  We discuss the fermionization of fusion category symmetries in
two-dimensional topological quantum field theories (TQFTs). When the symmetry
of a bosonic TQFT is described by the representation category $\mathrm{Rep}(H)$
of a semisimple weak Hopf algebra $H$, the fermionized TQFT has a superfusion
category symmetry $\mathrm{SRep}(\mathcal{H}^u)$, which is the supercategory of
super representations of a weak Hopf superalgebra $\mathcal{H}^u$. The weak
Hopf superalgebra $\mathcal{H}^u$ depends not only on $H$ but also on a choice
of a non-anomalous $\mathbb{Z}_2$ subgroup of $\mathrm{Rep}(H)$ that is used
for the fermionization. We derive a general formula for $\mathcal{H}^u$ by
explicitly constructing fermionic TQFTs with $\mathrm{SRep}(\mathcal{H}^u)$
symmetry. We also construct lattice Hamiltonians of fermionic gapped phases
when the symmetry is non-anomalous. As concrete examples, we compute the
fermionization of finite group symmetries, the symmetries of finite gauge
theories, and duality symmetries. We find that the fermionization of duality
symmetries depends crucially on $F$-symbols of the original fusion categories.
The computation of the above concrete examples suggests that our fermionization
formula of fusion category symmetries can also be applied to non-topological
QFTs.
