  It is possible to describe fermionic phases of matter and spin-topological
field theories in 2+1d in terms of bosonic "shadow" theories, which are
obtained from the original theory by "gauging fermionic parity". The
fermionic/spin theories are recovered from their shadow by a process of
fermionic anyon condensation: gauging a one-form symmetry generated by
quasi-particles with fermionic statistics. We apply the formalism to theories
which admit gapped boundary conditions. We obtain Turaev-Viro-like and
Levin-Wen-like constructions of fermionic phases of matter. We describe the
group structure of fermionic SPT phases protected by the product of fermion
parity and internal symmetry G. The quaternion group makes a surprise
appearance.
