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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeApr 28th 2014

I have edited at HQFT, touched the general formatting and structuring a good bit, trying to clean it up and beautify it a bit, and added a brief cross-pointer to the cobordisms hypothesis for cobordisms with maps into a base manifold.

• CommentRowNumber2.
• CommentAuthorDavid_Corfield
• CommentTimeApr 28th 2014

Are HQFTs taking place in some slice or context from the HoTT point of view?

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeApr 28th 2014

I think the good abstract way to think about them is given by that version of the cobordism hypothesis which I was alluding to above: $Bord^{fr}_n(X)$ is essentially the free $(\infty,n)$-category with duals not on the point, but on the $\infty$-groupoid $\Pi(X)$.