## 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.