A boundary state sum for the 3BF theory is constructed and proved to satisfy Atiyah's axioms, giving a TQFT functor for finite 3-groups on triangulable 4-manifolds.
Thiemann, Modern Canonical Quantum General Relativity, Cambridge University Press, Cambridge (2007)
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The 3BF theory as a TQFT
A boundary state sum for the 3BF theory is constructed and proved to satisfy Atiyah's axioms, giving a TQFT functor for finite 3-groups on triangulable 4-manifolds.