DHR bimodules and topological holography

Nets of associative algebras over metric spaces are a clean, algebraic way to axiomatize the local kinematics of quantum systems with spatial degrees of freedom. In this talk, we will introduce the braided tensor category of DHR bimodules associated to a net of algebras, and show how to compute it in some 1+1D examples coming from fusion categories. Then we will discuss how this can be used to formalize the recent idea of topological holography emerging from the physics literature, and how this is used in the study of topologically ordered spin systems and fusion categorical symmetries of quantum field theories.