An algebraic interpretation of the Wheeler - DeWitt equation

We make a direct connection between the construction of three-dimensional topological state sums from tensor categories and three-dimensional quantum gravity by noting that the discrete version of the Wheeler - DeWitt equation is exactly the pentagon for the associator of the tensor category - the Biedenharn - Elliott identity. A crucial role is played by an asymptotic formula relating 6j-symbols to rotation matrices given by Edmonds.