Abstract
We construct a 3D membrane-net model based on a spherical fusion 2-category. The partition function and lattice Hamiltonian of the membrane-net model are constructed using the state sum of the spherical fusion 2-category. We also construct the 3D tube algebra of the membrane-net model to study excitations in the model. We conjecture that all intrinsic excitations in the membrane-net model have a one-to-one correspondence with the irreducible central idempotents of the 3D tube algebra. The model can be used to systematically study all general 3D TOs with gapped boundaries.
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