We begin by outlining our motivation from the representation theory of vertex algebras for studying *-autonomous categories, also recently referred to as Grothendieck-Verdier categories, as well as module categories over them. We then explore the concept of relative Serre functors for module categories and show how these functors can be used to construct Frobenius algebras.
Based on work with Jürgen Fuchs, Gregor Schaumann and Simon Wood