REU Meeting - 2026-07-13

This following is a brief summary of our research meeting on 2026-07-13.

Meeting summary

We discussed the categorical definition of trace, which required more lead-up than it might sound. First we talked about enriched categories and 2-categories, including many examples in the Kapranov paper. Then we slowly worked through the idea of 2-arrows from a identity 1-arrow to another 1-arrow, finally leading to a functor $\mathbf{T}\mathbf{r}:{\mathrm{Hom}}_C(1_x,A)\to \mathbf{S}\mathbf{e}\mathbf{t}$ .

Tasks for next meeting

Let's continue to tackle the papers by Ponto-Shulman and Kapranov-Ganter until we get a better feel for the categorical characteristic.

References

Traces in symmetric monoidal categories, by Kate Ponto and Michael Shulman
Representations and character theory in 2-categories, by Nora Ganter and Mikhail Kapranov