REU Meeting - 2026-07-16
This following is a brief summary of our research meeting on 2026-07-16.
Meeting summary
We went over the various properties of the category of Lie groups, focusing mainly on the case of finite-dimensional Lie groups. We noted that the category of finite-dimensional Lie groups possesses the following properties:
- A initial and terminal object, namely the one-point space (with trivial group structure). It thus serves as a/the null object in the category
- Finite products
- Pullbacks
- Equalizers
- Kernels
- Quotients
- An analogue of the First Iso Theorem
It does not possess the following properties:
- Infinite products
- Coproducts (finite or otherwise)
- Pushouts
- Additive (as a category)
- Abelian (as a category)
Tasks for next meeting
Now we want to ask them same questions about the category of Lie algebras!