Relative Serre functors (Christoph Schweigert)

Orateur :  Christoph Schweigert

Lieu : salle des Séminaires M3 Résumé :  Relative Serre functors relate internal Homs of finite tensor categories to their duals.  In contrast to ordinary Serre functors, they can exist for non-semisimple monoidal categories (and module categories over them), but they are still related to Nakayama functors. We explain some of their applications:

1. Trivializations of relative Serre functors are a profilic source of Frobenius algebras, including Frobenius algebras in Drinfeld centers.
2. They allow a conceptual understanding of modified traces.
3. They naturally appear in Morita contexts that respect pivotal structures, i.e. identifications of an object and its bidual.