The shape of categorial things to come

The headline news: there is now a new version of my category theory notes, in one document, as Introducing Category Theory, available here.

In more detail: I’ve decided against my previous plan of two volumes, in part because there just wasn’t a satisfyingly natural way of carving things between them. (Friends and relations, by a large majority, also voted for one big book rather than two smaller ones.)

As the notes are now arranged, Part I says something about what can be found inside individual categories (products, quotients, limits more generally, exponentials and the like). Part II says a very little about those categories which are elementary toposes. Part III, which can be read independently of Part II, introduces the distinctive categorial  ideas of functors, natural transformations, the Yoneda Lemma, and adjunctions.

If you haven’t seen earlier versions, I have gone for a fairly conventional mode of presentation but at a pretty gentle pace (which makes for quite a long book — but I make no apology for that: faster-track alternatives are available in you want them!). The result is aimed at those who want an entry-level warm-up before taking on an industrial-strength graduate-level course, or perhaps just want to get an idea of that the categorial fuss is about.

The state of play? Part I should be in a good state. One chapter is missing from Part II. Part III needs a concluding note on further reading. The index needs work. But I’m getting there!

A print-on-demand version will be inexpensively available (Amazon only, to minimize cost) in due course — by the end of July, I hope.

A print-on-demand version of Part I (and a little more) has been available under the title Category Theory I: A Gentle Prologue. This now strikes me as making an unsatisfactory division of the material, stopping precipitously. [Updated] However, I have decided to keep it in print for the moment, and in a day or so a new version, updated to correct typos and a few thinkos, should go live on Amazon.

2 thoughts on “The shape of categorial things to come”

  1. Is there any possibility of having a 2-volume version, even if only temporarily? Since there’s a fairly natural division into Parts I, II, and III, it seems to me that there’d be a fairly natural division into two volumes too (with Vol 1 containing Part I, or Parts I and II, and Vol 2 containing the rest). (I’m encouraged by the current Vol 1 remaining available, for a while, despite its unsatisfactory division.)

    The preface to the June 8th version also suggests that there’s a natural division. After describing Parts I and II, it says

    Then, if you are sufficiently intrigued by these introductory chapters, and sufficiently happy with my particular presentational style, Part III is there as one option for continuing to explore the beginnings of category theory proper.

    I think I will find a single volume of 400+ pages a bit too large and unwieldy, and I’ve been looking forward to having a Volume 2 to go with Volume 1.

    (I’m thinking of books, printed on paper. If someone’s only going to use PDFs, the disadvantages of having everything in one large volume become less, and the advantages become greater.)

  2. I think you mean ‘One chapter is missing from Part Ⅱ’, not ‘Part Ⅰ’. Indeed! — corrected

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