Another new chapter of the notes, this time on exponentials. I hope the key idea is rather better explained/motivated than in the previous version.
I usually upload more than one newly revised chapter at a time. But on this occasion, I also wanted to correct a number of typos in earlier chapters, one or two of which were sense-destroying. The next instalment will revise a group of three chapters on limits which (I hope) won’t require so much new work. The chapter on subobjects will then follow. I hope this different ordering of topics will be more helpful too.
Anyway, here are the first fifteen chapters (pp. 129) of Category Theory I: Notes towards a gentle introduction.
[Added: updated to correct a couple of typos, and add a short new concluding §15.7 to Chapter 15.]