New book: Basic Category Theory

[Tom Leinster <Tom.Leinster@ed.ac.uk>]

Dear all,

It's not clear that the world needs another introductory book on category
theory, but I've written one:

    Tom Leinster, Basic Category Theory.
    Cambridge University Press, published 24 July 2014.

    http://www.maths.ed.ac.uk/~tl/bct

Its main features: it doesn't assume much, it sticks to the basics, and
it's short.  You can read some extracts at the web address above.

In 18 months, it will be both freely downloadable and freely editable.
So if it's not quite suitable for a course you're teaching, or if you
don't like the notation (and when have two category theorists ever agreed
on that?), you'll be able to change it.  More details when the time comes.


What the world does need, I think, is a *second* book on category theory,
picking up where Categories for the Working Mathematician leaves off.  Of
course, we already have Francis Borceux's magnum opus, but I think there's
also a market for something much shorter.  I'm envisaging a book of
similar length to CWM, and written with a similarly selective ethos.
Tentative list of chapters, in no particular order:

* Enriched categories
* 2-categories (and a little on higher categories)
* Ends and Kan extensions (already in CWM, but maybe worth another pass)
* Topos theory (clearly just an introduction!) and categorical set theory
* Fibrations
* Bimodules, Morita equivalence, Cauchy completeness & absolute colimits
* Flat functors and locally presentable categories
* Operads and Lawvere theories
* Categorical logic (again, just a little) and internal category theory
* Derived categories.

Someone else should definitely write a book like that.

Best wishes,
Tom

-- 
The University of Edinburgh is a charitable body, registered in
Scotland, with registration number SC005336.



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