REU Meeting - 2026-08-05

This following is a brief summary of our research meeting on 2026-08-05.

Meeting summary

We spent our time digesting Tannaka duality in the land of group representations, and how the (tensor-product-preserving) endomorphisms of the forgetful functor $\mathbf{R}\mathbf{e}\mathbf{p}(G)\to {\mathbf{V}\mathbf{e}\mathbf{c}}_k$ seem to be the replacement for the characters of classical representation theory. Another hint in that direction comes from Krein's theorem, which talks about "minimal" objects, decompositions and hom-objects between minimal objects.

Tasks for next meeting

• Try to explain in your own words how the classical isomorphism of $G$ with its character group is replaced/generalized by Tannaka duality
• "Prove" that result by adapting our "enriched Yoneda" proof of Tannaka
• Continue writing up what we've learned/done
• Think about the poster

References

nLab