  We discuss invertible and non-invertible topological condensation defects
arising from gauging a discrete higher-form symmetry on a higher codimensional
manifold in spacetime, which we define as higher gauging. A $q$-form symmetry
is called $p$-gaugeable if it can be gauged on a codimension-$p$ manifold in
spacetime. We focus on 1-gaugeable 1-form symmetries in general 2+1d QFT, and
gauge them on a surface in spacetime. The universal fusion rules of the
resulting invertible and non-invertible condensation surfaces are determined.
In the special case of 2+1d TQFT, every (invertible and non-invertible) 0-form
global symmetry, including the $\mathbb{Z}_2$ electromagnetic symmetry of the
$\mathbb{Z}_2$ gauge theory, is realized from higher gauging. We further
compute the fusion rules between the surfaces, the bulk lines, and lines that
only live on the surfaces, determining some of the most basic data for the
underlying fusion 2-category. We emphasize that the fusion "coefficients" in
these non-invertible fusion rules are generally not numbers, but rather 1+1d
TQFTs. Finally, we discuss examples of non-invertible symmetries in
non-topological 2+1d QFTs such as the free $U(1)$ Maxwell theory and QED.
