A new version of the Gentle Introduction to Category Theory (version of Feb 8th, pp. x + 273) is now online. Get it (by preference) from my academia.edu page or alternatively download it from the categories page here. Nearly all the sections from the old Notes on Category Theory have now been woven into the much re-arranged Gentle Intro — though for the last three chapters, the inclusion is just by the brute-force method of cutting’n’pasting from the old Notes without revision! Anyway, I have now taken the old Notes off-line and hereby cheerfully repudiate them as, erm, juvenilia. So to speak.
I’m still very much trying to nail down some of the basic categorial technicalities to my own satisfaction, aiming to make them seems as “obvious” as I can. In due course, there should be more episodes of discursive chat; and there is quite a bit more technical material I want to cover too. But I hope that even in its rather unpolished and very incomplete state, the Gentle Intro will be useful to those who would like something which is perhaps, in various respects, a bit more accessible(?) than e.g. Awodey’s or Leinster’s fine books.