There's a lot of current interest in applying tensor category theory to VOA representation theory (and quite rightly). However, it's rather difficult to concretely work through any examples honestly. I'll  try to work through a very simple example, focusing on modular things, with the aim being to illustrate the obstacles. Hopefully, you can help! If time permits, I'll also sketch some further issues that arise with another simple, but this time non-semisimple, example.