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