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We study the gauging of a global U(1) symmetry in a gapped system in (2+1)d.The gauging procedure has been well-understood for a finite global symmetrygroup, which leads to a new gapped phase with emergent gauge structure and canbe described algebraically using the mathematical framework of modular tensorcategory (MTC). We develop a categorical description of U(1) gauging in an MTC,taking into account the dynamics of U(1) gauge field absent in the finite groupcase. When the ungauged system has a non-zero Hall conductance, the gaugedtheory remains gapped and we determine the complete set of anyon data for thegauged theory. On the other hand, when the Hall conductance vanishes, we arguethat gauging has the same effect of condensing a special Abelian anyonnucleated by inserting $2\pi$ U(1) flux. We apply our procedure to theSU(2)$_k$ MTCs and derive the full MTC data for the $\mathbb{Z}_k$ parafermionMTCs. We also discuss a dual U(1) symmetry that emerges after the original U(1)symmetry of an MTC is gauged.

Gauging U(1) symmetry in (2+1)d topological phases