New book: Basic Category Theory

New book: Basic Category Theory

[Tom Leinster]

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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Re: New book: Basic Category Theory

[Harley D. Eades III]

Hi, Tom.

Congrats on the successful completion of your book!

I really like your idea on a second book.  Such a book would be
very helpful for young researchers and students in my opinion.

Has anyone thought about doing it as a group effort in the same
spirit as the homotopy type theory book was?

A number of authors would make the writing burden far less per author,
and potentially speed up the writing process.

Anyway, just an idea.

I really like how you're are making your new book editable and readable for
free in 18 months.  This is a great idea, and a service to the community.

The second book should do the same.

Very best,
.\ Harley

On Jul 27, 2014, at 3:15 PM, Tom Leinster <Tom.Leinster@ed.ac.uk> wrote:

> 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.
>


[For admin and other information see: http://www.mta.ca/~cat-dist/ ]

Re: New book: Basic Category Theory

[Tom Leinster]

Dear Harley,

Thanks!

Actually, some of us were just discussing the possibility of writing a
second category theory book as a collaborative venture:

http://golem.ph.utexas.edu/category/2014/07/basic_category_theory.html#c046968

(But personally, I've probably had enough book-writing for a while.)

Best wishes,
Tom


On Tue, 29 Jul 2014, Harley D. Eades III wrote:

> Hi, Tom.
>
> Congrats on the successful completion of your book!
>
> I really like your idea on a second book.  Such a book would be
> very helpful for young researchers and students in my opinion.
>
> Has anyone thought about doing it as a group effort in the same
> spirit as the homotopy type theory book was?
>
> A number of authors would make the writing burden far less per author,
> and potentially speed up the writing process.
>
> Anyway, just an idea.
>
> I really like how you're are making your new book editable and readable for
> free in 18 months.  This is a great idea, and a service to the community.
>
> The second book should do the same.
>
> Very best,
> .\ Harley
>

[For admin and other information see: http://www.mta.ca/~cat-dist/ ]