I’m trying hard not to be logically distracted from the long-promised revision of the old Beginning Category Theory theory notes. Which makes for a very dull blog! And indeed, this is just another of those “I’ve updated more chapters” posts. Exciting or what?
This time I’ve updated Ch. 16 on limits, Ch. 17 on pullbacks and pushouts, and Ch. 18 which proves the completeness theorem that a category with terminal objects, binary products and equalizers has all finite limits.
However, in doing this, I found that the version of the completeness proof in Beginning Category Theory was hopelessly confused. Ouch. I guess that’s the first real foul-up that I have discovered in revising the notes, so I suppose I shouldn’t be too upset. But it does means that it is time to fully retire those old notes, and finally take them offline.
Therefore I’ve replaced them by Category Theory: Notes towards a gentle introduction which — as of February 28 — has the eighteen newly revised chapters but now followed by the same number of old unrevised chapters. So everything, revised and waiting-to-be-revised, is conveniently in one pdf.
What next? Over the coming weeks, I will be revising and expanding the rest of Part I, meaning the chapters before we start looking at functors between categories in Part II (when, many would say, the real categorial fun starts). So I will be revising the chapter on sub-objects, splitting and then improving the chapters on natural number objects and groups-in-categories. I also envisage adding to Part I a preliminary look at the idea of a topos if I can organize a dozen sensible and useful pages.
Having knocked Part I into an overall shape that I’m happier with, I intend next to polish up these chapters to make them more consistent in level and friendliness. Which is another way of saying that I won’t be getting round to revising Part II for some months. But I may well set up an at-cost paperback “beta version” of Part I for people to comment on, as so many (including me) prefer working from a printed version. We’ll see …