Bosonization of fermionic categorical symmetries

Bosonization has proven to be an effective tool in the study of fermionic phases of matter. In this work, we study the bosonization of (1+1)d fermionic lattice systems with a focus on the generalized symmetry. First we bosonize the (1+1)d edge lattice model of a fermionic symmetry-protected topological phase in (2+1)d, and derive how the symmetry and 't Hooft anomaly are represented in the bosonic system. We will then discuss the bosonization map of fermionic categorical symmetries into bosonic categorical symmetries in anyon chains.