  We study a 4d gauge theory $U(1)^{N-1}\rtimes S_N$ obtained from a
$U(1)^{N-1}$ theory by gauging a 0-form symmetry $S_N$. We show that this
theory has a global continuous 2-category symmetry, whose structure is
particularly rich for $N>2$. This example allows us to draw a connection
between the higher gauging procedure and the difference between local and
global fusion, which turns out to be a key feature of higher category
symmetries. By studying the spectrum of local and extended operators, we find a
mapping with gauge invariant operators of 4d $SU(N)$ Yang-Mills theory. The
largest group-like subcategory of the non-invertible symmetries of our theory
is a $\mathbb{Z}_N^{(1)}$ 1-form symmetry, acting on the Wilson lines in the
same way as the center symmetry of Yang-Mills theory does. Supported by a
path-integral argument, we propose that the $U(1)^{N-1}\rtimes S_N$ gauge
theory has a relation with the ultraviolet limit of $SU(N)$ Yang-Mills theory
in which all Gukov-Witten operators become topological, and form a continuous
non-invertible 2-category symmetry, broken down to the center symmetry by the
RG flow.
