  We use the language of categorical condensation to give a procedure for
gauging nonabelian anyons, which are the manifestations of categorical
symmetries in three spacetime dimensions. We also describe how the condensation
procedure can be used in other contexts such as for topological cosets and
constructing modular invariants. By studying a generalization of which anyons
are condensable, we arrive at representations of congruence subgroups of the
modular group. We finally present an analysis for ungauging anyons, which is
related to the problem of constructing a Drinfeld center for a fusion category;
this procedure we refer to as bulk reconstruction. We introduce a set of
consistency relations regarding lines in the parent theory and wall category.
Through use of these relations along with the $S$-matrix elements of the child
theory, we construct $S$-matrix elements of a parent theory in a number of
examples.
