I have searched google and the Magento forum to no avail.
Is it possible to assign different shipping rates to each of the categories?
Certainly, but you would need to implement your own shipping plugin to do that.
This magento wiki article will be a good place to start.
As an implementation caveat, remember that products can be in multiple categories.
It's the cop-out answer, but there are modules that allow you to assign items to groups and have shipping rates per-group.
http://www.webshopapps.com/uk/shipping/productmatrix-shipping-extension.html