Notes on Category Theory, (partial) version #2

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

  1. Categories defined
  2. Duality, kinds of arrows (epics, monics, isomorphisms …)
  3. Functors
  4. More about functors and categories (and the category of categories!)
  5. Natural transformations (with rather more than usual on the motivation)
  6. Equivalence of categories (again with a section on motivation, why we want ‘equivalence’ rather than full isomorphism)
  7. The Yoneda embedding (shown to indeed be an embedding by using an easy restricted version of the Yoneda Lemma)
  8. 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.

Download the new version of the notes here

1 thought on “Notes on Category Theory, (partial) version #2”

  1. 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.

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