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Much of the content of the page seemed to derive from very early edits and concerns the cobordism hypothesis and so ought to be there. I’ve edited heavily and removed the following which is covered already at cobordism hypothesis.
In extended topological quantum field theory, which is really the representation theory of these cobordism $n$-categories, we expect: +– {: .un_prop}
An $n$-dimensional unitary extended TQFT is a weak $n$-functor, preserving all levels of duality, from the $n$-category $n Cob$ of cobordisms to $n Hilb$, the $n$-category of $n$-Hilbert spaces. =–
Putting the extended TQFT hypothesis and the cobordism hypothesis together, we obtain: +– {: .un_prop}
An $n$-dimensional unitary extended TQFT is completely described by the $n$-Hilbert space it assigns to a point. =–
Further discussion can be found here:
Around 2009, Mike Hopkins and Jacob Lurie have claimed (see Hopkins-Lurie on Baez-Dolan) to have formalized and proven this hypothesis in the context of (infinity,n)-categories modeled on complete Segal spaces. See:
where an (infinity,n)-category of cobordisms is defined and shown to lead to a formalization and proof of the cobordism hypothesis. Lurie explains his work here:
Lecture notes for Lurie’s talks are available at the Geometry Research Group website.
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