You can now download here the first instalment (88pp.) of a Gentle Introduction to category theory, reworked from my Notes on Category Theory.
Gentleness is relative, of course. Peter Johnstone plans, in his first 13 lectures for this (academic) year’s Part III course, to get through rather more that I’ll be covering in 250+ pages: so compared with that relentless, take-no-prisoners, pace, I’m taking things very gently indeed. Some might well think too gently: I can only say that in my experience taking the beginnings of category theory slowly, firmly nailing down the basics, really pays off when it comes to tackling more advanced stuff.
On the other hand, some logic-minded philosophers without much mathematical background, but having heard that category theory is supposed to be illuminating about structuralism and foundational matters, will probably still find my Gentle Introduction pretty tough. All I can say to them is that I’ve tried to make things a lot more accessible than some of the alternative available routes into category theory.
One major change from the previous Notes, which followed roughly the order of the syllabus of the Part III course last year, is that I will be tackling topics in a different order (different too from that given in Peter Johnstone’s outline for this year). The plan is to look first at what happens inside categories (limits, exponentials, etc.) before looking at maps between categories (functors) before looking at relationships between maps-between-categories (natural transformations, eventually adjunctions). McLarty in the first two parts of his much faster-paced Elementary Categories, Elementary Toposes, did things this way, and it surely has a certain logical appeal.
I toyed with the idea of releasing small segments of the Gentle Introduction week-by-week, alongside some exercises to go along with the segments. But I then thought better of it. It’s just too unpredictable when writing will zoom ahead, when it will hit blocks. So I’ll just release updates of the Gentle Introduction when they are ready (check the categories page here for the date of the latest version, and for an indication of which remaining chapters from the old Notes you might want to go on to read.) Maybe I’ll run an online “course” with exercises some time in the new (calendar) year when I’ve got a full set of updated notes in the bag.