Hi, Michael, I am in the same predicament but, since I am speaking at this math club one week after you (November 6), I do hope to be able to use anything you do in your own talk! I also thought a lot about this problem and discarded one topic after another. Finally, I have decided to speak about the uses of infinitesimals in the synthetic calculus of variations, aiming at giving an algebraic (synthetic) proof of the well known fact that, for a paths functional ("energy"), its critical points agree with the geodesics. This requires that I introduce adjoint functors and cartesian closed categories and the notion of a ring object of line type. If you will do any of these yourself I could use it. Informally, I will argue constructively and acually prove things. Historical considerations may be briefly mentioned at the beggining of the talk, and the conceptual advantages of the synthetic method at the end. This will be an expanded portion of my paper "Synthetic Calculus of Variations" (with M. Heggie) in Contemporary Mathematics 30, 1983. I hope that this helps you as well as me. Best wishes, Marta
From: Michael Barr <barr@math.mcgill.ca> To: Categories list <categories@mta.ca> Subject: categories: Help! Date: Fri, 5 Oct 2007 08:52:29 -0400 (EDT)
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?
Michael
_________________________________________________________________ Send a smile, make someone laugh, have some fun! Check out freemessengeremoticons.ca