REU Meeting - 2026-07-02

This following is a brief summary of our research meeting on 2026-07-02.

Meeting summary

We briefly talked about the previous reading before quickly moving on to the new plan: get category theory in the picture!

Tasks for next meeting

We now want to lay the groundwork for studying Lie theory from a categorical point of view. We will begin by learning about monoidal structures on categories.

• Read Sections 1 of Chapters VII and XI in Mac Lane's Categories for the Working Mathematician. Then try the following exercises at the end Section 1 in Chapter VII:
  • Exercise 4
  • Exercise 5
• Find two monoidal structures on the category of sets
• Suppose a category $C$ has a all finite products and a terminal object. Construct a monoid structure on $C$

References

Saunders Mac Lane, Categories for the Working Mathematician (Chapters VII and XI)