# 2024-10-07

This following is a very brief summary of what happened in class on 2024-10-07.

We introduced the notion of a natural transformation between two functors. Intuitively, a natural transformation between two functors

We took a peek at our first few examples of natural transformations, namely:

- the determinant
- the "insertion of generators" in the free vector space construction
- the idea/definition of maps between diagrams of the same shape

We also defined functor categories. For given categories

- objects: all functors
- arrows: natural transformations between such functors

We also quickly looked at few small examples, noting that the functor category

## Concepts

## References

- Mac Lane: pages 16-18