A categorial end in sight

I haven’t been posting regular updates about work on the revised version of Introducing Category Theory, not because there’s been no progress, but because there has been little of wider interest to report.

But the end is at last in sight. I have just one chapter needing significant revision. So, the plan is to withdraw the current paperback at the end of the year. I’ll post a draft Version 2.0 online in early January, with the aim of carefully proof-reading over the following two or three weeks, and getting a new paperback out by the beginning of February. So, this is a ‘heads-up’ as they say: you probably don’t want to rush to buy yourself a copy of the current paperback for Christmas, only to find it superseded in a few weeks. …

Not that I have found much actually wrong with the current version, apart from minor typos. There’s been a lot of minor rephrasing, adding a few words here or there for clarity: and a few issues (e.g. matters of ‘size’) are — I hope — somewhat better explained. However, I have also latterly settled on one big change.

Currently — after looking inside categories in Part I, talking about products, equalizers, exponentials, etc. — I go on to discuss one particular kind of category, elementary toposes, in Part II; and only in Part III do we meet those core categorial ideas, functors, natural transformations, Yoneda, adjunctions. This is a sort-of logical progression as we certainly can make a first acquaintance with toposes, their internal logic, and eventually e.g. with ETCS, without having to wield the more abstract categorial apparatus. But many, I know, do find this unusual order of business a bit off-putting (even though I loudly say that you can jump over Part II if you want). So, in Version 2.0, I’ve decided with some regrets to take after all the more conventional path and I have swapped the order of the materials: subobjects and their classifiers get moved to Part I; functors etc. etc. now appear in Part II; Part III is by way of an afterword on toposes. (This swap didn’t in fact occasion a significant amount of work in itself.)

I suppose this kind of major structural change could warrant calling the result a new edition. But having rather messed up previously, stupidly putting out into the world PDF versions with different titles, and paperbacks with three different ISBNs, I won’t complicate things any more: I’ll preserve the title and current ISBN. Watch this space for more news in due course.

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