Title: Module categories and
generalised 6j symbols for G-graded vector spaces
Abstract: This talk will be based on my Master’s thesis “Generalised 6j symbols over the category of G -graded vector spaces”. We will review the notion of module categories over a monoidal category and present a basic classification result in the case where the underlying monoidal category is the category of G-graded vector spaces. This serves as preparation to consider the notions of module functors and module natural transformations, the main theorem being a classification of simple module functors when G is a finite cyclic group. Monoidal categories, module categories, module functors and module natural transformations are of interest as they give rise to so-called generalised 6j symbols, which can be used to compute a generalisation of Turaev-Viro invariants for 3-manifolds with defects, cf. recent work of Catherine Meusburger.