Dear Mike Some categories that are easily described (even to talented high school students) are: the category fun of functions (where objects are natural numbers and morphisms are functions); the category mat of matrices (again the objects are natural numbers); the category brd of braids; and, the category tang of tangles. There are enough functors amongst these to be interesting. They are all monoidal categories. One can try to discuss other structure the categories have in common so that strong monoidal functors (although I probably wouldn't introduce too much such terminology) preserve it. For example, duals in mat and tang; trace and braid closure; etc. One could try to show how the specialized, seemingly ad hoc Reidemeister moves translate naturally into the braided monoidal setting. A hint about how the "new" (mid 1980s) polynomial link invariants come from a functor tang --> mat might be of interest. Best wishes, Ross On 05/10/2007, at 10:52 PM, 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?