Re: Help!

[Toby Bartels <toby+categories@ugcs.caltech.edu>]

Michael Barr wrote:

>What would you say to an undergraduate math club about categories?  I have
>been thinking about it, but I am not sure what to say.  Talk about
>cohomology, which is what motivated E-M?  I don't think so.  Talk about
>dual spaces of finite-dimensional vector spaces?  Maybe, but then what?

When I was a graduate student (recently),
I gave a talk on category theory to other (mostly new) grad students
(as part of a series where advanced students discussed their work).
I began with my definition of category theory for nonmathematicians
("a general theory of how mathematical structures can fit together"),
then gave some basic definitions and an example
(duality in finite-dimensional vector spaces).

Then I asked the audience a very open-ended question:
Tell me what's your favourite branch of mathematics,
and I'll tell you what category theory has to say about it
(to justify the generality in my beginning statement).
What attracted me first to category theory,
and what I think remains impressive about it,
is that you can you can really make good on this challenge.
(It helps to know ahead of time what answers are likely;
 fortunately there were no pure number theorists at my school.)


--Toby Bartels