Re: A well kept secret?

[Ross Street <street@ics.mq.edu.au>]

On 15/12/2009, at 5:41 AM, Andrew Stacey wrote:

>  In my department, the colloquium is called
> "Mathematical Pearls"
> I'm giving this talk in January.
>
> But for such a talk, I need a story.

Dear Andrew

Back in the early 90s Todd Trimble gave a beautiful colloquium talk to
our Mathematics Department at Macquarie. It was based on a question in
a book by Halmos which involved finding some group (topological I
think) doing something or other. It was not a categorical problem as
such.

Todd spoke about groups in a category with finite products. The only
categorical theorem he needed was that finite product preserving
functors take groups to groups. I believe he took the definition of
category as known but defined functor, product and internal group.

My vague memory is that he found a group solving the analogous problem
in some fairly combinatorial (presheaf?) category, then found a
product preserving functor to topological spaces to obtain the desired
group.

I hope Todd is reading this and I have jogged his memory enough to
write in more detail. It takes work and ingenuity to design such pearls.

Best wishes,
Ross

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