*Basic Category Theory* Free Online

#### Posted by Tom Leinster

My textbook *Basic Category Theory*, published by Cambridge University Press, is now also available free as arXiv:1612.09375.

As I wrote when I first announced the book:

- It doesn’t assume much.
- It sticks to the basics.
- It’s short.

I can now add a new property:

- It’s free.

And it’s not only free, it’s freely *editable*. The book’s released under a Creative Commons licence that allows you to edit and redistribute it, just as long as you state the authorship accurately, don’t use it for commercial purposes, and preserve the licence. Click the link for details.

Why might you want to edit it?

Well, maybe you want to use it to teach a category theory course, but none of your students have taken topology, so you’d rather remove all the topological examples. That’s easy to do. Or maybe you want to *add* some examples, or remove whole sections. Or it could just be that you can’t stand some of the notation, in which case all you need to do is change some macros. All easy.

Alternatively, perhaps you’re not planning to teach from it — you just want to *read* it, but you want to change the formatting so that it’s comfortable to read on your favourite device. Again, this is very easy to do.

Emily recently announced the dead-tree debut of her own category theory textbook, published by Dover. She did it the other way round from me: the online edition came first, then the paper version. (I also did it that way round for my first book.) But the deal I had with Cambridge was that they’d publish first, then I could put it on the arXiv under a Creative Commons licence 18 months later.

We’ve talked a lot on this blog about parasitic academic publishers, so I’d like to emphasize here what a positive contribution Cambridge University Press has made, and is continuing to make, to the academic community. CUP is a part of Cambridge University, and I think I’m right in saying that it’s not allowed to make a profit. *(Correction: I was wrong. However, maximizing profits is not CUP’s principal aim.)* It has led the way in allowing mathematics authors to post free versions of their books online. For instance, apart from my own two books, you quite likely know of Allen Hatcher’s very successful book *Algebraic Topology*, also published in paper form by CUP and, with their permission, available free online.

Since a few people have asked me privately for opinions on publishers, I’ll also say that working with CUP for this book was extremely smooth. The contract (including the arXiv release) was easily arranged, and the whole production process was about as low-stress as I can imagine it being. This wasn’t the case for my first book in 2003, also with CUP, which because of editing/production problems was a nightmare of stress. That made me very reluctant to go with CUP again, but I’m really glad that I chose to do so.

The low stress this time was partly because of one key request that I made at the beginning: we agreed that I would not share the Latex files with anyone at CUP. Thus, all I ever sent CUP was the PDF, and no one except me had ever seen my Latex source until the arXiv release just now. What that meant was that all changes, down to the comma, had to go through me. For example, the way the proofreading worked was that the proofreader would send me corrections and suggestions and I’d implement them, rather than him making changes first and me approving or reverting them second.

For anyone with a perfectionist/pedantic/… streak like mine (insert your own word), that’s an enormous stress relief. I’d recommend it to any authors of a similar personality. Again, it’s to CUP’s credit that they agreed to doing things this way — I’m not sure that all publishers would.

So the book’s now free to all. If you make heavy use of it and can afford to do so, I hope you’ll reciprocate the support that CUP has shown the mathematical community by buying a copy. But in any case, I hope you enjoy it.

## Re: Basic Category Theory Free Online

Hooray and congratulations! That’s amazing that CUP agreed to let you do all the LaTeXing. Given my experiences with copyeditors for short journal articles, I can imagine the hell that it would be to deal with them fubaring my LaTeX for an entire book.

What would you say the advantages are, for an academic book, of using a “real” publisher like CUP over self-publishing with a place like Lulu? The latter has worked fine for the HoTT book, with the additional advantage that as we receive errata we can easily fix them not only in the online version but also in all newly printed copies (I’m guessing that that still isn’t possible with a place like CUP, although it would be great if I were wrong). I suppose that CUP will do more publicity for you, and maybe libraries are more likely to buy from a real publishing house?