Here are some student's notes from a seminar on category theory. The goal this quarter was not to introduce technical concepts of category theory. Rather, I tried to explain how category theory unifies mathematics and makes it easier to learn. We began with a study of duality, and then moved on to a very general approach to Galois theory and Klein geometry, getting a taste of 'stacks'.
For a more systematic course starting from scratch, see the Winter 2016 notes.
If you discover any errors in the notes, please email me, and I'll add them to the list of errors.
You can get all 10 weeks of notes in a single file here. Take a look; then pick your favorite student:
Or, you can read notes of individual lectures here:
Also try this:
To see this worked out in the most familiar example, see: