After a bit of a gap, I’ve been able to get back to writing up my notes. The current instalment of the notes (61 pp.) corrects some typos in the first six chapters — and it is those needed corrections that prompt me quickly to post another version even though I’ve only added two new chapters this time. So far, then, I cover
- Categories defined
- Duality, kinds of arrows (epics, monics, isomorphisms …)
- More about functors and categories (and the category of categories!)
- Natural transformations (with rather more than usual on the motivation)
- Equivalence of categories (again with a section on motivation, why we want ‘equivalence’ rather than full isomorphism)
- The Yoneda embedding (shown to indeed be an embedding by using an easy restricted version of the Yoneda Lemma)
- The Yoneda Lemma (how to get to the full-dress version by two conceptually easy steps from the restricted version).
It took me a while to see how best(?) to split the proof of the Yoneda Lemma into obviously well-motivated chunks: maybe some others new(ish) to category theory will find the treatment in Chs 7 and 8 helpful.
1 thought on “Notes on Category Theory, (partial) version #2”
On page 4, in the definition of pre-ordered set, there is a typo. I believe you wanted to say the binary relation is reflexive—xRx for all x. But what appears is xRy for all x,y.