We discuss invertible and non-invertible topological defects arising from gauging a discrete higher-form symmetry on a higher codimensional manifold in spacetime, which we define as higher gauging. A higher-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 ordinary global symmetry is realized from higher gauging. We further determine the fusion rules be- tween the surfaces, lines, and lines that only live on the surfaces, making the first step towards building a fusion 2-category. We emphasize that the fusion “coefficients” in these non-invertible fusion rules are generally not numbers, but 1+1d TQFTs. Finally, we discuss examples of non-invertible symmetries in non-topological QFT such as the free compact scalar theory and QED.
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