How can I use an alias for a category? I have a category group called country, with each category being the name of a country.  I used the full name of the country.
I realize I might want to use each country's 2-digit code.  For example, AU for Australia.

How might I implement the abbreviations to associate with the category?  

Put another way, how can I use the 2-digit code as an alias for the full country name?
You could use the category handle.

If that doesn't suit your requirements, you can associate custom fields with categories, same as you can with entries.