REU Meeting - 2026-07-09

This following is a brief summary of our research meeting on 2026-07-09.

Meeting summary

We discussed dualizable objects and the notion of categorical trace. We also verified the claims about the monoidal structure on the category of representations of a group, and how the categorical trace recovers the classical trace in that context.

Tasks for next meeting

It's time to study categorical characters and a generalization of classical representation theory to categorified representation theory.

• Skim through this nLab page about actions on monoidal categories.
• Try to make sense of this claim from Gemini:
• Check out this paper by Kapranov and Ganter

References

(embedded in the above tasks)