  We derive new dualities of topological quantum field theories in three
spacetime dimensions that generalize the familiar level-rank dualities of
Chern-Simons gauge theories. The key ingredient in these dualities is
non-abelian anyon condensation, which is a gauging operation for topological
lines with non-group-like i.e. non-invertible fusion rules. We find that,
generically, dualities involve such non-invertible anyon condensation and that
this unifies a variety of exceptional phenomena in topological field theories
and their associated boundary rational conformal field theories, including
conformal embeddings, and Maverick cosets (those where standard algorithms for
constructing a coset model fail.) We illustrate our discussion in a variety of
isolated examples as well as new infinite series of dualities involving
non-abelian anyon condensation including: i) a new description of the
parafermion theory as $(SU(N)_{2} \times Spin(N)_{-4})/\mathcal{A}_{N},$ ii) a
new presentation of a series of points on the orbifold branch of $c=1$
conformal field theories as $(Spin(2N)_{2} \times Spin(N)_{-2} \times
Spin(N)_{-2})/\mathcal{B}_{N}$, and iii) a new dual form of $SU(2)_{N}$ as
$(USp(2N)_{1} \times SO(N)_{-4})/\mathcal{C}_{N}$ arising from conformal
embeddings, where $\mathcal{A}_{N}, \mathcal{B}_{N},$ and $\mathcal{C}_{N}$ are
appropriate collections of gauged non-invertible bosons.
