Oh yes, you could. But the original page URL wouldn't change because you'd be loading content via AJAX. To get around this, people end up using URLs like:
http://www.mysite.com/#category/page
and change the part after the # dynamically. It's not a big issue (Facebook gets away with it quite nicely) but it offends my OCD tendencies.
It is one of the reasons I've been looking at XSLT/XML pages. The XSLT files are totally cachable, so when you're looking at similar pages of content (i.e., forum posts) you can use the template over and over again.
Low bandwidth! Huzzah!