Another categorial update

It’s been a month since I last posted about the category theory project, so a quick update  — and the end really is in sight!

  • I’ve just put online another revised version of Category Theory I. Little has changed except for some more corrections of typos (with particular thanks to Georg Meyer) and a few small changes for added clarity (with particular thanks to John Zajac). I’ve also made a few very small changes to better fit with what happens in Category Theory II as I steadily revise that.
  • More significantly, there is another version of Category Theory II linked on the category theory page. The old chapters on adjunctions are now in a much better state. I don’t think I found any horrendous errors, but the story is (I certainly hope!) a lot clearer in a number of key places.
  • In fact, the bit of recent work on this that I’m most pleased with is probably the proof of ‘RAPL’ (Right Adoints Preserve Limits). Tom Leinster and Steve Awodey offer fancy-but-unilluminating proofs. I spell out the sort of bread-and-butter proof idea I got from Peter Johnstone’s lectures (and my version is perhaps a little clearer for a first encounter than Emily Riehl’s?).
  • It’s a judgement call where to stop. For example, I still reckon (as I did before) that the Adjoint Functor Theorems are just over the boundary, as far as what is really appropriate for an entry-level introduction. However, I do now say just a very little about monads (so at least you know what the idea is), though I might yet add another example or two.
  • I still need to revise the last three chapters of Category Theory II. They should be in a reasonable basic state as these are the same final chapters that — in the previous arrangement — appeared as the last chapters in the 2023 published version of Category Theory I. However, in the somewhat more advanced context of Category Theory II it might be appropriate to expand the discussions a bit.

I’d hoped that Category Theory II would be paperback-ready by the end of this month. There have been unforeseen distractions. But I’m not far off. Watch this space.

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