I'd imagine you could do this with a custom query. I know you can do it on the index page of your blog, so I don't see why you couldn't do it with categories, as well. Of course, depending on how many categories you have, it could be a pain in the butt, because I don't thin you can "automate" it in any way - you'd have to do it manually (so to speak - but someone smarter might come along and know exactly how to do that!)
So you're looking to do something like this: if you have a "Category.php" file, then you want that. Most likely, you don't - but you can create one. If you don't want to, then you'll want to put this in your index.php file - but it might be "cleaner" to create a copy of index.php, name it "category.php" and do it all in there, since this is a category-specific thing.
In any case, you'll want to take a look at this tutorial. it'll explain how to do it. There may also be some plugins for doing this so you don't have to code yourself, try googling for that :)