  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 symmetry
group, which leads to a new gapped phase with emergent gauge structure and can
be described algebraically using the mathematical framework of modular tensor
category (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 group
case. When the ungauged system has a non-zero Hall conductance, the gauged
theory remains gapped and we determine the complete set of anyon data for the
gauged theory. On the other hand, when the Hall conductance vanishes, we argue
that gauging has the same effect of condensing a special Abelian anyon
nucleated by inserting $2\pi$ U(1) flux. We apply our procedure to the
SU(2)$_k$ MTCs and derive the full MTC data for the $\mathbb{Z}_k$ parafermion
MTCs. We also discuss a dual U(1) symmetry that emerges after the original U(1)
symmetry of an MTC is gauged.
