Title: State Sum Invariants of Three Manifolds from Spherical Multi-fusion Categories,
Abstract: We define a family of quantum invariants of closed oriented $3$-manifolds
using spherical multi-fusion categories. The state sum nature of this invariant
leads directly to $(2+1)$-dimensional topological quantum field theories
($\text{TQFT}$s), which generalize the Turaev-Viro-Barrett-Westbury
($\text{TVBW}$) $\text{TQFT}$s from spherical fusion categories. The invariant
is given as a state sum over labeled triangulations, which is mostly parallel
to, but richer than the $\text{TVBW}$ approach in that here the labels live not
only on $1$-simplices but also on $0$-simplices. It is shown that a
multi-fusion category in general cannot be a spherical fusion category in the
usual sense. Thus we introduce the concept of a spherical multi-fusion category
by imposing a weakened version of sphericity. Besides containing the
$\text{TVBW}$ theory, our construction also includes the recent higher gauge
theory $(2+1)$-$\text{TQFT}$s given by Kapustin and Thorngren, which was not
known to have a categorical origin before.