Incrementing a counter

I'm a newbie to XSLT, but have a lot of scripting experience.

I have a problem that I cannot solve and would appreciate some help.
>From what I understand about variables in XSLTs, you can't change the
value. So if that's true, how can I increment a counter?

My problem is that I need to to create a single header that appears over
a list of similar items. In the XML file, we store the "Category"
attribute. So I may have 20 Sports items, 10 News items and 5 Features
items. I need to transform the XML into a text file that should look like
this:

Sports
1.
2.
3.
etc

News
1.
2.
3.
etc

Features
1.
2.
3.
etc

In my scripting experience, I would sort the list by category, create
a counter and loop through the list of items comparing each subsequent
item to the previous item. It it was the same, I would ignore the
category. That may not be the most elegant solution, but it works

How would I achieve that with XSLT?

Thanks,
KW