? –  Steven Gubkin May 21 '13 at 12:38

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