REU Meeting - 2025-07-01

This following is a brief summary of our research meeting on 2025-07-01.

Meeting summary

We briefly chatted about our goal for this first week of our project, namely to learn the three basic objects category theory:

• Categories
• Functors
• Natural transformations

We also talked briefly about how the objects of categories should be viewed as "dots" or "pegs", which in general have no additional structure (e.g., elements). Along those same lines, arrows should be viewed as ... arrows. In particular, the arrows do not need to correspond to actual set maps of any type. Keeping these two pictures in mind will help guide our decisions in the future as we attempt to slowly repackage "every" concept as a statement about an arrow.

Tasks for next meeting

• In Categories for the Working Mathematician:
  • Read Sections 1.2-1.4
  • Try the following exercises:
    • 1.3: 2, 3c, 4
    • 1.4: 1, 3, 6
• In The Joy of Cats, read/skim:
  • Section 1
  • Sections 3.1-3.3, 3.17-3.20
  • Sections 6.1-6.4

References

Adamek-Herrlich-Strecker - The Joy of Cats: Selected material from Sections 1, 3 and 6
Mac Lane - Categories for the Working Mathematician: Chapter 1, Sections 2-4