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It has long been argued that higher categories provide the proper algebraic structure underlying state sum invariants of 4-manifolds.
G. Ponzano and T. Regge, Semiclassical limits of Racah coefficients, in Spectroscopic and Group Theoretical Methods in Physics: Racah Memorial Volume, ed. F. Bloch, North-Holland, Amsterdam, 1968, pp. 75–103
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