  Recently, many studies are focused on generalized global symmetry, a mixture
of both invertible and non-invertible symmetries in various space-time
dimensions. The complete structure of generalized global symmetry is described
by higher fusion category theory. In this paper, We first review the
construction of fusion 2-category symmetry $\Sigma \cal B$ where $\cal B$ is a
a braided fusion category. In particular, we elaborate on the monoidal
structure of $\Sigma \cal B$ which determines fusion rules and controls the
dynamics of topological operators/defects. We then take $\Sigma \mathrm{sVec}$
as an example to demonstrate how we calculate fusion rule, quantum dimension
and 10j-symbol of the fusion 2-category. With our algorithm, all these data can
be efficiently encoded and computed in computer program. The complete program
will be uploaded to github soon. Our work can be thought as explicitly
computing the representation theory of $\cal B$, in analogy to, for example the
representation theory of $SU(2)$. The choice of basis bimodule maps are in
analogy to the Clebsch-Gordon coefficients and the 10j-symbol are in analogy to
the 6j-symbol.
