On Fri, 5 Oct 2007, 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?
How about talking about simultaneously existing results in several categories? The Noetherian isomorphism theorems, while not necessarily the easiest to nail down exactly when they hold, have always been a strong motivator at the back of my head for why one might want to look at algebraic entities codifying things like "All Xs and maps between them". -- Mikael Vejdemo Johansson | To see the world in a grain of sand mik@math.su.se | And heaven in a wild flower | To hold infinity in the palm of your hand | And eternity for an hour