Two category theory books

One of the best freely available sets of lecture notes on category theory available is the one by Paulo Perrone, which can be downloaded from the arXiv here. He has now turned these notes into a printed book, Starting Category Theory from World Scientific. There is a long added chapter on monoidal categories, but the earlier five chapters appear again with only some small additions as far as I can see on a quick browse (the significantly higher page count for these chapters being mostly due to the difference in formatting).

Since the lecture-note version is freely and officially available, I won’t comment in detail here: suffice to say that Perrone makes the material pretty accessible, and I can well imagine many students liking his style. I really, really doubt that they (or you) will want to fork out for the book, however. Its USA price is $148 (there’s a whopping $11 discount on Amazon); its UK price is £135. That is worse than absurd.


I may just possibly have said something here about another category theory book’s being on its way. Namely, my Category Theory II. But plans are a bit fluid right now. For various reasons, I’m increasingly minded to in fact combine Parts I and II (with again a slightly re-arranged ordering of chapters) into a single big book, perhaps reverting to that earlier title Category Theory: Notes towards a gentle introduction for the whole.

In fact the cost of one big printed book would only be about the price of a large coffee more than a separate Category Theory II, and the small additional overall cost to someone who already has Category Theory I would be more than compensated by avoiding the repeated annoyance of having to chase up cross-references between books (or between PDFs). And there are other significant potential gains too: the combined book as I now see it has a nicer shape. But I’ll keep thinking this through: so watch this space.

3 thoughts on “Two category theory books”

  1. “From World Scientific”, so naturally it’s insanely expensive. I am increasingly disinclined to indulge authors who do this.

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    I strongly prefer having Category Theory II as a separate volume. I’d much rather have two volumes (in this case) than one larger one, and if a reference has to be chased up, it would have to be chased in the single volume too. It’s not necessarily easier to hold one book open at two places than to have each of two books open at one, and although there are advantages to having one PDF (such as when using search), I fairly often find myself having a PDF open in two different places in two separate windows anyway.

    I’m not sure how the title Notes towards a gentle introduction will be interpreted. It can seem to be saying this is something to read even before you read a gentle introduction (i.e., something even gentler and less advanced). I don’t think that’s what the Notes actually are. Or it might be understood as saying this is something like a preliminary study of the material that might be covered by a gentle introduction that does not yet exist. I don’t think that’s what the Notes are either.

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    Not Category Theory, but I saw this new book which might be interesting: Intuitive Axiomatic Set Theory by José L Garciá. (I think it’s more expensive than it should be, but not insanely so.)

    1. BTW, a book discussed in the Logic Matters blog here in February 2022, Sharon Berry’s Potentialist Set Theory, is now available as a reasonably priced paperback (£22.88 on amazon UK). Back then

      It is, as is now the default for new CUP monographs, published at a ludicrous price.

  2. Please do make them into a single big volume.
    It’s gonna be way more convenient to work on! (By the way, I love the shape of a single big book too)

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