  We characterize discrete (anti-)unitary symmetries and their non-invertible
generalizations in $2+1$d topological quantum field theories (TQFTs) through
their actions on line operators and fusion spaces. We explain all possible
sources of non-invertibility that can arise in this context. Our approach gives
a simple $2+1$d proof that non-invertible generalizations of unitary symmetries
exist if and only if a bosonic TQFT contains condensable bosonic line operators
(i.e., these non-invertible symmetries are necessarily "non-intrinsic"). Moving
beyond unitary symmetries and their non-invertible cousins, we define a
non-invertible generalization of time-reversal symmetries and derive various
properties of TQFTs with such symmetries. Finally, using recent results on
2-categories, we extend our results to corresponding statements in $2+1$d
quantum field theories that are not necessarily topological.
