• axion Maxwell
• generalized symmetries
• non-invertible symmetries
• symmetry category

In recent years, the concept of "symmetries" has been vastly generalized. The goal of this thesis is to study the symmetry category of the axion Maxwell theory, as a first step in understanding what is the physical information encoded in this new mathematical structure, as well as how to detect it. We derive fusion rules for the non-invertible electric and shift symmetries of the theory, we computed their associator, and we explained how it can affect the correlation functions.
Moreover, we analyzed how the presence of a higher group structure is reflected in the associativity data of a symmetry, as well as proposed a relation between obstruction to condensing a symmetry on hypersurfaces of various dimensions.