Category theory for non-mathematicians

[Mark Carroll]

Are there any friendly introductory texts that people recommend that
would give me some intuition about monads, functors, etc.? I'm
starting to be able to use fmap and whatnot in Haskell more or less by
noting that things of certain forms work, so that's how I do them next
time, but gaining some working knowledge isn't meaning that these
things are making a whole lot of sense to me. So, my thinking is that
if I understand more about where these things come from, e.g. basic
category theory then, although it will hurt, my brain will be twisted
around so that it more naturally thinks in whatever strange ways the
designers of Haskell think and the 'obvious' way of writing functional
programs will start to come to me more easily. Unfortunately, highly
mathematical textbooks scare me - I liked things like Schey's informal
text on vector calculus, but books with as many equations (mostly
proofs) as prose probably aren't really what I'm looking for.

I was wondering about "Conceptual Mathematics: A First Introduction to
Categories". There are also titles like "Categories, Types, and
Structures: An Introduction to Category Theory for the Working
Computer Scientist", "An Introduction to Category Theory" and "Basic
Category Theory for Computer Scientists". Even my local library seems
to have a couple that I'll check out. Does anyone have any thoughts
or suggestions?

-- Mark

[Mike Kent]

> I was wondering about "Conceptual Mathematics: A First Introduction to
> Categories".

Fun, interesting, but coverage is idiosyncratic to say the
least: introduces topoi, doesn't even define adjoints,
and mentions functors only in the fleetest passing. I would
charactize it as categories "in the high aesthetic line".

> There are also titles like "Categories, Types, and
> Structures: An Introduction to Category Theory for the Working
> Computer Scientist", "An Introduction to Category Theory" and "Basic
> Category Theory for Computer Scientists".

I'm working through "Basic Category Theory" (Pierce) but in the
general spirit of Lawvere ("Conceptual Mathematics"). Pierce is
concise but pretty much covers what the title implies: enough
(and the right) topics so that you can grok the category theory
that underlies various areas/approaches in CS. Under 100 pages,
plenty of exercises.

[Mark Carroll]

In article <3B7C81A8...@home.com>, Mike Kent <mk...@acm.org> wrote:
>> I was wondering about "Conceptual Mathematics: A First Introduction to
>> Categories".
>
>Fun, interesting, but coverage is idiosyncratic to say the
>least: introduces topoi, doesn't even define adjoints,
>and mentions functors only in the fleetest passing. I would
>charactize it as categories "in the high aesthetic line".

Ah, right. Yes, I was most surprised to see that it doesn't even
mention what monads are, given that the blurb on the back mentions
computer scientists.

(snip)

>I'm working through "Basic Category Theory" (Pierce) but in the
>general spirit of Lawvere ("Conceptual Mathematics"). Pierce is
>concise but pretty much covers what the title implies: enough
>(and the right) topics so that you can grok the category theory
>that underlies various areas/approaches in CS. Under 100 pages,
>plenty of exercises.

Yes, he's indeed concise. What I really want is a book with the topics
that Pierce covers, covered as gently as Lawvere and Schanuel cover
things. Maybe I'm just a wimp. (-:

Thanks very much!

-- Mark