Licentiate seminar: Module categories, internal bimodules and Tambara modules

  • Date:
  • Location: Ångströmlaboratoriet, Lägerhyddsvägen 1 Å4001 + Zoom
  • Lecturer: Mateusz Stroinski
  • Organiser: Matematiska institutionen
  • Contact person: Mateusz Stroinski
  • Licentiatseminarium

Welcome to this licentiate seminar held by Mateusz Stroinski with the title "Module categories, internal bimodules and Tambara modules".

Abstract: We use the theory of Tambara modules to extend and generalize the reconstruction theorem for module categories over a rigid monoidal category to the non-rigid case. We show a biequivalence between the 2-category of cyclic module categories over a monoidal category C and the bicategory of algebra and bimodule objects in the category of Tambara modules on C. Using it, we prove that a cyclic module category can be reconstructed as the category of certain free module objects in the category of Tambara modules on C, and give a sufficient condition for its reconstructability as module objects in C. To that end, we extend the definition of the Cayley functor to the non-closed case, and show that Tambara modules give a proarrow equipment for C-module categories, in which C-module functors are characterized as 1-morphisms admitting a right adjoint. Finally, we show that the 2-category of all C-module categories embeds into the 2-category of categories enriched in Tambara modules on C, giving an “action via enrichment” result.

The article is available at Arxiv.

Participate on site or via Zoom (meeting ID: 65057904595, passcode: tambara).