
Category Theory for Scientists and Engineers (2013) [pdf] - cbennett
http://ocw.mit.edu/courses/mathematics/18-s996-category-theory-for-scientists-spring-2013/textbook/MIT18_S996S13_textbook.pdf
======
cbennett
Related course readings and assignments for self-learning:
[http://ocw.mit.edu/courses/mathematics/18-s996-category-
theo...](http://ocw.mit.edu/courses/mathematics/18-s996-category-theory-for-
scientists-spring-2013/readings/) couldn't manage to find any videos, though
:/

------
platz
the new version in html is available on spivak's homepage
[http://math.mit.edu/~dspivak/](http://math.mit.edu/~dspivak/)

~~~
agumonkey
Ha, the usual mit/sicp theme. Timeless.

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Dewie3
I like the idea of these "CT for X" books/resources. Sometimes when I want to
read about category theory, it opens with "you should perhaps have a
background in some abstract mathematical branch/theory". OK, I choose abstract
algebra to read about first[1]. Then _that_ intro recommends that I already
know linear algebra...

If I had a time machine, I would definitely have taken more math courses at
uni.

[1] And yes, probably biting over even _more_ than I could reasonably chew in
the process, compared to 'just' reading about CT.

~~~
JadeNB
As a mathematician, not a computer scientist or programmer, I think that one
of the common mistakes that people make is to think of category theory as an
end in itself. For me, the point of category theory is not its study on its
own (though there are people who do that!), but rather its capability to serve
as a unifying _language_ for a broad class of examples.

This is why, I think, many textbooks suggest prerequisites (not that you
argued that they shouldn't!); not so much that category theory can't be
_learnt_ without them, for it certainly can (it is actually very simple), but
rather that it can't be _understood_. Studying it on its own seems to me very
much like trying to learn a programming language without having any problem
that you want to use it to solve.

~~~
ekidd
When CS people use category theory, they're often looking for a framework
which allows them to build analogies between the lambda calculus (via a
cartesian closed category) and various categories for things like mathematical
logic, posets or probability. And category theory is a very natural framework
for thinking about these connections.

So it would be useful to have category textbooks for CS folks which spent less
time on topology, and more time on familiar categories.

(Also, I've never quite figured out the motivation for adjoint functors. I can
understand the definitions, but I don't understand why adjoints are useful.
The motivating examples almost always involve unfamiliar categories.)

~~~
JadeNB
> So it would be useful to have category textbooks for CS folks which spent
> less time on topology, and more time on familiar categories.

Agreed, and I should have been clearer in my post above that I was just airing
some thoughts on category theory rather than meaning to imply anything
negative about the importance and usefulness of X-flavoured viewpoints on
category theory for various values of X (including "computer science"). With
that said, don't knock topology! See Baez and Stay's 'Rosetta stone' article
[http://arxiv.org/abs/0903.0340](http://arxiv.org/abs/0903.0340) for a
plethora of connections between such seemingly abstruse concepts as topology,
and computer science.

> (Also, I've never quite figured out the motivation for adjoint functors. I
> can understand the definitions, but I don't understand why adjoints are
> useful. The motivating examples almost always involve unfamiliar
> categories.)

It may be helpful to think first of Galois connexions
([https://en.wikipedia.org/wiki/Galois_connection](https://en.wikipedia.org/wiki/Galois_connection)
and
[http://ncatlab.org/nlab/show/Galois+connection](http://ncatlab.org/nlab/show/Galois+connection)).
I can't find any relevant blog posts now, but I know I have seen them
discussed in a CS context that may seem more natural than that of 'abstract'
adjoint functors. Here is a non-free article:
[http://link.springer.com/chapter/10.1007%2F3-540-17162-2_130](http://link.springer.com/chapter/10.1007%2F3-540-17162-2_130)
.

~~~
agumonkey
IIRC Gershom Bazerman talk
[https://vimeo.com/72870861](https://vimeo.com/72870861) is about that
precisely. (galois, adjunctions)

