RE: Help!

["Marta Bunge" <martabunge@hotmail.com>]

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
>
>
>

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